NASA Astrophysics Data System (ADS)
Bagchi, Arjun; Basu, Rudranil; Kakkar, Ashish; Mehra, Aditya
2016-04-01
We investigate the symmetry structure of the non-relativistic limit of Yang-Mills theories. Generalising previous results in the Galilean limit of electrodynamics, we discover that for Yang-Mills theories there are a variety of limits inside the Galilean regime. We first explicitly work with the SU(2) theory and then generalise to SU( N) for all N, systematising our notation and analysis. We discover that the whole family of limits lead to different sectors of Galilean Yang-Mills theories and the equations of motion in each sector exhibit hitherto undiscovered infinite dimensional symmetries, viz. infinite Galilean Conformal symmetries in D = 4. These provide the first examples of interacting Galilean Conformal Field Theories (GCFTs) in D > 2.
Gravitino interactions from Yang-Mills theory
Bjerrum-Bohr, N. E. J.; Engelund, Oluf Tang
2010-05-15
We fabricate gravitino vertex interactions, using as only input on-shell Yang-Mills amplitudes and the Kawai-Lewellen-Tye gauge theory/gravity relations, aiming to achieve a better understanding of Kawai-Lewellen-Tye factorizations for gravitinos at an off-shell Lagrangian level. A useful by-product of this analysis is simpler tree-level Feynman rules for gravitino scattering than in traditional gauges. All results are explicitly verified until five-point scattering.
Duality in supersymmetric Yang-Mills theory
Peskin, M.E.
1997-02-01
These lectures provide an introduction to the behavior of strongly-coupled supersymmetric gauge theories. After a discussion of the effective Lagrangian in nonsupersymmetric and supersymmetric field theories, the author analyzes the qualitative behavior of the simplest illustrative models. These include supersymmetric QCD for N{sub f} < N{sub c}, in which the superpotential is generated nonperturbatively, N = 2 SU(2) Yang-Mills theory (the Seiberg-Witten model), in which the nonperturbative behavior of the effect coupling is described geometrically, and supersymmetric QCD for N{sub f} large, in which the theory illustrates a non-Abelian generalization of electric-magnetic duality. 75 refs., 12 figs.
Curving Yang-Mills-Higgs gauge theories
NASA Astrophysics Data System (ADS)
Kotov, Alexei; Strobl, Thomas
2015-10-01
We present a Yang-Mills-Higgs (YMH) gauge theory in which structure constants of the gauge group may depend on Higgs fields. The data of the theory are encoded in the bundle E →M , where the base M is the target space of Higgs fields and fibers carry information on the gauge group. M is equipped with a metric g and E carries a connection ∇. If ∇ is flat, R∇=0 , there is a local field redefinition which gives back the standard YMH gauge theory. If R∇≠0 , one obtains a new class of gauge theories. In this case, contrary to the standard wisdom of the YMH theory, the space (M ,g ) may have no isometries. We build a simple example which illustrates this statement.
Band structure in Yang-Mills theories
NASA Astrophysics Data System (ADS)
Bachas, Constantin; Tomaras, Theodore
2016-05-01
We show how Yang-Mills theory on S3 × ℝ can exhibit a spectrum with continuous bands if coupled either to a topological 3-form gauge field, or to a dynamical axion with heavy Peccei-Quinn scale. The basic mechanism consists in associating winding histories to a bosonic zero mode whose role is to convert a circle in configuration space into a helix. The zero mode is, respectively, the holonomy of the 3-form field or the axion momentum. In these models different θ sectors coexist and are only mixed by (non-local) volume operators. Our analysis sheds light on, and extends Seiberg's proposal for modifying the topological sums in quantum field theories. It refutes a recent claim that B + L violation at LHC is unsuppressed.
Integrable amplitude deformations for N =4 super Yang-Mills and ABJM theory
NASA Astrophysics Data System (ADS)
Bargheer, Till; Huang, Yu-Tin; Loebbert, Florian; Yamazaki, Masahito
2015-01-01
We study Yangian-invariant deformations of scattering amplitudes in 4d N =4 super Yang-Mills theory and 3d N =6 Aharony-Bergman-Jafferis-Maldacena (ABJM) theory. In particular, we obtain the deformed Graßmannian integral for 4d N =4 supersymmetric Yang-Mills theory, both in momentum and momentum-twistor space. For 3d ABJM theory, we initiate the study of deformed scattering amplitudes. We investigate general deformations of on-shell diagrams, and find the deformed Graßmannian integral for this theory. We furthermore introduce the algebraic R-matrix construction of deformed Yangian invariants for ABJM theory.
Einstein-Yang-Mills theory: Asymptotic symmetries
NASA Astrophysics Data System (ADS)
Barnich, Glenn; Lambert, Pierre-Henry
2013-11-01
Asymptotic symmetries of the Einstein-Yang-Mills system with or without cosmological constant are explicitly worked out in a unified manner. In agreement with a recent conjecture, one finds a Virasoro-Kac-Moody type algebra not only in three dimensions but also in the four-dimensional asymptotically flat case.
Path integral regularization of pure Yang-Mills theory
Jacquot, J. L.
2009-07-15
In enlarging the field content of pure Yang-Mills theory to a cutoff dependent matrix valued complex scalar field, we construct a vectorial operator, which is by definition invariant with respect to the gauge transformation of the Yang-Mills field and with respect to a Stueckelberg type gauge transformation of the scalar field. This invariant operator converges to the original Yang-Mills field as the cutoff goes to infinity. With the help of cutoff functions, we construct with this invariant a regularized action for the pure Yang-Mills theory. In order to be able to define both the gauge and scalar fields kinetic terms, other invariant terms are added to the action. Since the scalar fields flat measure is invariant under the Stueckelberg type gauge transformation, we obtain a regularized gauge-invariant path integral for pure Yang-Mills theory that is mathematically well defined. Moreover, the regularized Ward-Takahashi identities describing the dynamics of the gauge fields are exactly the same as the formal Ward-Takahashi identities of the unregularized theory.
Instanton Effective Action in Deformed Super Yang-Mills Theories
Nakajima, Hiroaki; Ito, Katsushi; Sasaki, Shin
2008-11-23
We study the ADHM construction of instantons in N = 2 supersymmetric Yang-Mills theory deformed in constant Ramond-Ramond (R-R) 3-form field strength background in type IIB superstrings. We compare the deformed instanton effective action with the effective action of fractional D3/D(-1) branes at the orbifold singularity of C{sup 2}/Z{sub 2} in the same R-R background. We find discrepancy between them at the second order in deformation parameters, which comes from the coupling of the translational zero modes of the D(-1)-branes to the R-R background. We improve the deformed action by adding a term with spacetime dependent gauge coupling such that the action reproduces the effective action of the fractional branes.
Yang-Mills Theory and Fermionic Path Integrals
NASA Astrophysics Data System (ADS)
Fujikawa, Kazuo
The Yang-Mills gauge field theory, which was proposed 60 years ago, is extremely successful in describing the basic interactions of fundamental particles. The Yang-Mills theory in the course of its developments also stimulated many important field theoretical machinery. In my talk I discuss the path integral techniques, in particular, the fermionic path integrals which were developed together with the successful applications of quantized Yang-Mills field theory. I start with the Faddeev-Popov path integral formula with emphasis on the treatment of fermionic ghosts as an application of Grassmann numbers. I then discuss the ordinary fermionic path integrals and the general treatment of quantum anomalies. The contents of this talk are mostly pedagogical except for a recent analysis of path integral bosonization.
Yang-Mills theory and fermionic path integrals
NASA Astrophysics Data System (ADS)
Fujikawa, Kazuo
2016-01-01
The Yang-Mills gauge field theory, which was proposed 60 years ago, is extremely successful in describing the basic interactions of fundamental particles. The Yang-Mills theory in the course of its developments also stimulated many important field theoretical machinery. In this brief review I discuss the path integral techniques, in particular, the fermionic path integrals which were developed together with the successful applications of quantized Yang-Mills field theory. I start with the Faddeev-Popov path integral formula with emphasis on the treatment of fermionic ghosts as an application of Grassmann numbers. I then discuss the ordinary fermionic path integrals and the general treatment of quantum anomalies. The contents of this review are mostly pedagogical except for a recent analysis of path integral bosonization.
Center vortex model for Sp(2) Yang-Mills theory
Engelhardt, M.; Sperisen, B.
2006-12-15
The question whether the center vortex picture of the strongly interacting vacuum can encompass the infrared dynamics of both SU(2) as well as Sp(2) Yang-Mills theory is addressed. These two theories contain the same center vortex degrees of freedom, and yet exhibit deconfinement phase transitions of different order. This is argued to be caused by the effective action governing the vortices being different in the two cases. To buttress this argument, a random vortex world-surface model is constructed which reproduces available lattice data characterizing Sp(2) Yang-Mills confinement properties. A new effective action term which can be interpreted in terms of a vortex stickiness serves to realize a first-order deconfinement phase transition, as found in Sp(2) Yang-Mills theory. Predictions are given for the behavior of the spatial string tension at finite temperatures.
Perturbation Theory of Massive Yang-Mills Fields
DOE R&D Accomplishments Database
Veltman, M.
1968-08-01
Perturbation theory of massive Yang-Mills fields is investigated with the help of the Bell-Treiman transformation. Diagrams containing one closed loop are shown to be convergent if there are more than four external vector boson lines. The investigation presented does not exclude the possibility that the theory is renormalizable.
Hamiltonian flow in Coulomb gauge Yang-Mills theory
Leder, Markus; Reinhardt, Hugo; Pawlowski, Jan M.; Weber, Axel
2011-01-15
We derive a new functional renormalization group equation for Hamiltonian Yang-Mills theory in Coulomb gauge. The flow equations for the static gluon and ghost propagators are solved under the assumption of ghost dominance within different diagrammatic approximations. The results are compared to those obtained in the variational approach and the reliability of the approximations is discussed.
Deconfinement in Yang-Mills Theory through Toroidal Compactification
Simic, Dusan; Unsal, Mithat; /Stanford U., Phys. Dept. /SLAC
2011-08-12
We introduce field theory techniques through which the deconfinement transition of four-dimensional Yang-Mills theory can be moved to a semi-classical domain where it becomes calculable using two-dimensional field theory. We achieve this through a double-trace deformation of toroidally compactified Yang-Mills theory on R{sup 2} x S{sub L}{sup 1} x S{sub {beta}}{sup 1}. At large N, fixed-L, and arbitrary {beta}, the thermodynamics of the deformed theory is equivalent to that of ordinary Yang-Mills theory at leading order in the large N expansion. At fixed-N, small L and a range of {beta}, the deformed theory maps to a two-dimensional theory with electric and magnetic (order and disorder) perturbations, analogs of which appear in planar spin-systems and statistical physics. We show that in this regime the deconfinement transition is driven by the competition between electric and magnetic perturbations in this two-dimensional theory. This appears to support the scenario proposed by Liao and Shuryak regarding the magnetic component of the quark-gluon plasma at RHIC.
Infrared propagators of Yang-Mills theory from perturbation theory
Tissier, Matthieu; Wschebor, Nicolas
2010-11-15
We show that the correlation functions of ghosts and gluons for the pure Yang-Mills theory in Landau gauge can be accurately reproduced for all momenta by a one-loop calculation. The key point is to use a massive extension of the Faddeev-Popov action. The agreement with lattice simulation is excellent in d=4. The one-loop calculation also reproduces all the characteristic features of the lattice simulations in d=3 and naturally explains the peculiarities of the propagators in d=2.
SL(2, r) Yang-Mills Theory on a Circle
NASA Astrophysics Data System (ADS)
Bengtsson, Ingemar; Hallin, Joakim
The kinematic of SL(2, ℝ) Yang-Mills theory on a circle is considered, for reasons that are spelt out. The gauge transformations exhibit hyperbolic fixed points, and this results in a physical configuration space with a non-Hausdorff “network” topology. The ambiguity encountered in canonical quantization is then much more pronounced than in the compact case and cannot be resolved through the kind of appeal made to group theory in that case.
Quantum Chromodynamics -- The Perfect Yang-Mills Gauge Field Theory
NASA Astrophysics Data System (ADS)
Gross, David
David Gross: My talk today is about the most beautiful of all Yang-Mills Theories (non-Abelian gauge theories), the theory of the strong nuclear interactions, Quantum Chromodynamics, QCD. We are celebrating 60 years of the publication of a remarkable paper which introduced the concept of non-Abelian local gauge symmetries, now called the Yang-Mills theory, to physics. In the introduction to this paper it is noted that the usual principle of isotopic spin symmetry is not consistent with the concept of localized fields. This sentence has drawn attention over the years because the usual principle of isotopic spin symmetry is consistent, it is just not satisfactory. The authors, Yang and Mills, introduced a more satisfactory notion of local symmetry which did not require one to rotate (in isotopic spin space) the whole universe at once to achieve the symmetry transformation. Global symmetries are thus are similar to `action at a distance', whereas Yang-Mills theory is manifestly local...
On matrix model formulations of noncommutative Yang-Mills theories
Azeyanagi, Tatsuo; Hirata, Tomoyoshi; Hanada, Masanori
2008-11-15
We study the stability of noncommutative spaces in matrix models and discuss the continuum limit which leads to the noncommutative Yang-Mills theories. It turns out that most noncommutative spaces in bosonic models are unstable. This indicates perturbative instability of fuzzy R{sup D} pointed out by Van Raamsdonk and Armoni et al. persists to nonperturbative level in these cases. In this sense, these bosonic noncommutative Yang-Mills theories are not well-defined, or at least their matrix model formulations studied in this paper do not work. We also show that noncommutative backgrounds are stable in a supersymmetric matrix model deformed by a cubic Myers term, though the deformation itself breaks supersymmetry.
A superspace formulation of Yang-Mills theory on sphere
NASA Astrophysics Data System (ADS)
Banerjee, Rabin; Deguchi, Shinichi
2010-05-01
A superspace approach to the Becchi-Rouet-Stora-Tyutin (BRST) formalism for the Yang-Mills theory on an n-dimensional unit sphere S1n is developed in a manifestly covariant manner based on the rotational supersymmetry characterized by the supergroup OSp(n +1∣2). This is done by employing an (n +2)-dimensional unit supersphere S1n∣2 parametrized by n commutative and two anticommutative coordinate variables so that it includes S1n as a subspace and realizes the OSp(n +1∣2) supersymmetry. In this superspace formulation, referred to as the supersphere formulation, the so-called horizontality condition is concisely expressed in terms of the rank-3 field strength tensor of a Yang-Mills superfield on S1n∣2. The supersphere formulation completely covers the BRST gauge-fixing procedure for the Yang-Mills theory on S1n provided by us [R. Banerjee and S. Deguchi, Phys. Lett. B 632, 579 (2006); arXiv:hep-th/0509161]. Furthermore, this formulation admits the (massive) Curci-Ferrari model defined on S1n, describing the gauge-fixing and mass terms on S1n together as a mass term on S1n∣2.
Yang-Mills theories at high energy accelerators
NASA Astrophysics Data System (ADS)
Sterman, George
2016-03-01
I will begin with a brief review of the triumph of Yang-Mills theory at particle accelerators, a development that began some years after their historic paper. This story reached a culmination, or at least local extremum, with the discovery at the Large Hadron Collider of a Higgs-like scalar boson in 2012. The talk then proceeds to a slightly more technical level, discussing how we derive predictions from the gauge field theories of the Standard Model and its extensions for use at high energy accelerators.
Yang-Mills Theories at High Energy Accelerators
NASA Astrophysics Data System (ADS)
Sterman, George
I will begin with a brief review of the triumph of Yang-Mills theory at particle accelerators, a development that began some years after their historic paper. This story reached a culmination, or at least local extremum, with the discovery at the Large Hadron Collider of a Higgs-like scalar boson in 2012. The talk then proceeds to a slightly more technical level, discussing how we derive predictions from the gauge field theories of the Standard Model and its extensions for use at high energy accelerators.
Ward identity implies recursion relations in Yang-Mills theory
NASA Astrophysics Data System (ADS)
Chen, Gang
2012-07-01
The Ward identity in gauge theory constrains the behavior of the amplitudes. We discuss the Ward identity for amplitudes with a pair of shifted lines with complex momenta. This will induce a recursion relation identical to Britto-Cachazo-Feng-Witten recursion relations at the finite poles of the complexified amplitudes. Furthermore, according to the Ward identity, it is also possible to transform the boundary term into a simple form, which can be obtained by a new recursion relation. For the amplitude with one off-shell line in pure Yang-Mills theory, we find this technique is effective for obtaining the amplitude even when there are boundary contributions.
Asymptotic symmetries of Yang-Mills theory
NASA Astrophysics Data System (ADS)
Strominger, Andrew
2014-07-01
Asymptotic symmetries at future null infinity ( +) of Minkowski space for electrodynamics with massless charged fields, as well as nonabelian gauge theories with gauge group G, are considered at the semiclassical level. The possibility of charge/color flux through + suggests the symmetry group is infinite-dimensional. It is conjectured that the symmetries include a G Kac-Moody symmetry whose generators are "large" gauge transformations which approach locally holomorphic functions on the conformal two-sphere at + and are invariant under null translations. The Kac-Moody currents are constructed from the gauge field at the future boundary of +. The current Ward identities include Weinberg's soft photon theorem and its colored extension.
MONOPOLES AND DYONS IN THE PURE EINSTEIN YANG MILLS THEORY
HOSOTANI,Y.; BJORAKER,J.
1999-08-16
In the pure Einstein-Yang-Mills theory in four dimensions there exist monopole and dyon solutions. The spectrum of the solutions is discrete in asymptotically flat or de Sitter space, whereas it is continuous in asymptotically anti-de Sitter space. The solutions are regular everywhere and specified with their mass, and non-Abelian electric and magnetic charges. In asymptotically anti-de Sitter space a class of monopole solutions have no node in non-Abelian magnetic fields, and are stable against spherically symmetric perturbations.
Transport coefficients in Yang-Mills theory and QCD.
Christiansen, Nicolai; Haas, Michael; Pawlowski, Jan M; Strodthoff, Nils
2015-09-11
We calculate the shear-viscosity-over-entropy-density ratio η/s in Yang-Mills theory from the Kubo formula using an exact diagrammatic representation in terms of full propagators and vertices using gluon spectral functions as external input. We provide an analytic fit formula for the temperature dependence of η/s over the whole temperature range from a glueball resonance gas at low temperatures, to a high-temperature regime consistent with perturbative results. Subsequently, we provide a first estimate for η/s in QCD. PMID:26406822
Shifman, M.
2015-03-15
We discuss similarities and differences between the resurgence program in quantum mechanics and the operator product expansion in strongly coupled Yang-Mills theories. In N = 1 super-Yang-Mills theories, renormalons are peculiar and are not quite similar to renormalons in QCD.
Solvable relativistic hydrogenlike system in supersymmetric Yang-Mills theory.
Caron-Huot, Simon; Henn, Johannes M
2014-10-17
The classical Kepler problem, as well as its quantum mechanical version, the hydrogen atom, enjoys a well-known hidden symmetry, the conservation of the Laplace-Runge-Lenz vector, which makes these problems superintegrable. Is there a relativistic quantum field theory extension that preserves this symmetry? In this Letter we show that the answer is positive: in the nonrelativistic limit, we identify the dual conformal symmetry of planar N = 4 super Yang-Mills theory with the well-known symmetries of the hydrogen atom. We point out that the dual conformal symmetry offers a novel way to compute the spectrum of bound states of massive W bosons in the theory. We perform nontrivial tests of this setup at weak and strong coupling and comment on the possible extension to arbitrary values of the coupling. PMID:25361249
Is the ground state of Yang-Mills theory Coulombic?
Heinzl, T.; Ilderton, A.; Langfeld, K.; Lavelle, M.; McMullan, D.; Lutz, W.
2008-08-01
We study trial states modelling the heavy quark-antiquark ground state in SU(2) Yang-Mills theory. A state describing the flux tube between quarks as a thin string of glue is found to be a poor description of the continuum ground state; the infinitesimal thickness of the string leads to UV artifacts which suppress the overlap with the ground state. Contrastingly, a state which surrounds the quarks with non-Abelian Coulomb fields is found to have a good overlap with the ground state for all charge separations. In fact, the overlap increases as the lattice regulator is removed. This opens up the possibility that the Coulomb state is the true ground state in the continuum limit.
Yang-Mills Gauge Theory and Higgs Particle
NASA Astrophysics Data System (ADS)
Wu, Tai Tsun; Wu, Sau Lan
Motivated by the experimental data on the Higgs particle from the ATLAS Collaboration and the CMS Collaboration at CERN, the standard model, which is a Yang-Mills non-Abelian gauge theory with the group U(1) × SU (2) × SU (3), is augmented by scalar quarks and scalar leptons without changing the gauge group and without any additional Higgs particle. Thus there is fermion-boson symmetry between these new particles and the known quarks and leptons. In a simplest scenario, the cancellation of the quadratic divergences in this augmented standard model leads to a determination of the masses of all these scalar quarks and scalar leptons. All these masses are found to be less than 100 GeV/c2, and the right-handed scalar neutrinos are especially light. Alterative procedures are given with less reliance on the experimental data, leading to the same conclusions.
Yang-Mills gauge theory and Higgs particle
NASA Astrophysics Data System (ADS)
Wu, Tai Tsun; Wu, Sau Lan
2015-12-01
Motivated by the experimental data on the Higgs particle from the ATLAS Collaboration and the CMS Collaboration at CERN, the standard model, which is a Yang-Mills non-Abelian gauge theory with the group U(1) × SU(2) × SU(3), is augmented by scalar quarks and scalar leptons without changing the gauge group and without any additional Higgs particle. Thus there is fermion-boson symmetry between these new particles and the known quarks and leptons. In a simplest scenario, the cancellation of the quadratic divergences in this augmented standard model leads to a determination of the masses of all these scalar quarks and scalar leptons. All these masses are found to be less than 100 GeV/c2, and the right-handed scalar neutrinos are especially light. Alterative procedures are given with less reliance on the experimental data, leading to the same conclusions.
Dual superconductivity and vacuum properties in Yang Mills theories
NASA Astrophysics Data System (ADS)
D'Alessandro, A.; D'Elia, M.; Tagliacozzo, L.
2007-07-01
We address, within the dual superconductivity model for color confinement, the question whether the Yang-Mills vacuum behaves as a superconductor of type I or type II. In order to do that we compare, for the theory with gauge group SU(2), the determination of the field penetration depth λ with that of the superconductor correlation length ξ. The latter is obtained by measuring the temporal correlator of a disorder parameter developed by the Pisa group to detect dual superconductivity. The comparison places the vacuum close to the border between type I and type II and marginally on the type II side. We also check our results against the study of directly measurable effects such as the interaction between two parallel flux tubes, obtaining consistent indications for a weak repulsive behaviour. Future strategies to improve our investigation are discussed.
A euclidean lattice formulation of D = 5 maximally supersymmetric Yang-Mills theory
NASA Astrophysics Data System (ADS)
Joseph, Anosh
2016-06-01
We construct lattice action for five-dimensional maximally supersymmetric Yang-Mills theory. This supersymmetric lattice formulation can be used to explore the non-perturbative regime of the continuum target theory, which has a known gravitational dual.
Thierry-Mieg, J.
1985-05-14
The reinterpretation of the BRS equations of Quantum Field Theory as the Maurer Cartan equation of a classical principal fiber bundle leads to a simple gauge invariant classification of the anomalies in Yang Mills theory and gravity.
Composite strings in (2+1)-dimensional anisotropic weakly coupled Yang-Mills theory
Orland, Peter
2008-01-15
The small-scale structure of a string connecting a pair of static sources is explored for the weakly coupled anisotropic SU(2) Yang-Mills theory in (2+1) dimensions. A crucial ingredient in the formulation of the string Hamiltonian is the phenomenon of color smearing of the string constituents. The quark-antiquark potential is determined. We close with some discussion of the standard, fully Lorentz-invariant Yang-Mills theory.
Masslessness of ghosts in equivariantly gauge-fixed Yang-Mills theories
Golterman, Maarten; Zimmerman, Leah
2005-06-01
We show that the one-loop ghost self-energy in an equivariantly gauge-fixed Yang-Mills theory vanishes at zero momentum. A ghost mass is forbidden by equivariant BRST symmetry, and our calculation confirms this explicitly. The four-ghost self interaction which appears in the equivariantly gauge-fixed Yang-Mills theory is needed in order to obtain this result.
Infrared singularities in Landau gauge Yang-Mills theory
Alkofer, Reinhard; Huber, Markus Q.; Schwenzer, Kai
2010-05-15
We present a more detailed picture of the infrared regime of Landau-gauge Yang-Mills theory. This is done within a novel framework that allows one to take into account the influence of finite scales within an infrared power counting analysis. We find that there are two qualitatively different infrared fixed points of the full system of Dyson-Schwinger equations. The first extends the known scaling solution, where the ghost dynamics is dominant and gluon propagation is strongly suppressed. It features in addition to the strong divergences of gluonic vertex functions in the previously considered uniform scaling limit, when all external momenta tend to zero, also weaker kinematic divergences, when only some of the external momenta vanish. The second solution represents the recently proposed decoupling scenario where the gluons become massive and the ghosts remain bare. In this case we find that none of the vertex functions is enhanced, so that the infrared dynamics is entirely suppressed. Our analysis also provides a strict argument why the Landau-gauge gluon dressing function cannot be infrared divergent.
Towards the fundamental spectrum of the quantum Yang-Mills theory
NASA Astrophysics Data System (ADS)
Liegener, Klaus; Thiemann, Thomas
2016-07-01
In this work we focus on the quantum Einstein-Yang-Mills sector quantized by the methods of loop quantum gravity. We point out the improved UV behavior of the coupled system as compared to pure quantum Yang-Mills theory on a fixed, classical background spacetime as was considered in a seminal work by Kogut and Susskind. Furthermore, we develop a calculational scheme by which the fundamental spectrum of the quantum Yang-Mills Hamiltonian can be computed in principle and by which one can make contact with the Wilsonian renormalization group, possibly purely within the Hamiltonian framework. Finally, we comment on the relationship of the fundamental spectrum to that of pure Yang-Mills theory on a (flat) classical spacetime.
Surface-invariants in 2D classical Yang-Mills theory
Diaz, Rafael; Fuenmayor, E.; Leal, Lorenzo
2006-03-15
We study a method to obtain invariants under area-preserving diffeomorphisms associated to closed curves in the plane from classical Yang-Mills theory in two dimensions. Taking as starting point the Yang-Mills field coupled to nondynamical particles carrying chromo-electric charge, and by means of a perturbative scheme, we obtain the first two contributions to the on-shell action, which are area-invariants. A geometrical interpretation of these invariants is given.
String theories as the adiabatic limit of Yang-Mills theory
NASA Astrophysics Data System (ADS)
Popov, Alexander D.
2015-08-01
We consider Yang-Mills theory with a matrix gauge group G on a direct product manifold M =Σ2×H2 , where Σ2 is a two-dimensional Lorentzian manifold and H2 is a two-dimensional open disc with the boundary S1=∂H2 . The Euler-Lagrange equations for the metric on Σ2 yield constraint equations for the Yang-Mills energy-momentum tensor. We show that in the adiabatic limit, when the metric on H2 is scaled down, the Yang-Mills equations plus constraints on the energy-momentum tensor become the equations describing strings with a world sheet Σ2 moving in the based loop group Ω G =C∞(S1,G )/G , where S1 is the boundary of H2. By choosing G =Rd -1 ,1 and putting to zero all parameters in Ω Rd -1 ,1 besides Rd -1 ,1 , we get a string moving in Rd -1 ,1 . In another paper of the author, it was described how one can obtain the Green-Schwarz superstring action from Yang-Mills theory on Σ2×H2 while H2 shrinks to a point. Here we also consider Yang-Mills theory on a three-dimensional manifold Σ2×S1 and show that in the limit when the radius of S1 tends to zero, the Yang-Mills action functional supplemented by a Wess-Zumino-type term becomes the Green-Schwarz superstring action.
Karanikas, A.I.; Ktorides, C.N.
1987-02-15
We confront the general problem posed by nonperturbative calculations in non-Abelian gauge theories, pertaining to the Wilson loop operator, away from strong coupling. We adopt a nonperturbatively regularized formulation of Yang-Mills theories in the continuum which has already been discussed in the preceding paper. We study, in particular, Yang-Mills duality, within our regularized context, with respect to the full SU(N) group and not simply its center Z/sub N/. We further show that, from the present viewpoint, duality emerges through a distinction between the regularization length on one hand and the scale by which the Yang-Mills system is observed on the other. Finally, we are able to derive a Makeenko-Migdal-type equation for finite N.
Hamiltonian Approach to Yang-Mills Theory in Coulomb Gauge--Revisited
Reinhardt, Hugo; Campagnari, Davide R.; Leder, Markus; Burgio, Giuseppe; Quandt, Markus; Pawlowski, Jan M.; Weber, Axel
2011-05-24
I briefly review results obtained within the variational Hamiltonian approach to Yang-Mills theory in Coulomb gauge and confront them with recent lattice data. The variational approach is extended to non-Gaussian wave functionals including three- and four-gluon kernels in the exponential of the vacuum wave functional and used to calculate the three-gluon vertex. A new functional renormalization group flow equation for Hamiltonian Yang-Mills theory in Coulomb gauge is solved for the gluon and ghost propagator under the assumption of ghost dominance. The results are compared to those obtained in the variational approach.
Hamiltonian Approach to Yang-Mills Theory in Coulomb Gauge—Revisited
NASA Astrophysics Data System (ADS)
Reinhardt, Hugo; Campagnari, Davide R.; Leder, Markus; Burgio, Giuseppe; Pawlowski, Jan M.; Quandt, Markus; Weber, Axel
2011-05-01
I briefly review results obtained within the variational Hamiltonian approach to Yang-Mills theory in Coulomb gauge and confront them with recent lattice data. The variational approach is extended to non-Gaussian wave functionals including three- and four-gluon kernels in the exponential of the vacuum wave functional and used to calculate the three-gluon vertex. A new functional renormalization group flow equation for Hamiltonian Yang-Mills theory in Coulomb gauge is solved for the gluon and ghost propagator under the assumption of ghost dominance. The results are compared to those obtained in the variational approach.
Perturbation theory in the Hamiltonian approach to Yang-Mills theory in Coulomb gauge
Campagnari, Davide R.; Reinhardt, Hugo; Weber, Axel
2009-07-15
We study the Hamiltonian approach to Yang-Mills theory in Coulomb gauge in Rayleigh-Schroedinger perturbation theory. The static gluon and ghost propagator as well as the potential between static color sources are calculated to one-loop order. Furthermore, the one-loop {beta} function is calculated from both the ghost-gluon vertex and the static potential and found to agree with the result of covariant perturbation theory.
Thermodynamics of SU(2) quantum Yang-Mills theory and CMB anomalies
NASA Astrophysics Data System (ADS)
Hofmann, Ralf
2014-04-01
A brief review of effective SU(2) Yang-Mills thermodynamics in the deconfining phase is given, including the construction of the thermal ground-state estimate in terms of an inert, adjoint scalar field φ, based on non-propagating (anti)selfdual field configurations of topological charge unity. We also discuss kinematic constraints on interacting propagating gauge fields implied by the according spatial coarse-graining, and we explain why the screening physics of an SU(2) photon is subject to an electric-magnetically dual interpretation. This argument relies on the fact that only (anti)calorons of scale parameter ρ ˜ |φ|-1 contribute to the coarse-graining required for thermal-ground-state emergence at temperature T. Thus, use of the effective gauge coupling e in the (anti)caloron action is justified, yielding the value ħ for the latter at almost all temperatures. As a consequence, the indeterministic transition of initial to final plane waves caused by an effective, pointlike vertex is fundamentally mediated in Euclidean time by a single (anti)caloron being part of the thermal ground state. Next, we elucidate how a low-frequency excess of line temperature in the Cosmic Microwave Background (CMB) determines the value of the critical temperature of the deconfining-preconfining phase transition of an SU(2) Yang-Mills theory postulated to describe photon propagation, and we describe how, starting at a redshift of about unity, SU(2) photons collectively work 3D temperature depressions into the CMB. Upon projection along a line of sight, a given depression influences the present CMB sky in a cosmologically local way, possibly explaining the large-angle anomalies confirmed recently by the Planck collaboration. Finally, six relativistic polarisations residing in the SU(2) vector modes roughly match the number of degrees of freedom in cosmic neutrinos (Planck) which would disqualify the latter as radiation. Indeed, if interpreted as single center-vortex loops in
Fermion actions extracted from lattice super Yang-Mills theories
NASA Astrophysics Data System (ADS)
Misumi, Tatsuhiro
2013-12-01
We revisit 2D = (2, 2) super Yang-Mills lattice formulation (Sugino model) to investigate its fermion action with two (Majorana) fermion flavors and exact chiral-U(1) R symmetry. We show that the reconcilement of chiral symmetry and absence of further species-doubling originates in the 4D clifford algebra structure of the action, where 2D two flavors are spuriously treated as a single 4D four-spinor with four 4D gamma matrices introduced into kinetic and Wilson terms. This fermion construction based on the higher-dimensional clifford algebra is extended to four dimensions in two manners: (1) pseudo-8D sixteen-spinor treatment of 4D four flavors with eight 8D gamma matrices, (2) pseudo-6D eight-spinor treatment of 4D two flavors with five out of six 6D gamma matrices. We obtain 4D four-species and two-species lattice fermions with unbroken subgroup of chiral symmetry and other essential properties. We discuss their relations to staggered and Wilson twisted-mass fermions. We also discuss their potential feedback to 4D super Yang-Mills lattice formulations.
Center-stabilized Yang-Mills Theory:Confinement and Large N Volume Independence
Unsal, Mithat; Yaffe, Laurence G.; /Washington U., Seattle
2008-03-21
We examine a double trace deformation of SU(N) Yang-Mills theory which, for large N and large volume, is equivalent to unmodified Yang-Mills theory up to O(1/N{sup 2}) corrections. In contrast to the unmodified theory, large N volume independence is valid in the deformed theory down to arbitrarily small volumes. The double trace deformation prevents the spontaneous breaking of center symmetry which would otherwise disrupt large N volume independence in small volumes. For small values of N, if the theory is formulated on R{sup 3} x S{sup 1} with a sufficiently small compactification size L, then an analytic treatment of the non-perturbative dynamics of the deformed theory is possible. In this regime, we show that the deformed Yang-Mills theory has a mass gap and exhibits linear confinement. Increasing the circumference L or number of colors N decreases the separation of scales on which the analytic treatment relies. However, there are no order parameters which distinguish the small and large radius regimes. Consequently, for small N the deformed theory provides a novel example of a locally four-dimensional pure gauge theory in which one has analytic control over confinement, while for large N it provides a simple fully reduced model for Yang-Mills theory. The construction is easily generalized to QCD and other QCD-like theories.
Covariant gauges without Gribov ambiguities in Yang-Mills theories
NASA Astrophysics Data System (ADS)
Serreau, J.; Tissier, M.; Tresmontant, A.
2014-06-01
We propose a one-parameter family of nonlinear covariant gauges which can be formulated as an extremization procedure that may be amenable to lattice implementation. At high energies, where the Gribov ambiguities can be ignored, this reduces to the Curci-Ferrari-Delbourgo-Jarvis gauges. We further propose a continuum formulation in terms of a local action which is free of Gribov ambiguities and avoids the Neuberger zero problem of the standard Faddeev-Popov construction. This involves an averaging over Gribov copies with a nonuniform weight, which introduces a new gauge-fixing parameter. We show that the proposed gauge-fixed action is perturbatively renormalizable in four dimensions and we provide explicit expressions of the renormalization factors at one loop. We discuss the possible implications of the present proposal for the calculation of Yang-Mills correlators.
Yang-Mills Gauge Theory and the Higgs Boson Family
NASA Astrophysics Data System (ADS)
Chang, Ngee-Pong
The gauge symmetry principles of the Yang-Mills field of 1954 provide the solid rock foundation for the Standard Model of particle physics. To give masses to the quarks and leptons, however, SM calls on the solitary Higgs field using a set of mysterious complex Yukawa coupling matrices. We enrich the SM by reducing the Yukawa coupling matrices to a single Yukawa coupling constant, and endowing it with a family of Higgs fields that are degenerate in mass. The recent experimental discovery of the Higgs resonance at 125.09±0.21 GeV does not preclude this possibility. Instead, it presents an opportunity to explore the interference effects in background events at the LHC. We present a study based on the maximally symmetric Higgs potential in a leading hierarchy scenario.
Yang-Mills gauge theory and the Higgs boson family
NASA Astrophysics Data System (ADS)
Chang, Ngee-Pong
2016-01-01
The gauge symmetry principles of the Yang-Mills field of 1954 provide the solid rock foundation for the Standard Model of particle physics. To give masses to the quarks and leptons, however, SM calls on the solitary Higgs field using a set of mysterious complex Yukawa coupling matrices. We enrich the SM by reducing the Yukawa coupling matrices to a single Yukawa coupling constant, and endowing it with a family of Higgs fields that are degenerate in mass. The recent experimental discovery of the Higgs resonance at 125.09 ± 0.21 GeV does not preclude this possibility. Instead, it presents an opportunity to explore the interference effects in background events at the LHC. We present a study based on the maximally symmetric Higgs potential in a leading hierarchy scenario.
Hamiltonian Dyson-Schwinger and FRG Flow Equations of Yang-Mills Theory in Coulomb Gauge
Reinhardt, Hugo; Leder, Markus; Pawlowski, Jan M.; Weber, Axel
2011-05-23
A new functional renormalization group equation for Hamiltonian Yang-Mills theory in Coulomb gauge is presented and solved for the static gluon and ghost propagators under the assumption of ghost dominance. The results are compared to those obtained in the variational approach.
Real-time dynamics of a hot Yang-Mills theory: a numerical analysis
NASA Astrophysics Data System (ADS)
Ambjørn, J.; Anagnostopoulos, K. N.; Krasnitz, A.
2002-03-01
We discuss recent results obtained from simulations of high temperature, classical, real time dynamics of SU(2) Yang-Mills theory at temperatures of the order of the electroweak scale. Measurements of gauge covariant and gauge invariant autocorrelations of the fields indicate that the ASY-Bödecker scenario is irrelevant at these temperatures.
Real-time dynamics of a hot Yang-Mills theory: a numerical analysis
NASA Astrophysics Data System (ADS)
Ambjørn, J.; Anagnostopoulos, K. N.; Krasnitz, A.
We discuss recent results obtained from simulations of high temperature, classical, real time dynamics of SU(2) Yang-Mills theory at temperatures of the order of the electroweak scale. Measurements of gauge covariant and gauge invariant autocorrelations of the fields indicate that the ASY-Bödecker scenario is irrelevant at these temperatures.
Explicit non-Abelian monopoles and instantons in SU(N) pure Yang-Mills theory
Popov, Alexander D.
2008-06-15
It is well known that there are no static non-Abelian monopole solutions in pure Yang-Mills theory on Minkowski space R{sup 3,1}. I show that such solutions exist in SU(N) gauge theory on the spaces R{sup 2}xS{sup 2} and RxS{sup 1}xS{sup 2} with Minkowski signature (-+++). In the temporal gauge they are solutions of pure Yang-Mills theory on TxS{sup 2}, where T is R or S{sup 1}. Namely, imposing SO(3) invariance and some reality conditions, I consistently reduce the Yang-Mills model on the above spaces to a non-Abelian analog of the {phi}{sup 4} kink model whose static solutions give SU(N) monopole (-antimonopole) configurations on the space R{sup 1,1}xS{sup 2} via the above-mentioned correspondence. These solutions can also be considered as instanton configurations of Yang-Mills theory in 2+1 dimensions. The kink model on RxS{sup 1} admits also periodic sphaleron-type solutions describing chains of n kink-antikink pairs spaced around the circle S{sup 1} with arbitrary n>0. They correspond to chains of n static monopole-antimonopole pairs on the space RxS{sup 1}xS{sup 2} which can also be interpreted as instanton configurations in 2+1 dimensional pure Yang-Mills theory at finite temperature (thermal time circle). I also describe similar solutions in Euclidean SU(N) gauge theory on S{sup 1}xS{sup 3} interpreted as chains of n instanton-anti-instanton pairs.
Isotropy theorem for cosmological Yang-Mills theories
NASA Astrophysics Data System (ADS)
Cembranos, J. A. R.; Maroto, A. L.; Jareño, S. J. Núñez
2013-02-01
We consider homogeneous non-Abelian vector fields with general potential terms in an expanding universe. We find a mechanical analogy with a system of N interacting particles (with N the dimension of the gauge group) moving in three dimensions under the action of a central potential. In the case of bounded and rapid evolution compared to the rate of expansion, we show by making use of a generalization of the virial theorem that for an arbitrary potential and polarization pattern, the average energy-momentum tensor is always diagonal and isotropic despite the intrinsic anisotropic evolution of the vector field. We consider also the case in which a gauge-fixing term is introduced in the action and show that the average equation of state does not depend on such a term. Finally, we extend the results to arbitrary background geometries and show that the average energy-momentum tensor of a rapidly evolving Yang-Mills field is always isotropic and has the perfect fluid form for any locally inertial observer.
Quantum equivalence of noncommutative and Yang-Mills gauge theories in 2D and matrix theory
Ydri, Badis
2007-05-15
We construct noncommutative U(1) gauge theory on the fuzzy sphere S{sub N}{sup 2} as a unitary 2Nx2N matrix model. In the quantum theory the model is equivalent to a non-Abelian U(N) Yang-Mills theory on a two-dimensional lattice with two plaquettes. This equivalence holds in the 'fuzzy sphere' phase where we observe a 3rd order phase transition between weak-coupling and strong-coupling phases of the gauge theory. In the matrix phase we have a U(N) gauge theory on a single point.
Solution to the nonlinear field equations of ten dimensional supersymmetric Yang-Mills theory
NASA Astrophysics Data System (ADS)
Mafra, Carlos R.; Schlotterer, Oliver
2015-09-01
In this paper, we present a formal solution to the nonlinear field equations of ten-dimensional super Yang-Mills theory. It is assembled from products of linearized superfields which have been introduced as multiparticle superfields in the context of superstring perturbation theory. Their explicit form follows recursively from the conformal field theory description of the gluon multiplet in the pure spinor superstring. Furthermore, superfields of higher-mass dimensions are defined and their equations of motion are spelled out.
Kuerkcueoglu, Seckin
2010-11-15
We consider a U(2) Yang-Mills theory on MxS{sub F}{sup 2}, where M is an arbitrary noncommutative manifold, and S{sub F}{sup 2} is a fuzzy sphere spontaneously generated from a noncommutative U(N) Yang-Mills theory on M, coupled to a triplet of scalars in the adjoint of U(N). Employing the SU(2)-equivariant gauge field constructed in [D. Harland and S. Kurkcuoglu, Nucl. Phys. B 821, 380 (2009).], we perform the dimensional reduction of the theory over the fuzzy sphere. The emergent model is a noncommutative U(1) gauge theory coupled adjointly to a set of scalar fields. We study this model on the Groenewald-Moyal plane M=R{sub {theta}}{sup 2} and find that, in certain limits, it admits noncommutative, non-Bogomol'nyi-Prasad-Somerfield vortex as well as flux-tube (fluxon) solutions and discuss some of their properties.
PP-wave string interactions from perturbative Yang-Mills theory
NASA Astrophysics Data System (ADS)
Constable, Neil R.; Freedman, Daniel Z.; Headrick, Matthew; Minwalla, Shiraz; Motl, Lubos; Postnikov, Alexander; Skiba, Witold
2002-07-01
Recently, Berenstein et al. have proposed a duality between a sector of Script N = 4 super-Yang-Mills theory with large R-charge J, and string theory in a pp-wave background. In the limit considered, the effective 't Hooft coupling has been argued to be λ' = gYM2N/J2 = 1/(μp+α')2. We study Yang-Mills theory at small λ' (large μ) with a view to reproducing string interactions. We demonstrate that the effective genus counting parameter of the Yang-Mills theory is g22 = J4/N2 = (4πgs)2(μp+α')4, the effective two-dimensional Newton constant for strings propagating on the pp-wave background. We identify g2(λ')1/2 as the effective coupling between a wide class of excited string states on the pp-wave background. We compute the anomalous dimensions of BMN operators at first order in g22 and λ' and interpret our result as the genus one mass renormalization of the corresponding string state. We postulate a relation between the three-string vertex function and the gauge theory three-point function and compare our proposal to string field theory. We utilize this proposal, together with quantum mechanical perturbation theory, to recompute the genus one energy shift of string states, and find precise agreement with our gauge theory computation.
Variational Approach to Yang-Mills Theory with non-Gaussian Wave Functionals
NASA Astrophysics Data System (ADS)
Campagnari, Davide R.; Reinhardt, Hugo
2011-05-01
A general method for treating non-Gaussian wave functionals in quantum field theory is presented and applied to the Hamiltonian approach to Yang-Mills theory in Coulomb gauge in order to include a three-gluon kernel in the exponential of the vacuum wave functional. The three-gluon vertex is calculated using the propagators found in the variational approach with a Gaussian trial wave functional as input.
Multiscale Monte Carlo equilibration: Pure Yang-Mills theory
Endres, Michael G.; Brower, Richard C.; Orginos, Kostas; Detmold, William; Pochinsky, Andrew V.
2015-12-29
In this study, we present a multiscale thermalization algorithm for lattice gauge theory, which enables efficient parallel generation of uncorrelated gauge field configurations. The algorithm combines standard Monte Carlo techniques with ideas drawn from real space renormalization group and multigrid methods. We demonstrate the viability of the algorithm for pure Yang-Mills gauge theory for both heat bath and hybrid Monte Carlo evolution, and show that it ameliorates the problem of topological freezing up to controllable lattice spacing artifacts.
Yangian symmetry of smooth Wilson loops in super Yang-Mills theory
NASA Astrophysics Data System (ADS)
Müller, Dennis; Münkler, Hagen; Plefka, Jan; Pollok, Jonas; Zarembo, Konstantin
2013-11-01
We show that appropriately supersymmetrized smooth Maldacena-Wilson loop operators in super Yang-Mills theory are invariant under a Yangian symmetry Y [(2, 2|4)] built upon the manifest superconformal symmetry algebra of the theory. The existence of this hidden symmetry is demonstrated at the one-loop order in the weak coupling limit as well as at leading order in the strong coupling limit employing the classical integrability of the dual AdS5 × S 5 string description. The hidden symmetry generators consist of a canonical non-local second order variational derivative piece acting on the superpath, along with a novel local path dependent contribution. We match the functional form of these Yangian symmetry generators at weak and strong coupling and find evidence for an interpolating function. Our findings represent the smooth counterpart to the Yangian invariance of scattering superamplitudes dual to light-like polygonal super Wilson loops in the super Yang-Mills theory.
On Twisted N = 2 5D Super Yang-Mills Theory
NASA Astrophysics Data System (ADS)
Qiu, Jian; Zabzine, Maxim
2016-01-01
On a five-dimensional simply connected Sasaki-Einstein manifold, one can construct Yang-Mills theories coupled to matter with at least two supersymmetries. The partition function of these theories localises on the contact instantons, however, the contact instanton equations are not elliptic. It turns out that these equations can be embedded into the Haydys-Witten equations (which are elliptic) in the same way the 4D anti-self-dual instanton equations are embedded in the Vafa-Witten equations. We show that under some favourable circumstances, the latter equations will reduce to the former by proving some vanishing theorems. It was also known that the Haydys-Witten equations on product manifolds {M_5 = M_4 × R} arise in the context of twisting the 5D maximally supersymmetric Yang-Mills theory. In this paper, we present the construction of twisted N = 2 Yang-Mills theory on Sasaki-Einstein manifolds, and more generally on K-contact manifolds. The localisation locus of this new theory thus provides a covariant version of the Haydys-Witten equation.
Physical unitarity for a massive Yang-Mills theory without the Higgs field: A perturbative treatment
NASA Astrophysics Data System (ADS)
Kondo, Kei-Ichi; Suzuki, Kenta; Fukamachi, Hitoshi; Nishino, Shogo; Shinohara, Toru
2013-01-01
In a series of papers, we examine the physical unitarity in a massive Yang-Mills theory without the Higgs field in which the color gauge symmetry is not spontaneously broken and kept intact. For this purpose, we use a new framework proposed in the previous paper Kondo [arXiv:1208.3521] based on a nonperturbative construction of a non-Abelian field describing a massive spin-one vector boson field, which enables us to perform the perturbative and nonperturbative studies on the physical unitarity. In this paper, we present a new perturbative treatment for the physical unitarity after giving the general properties of the massive Yang-Mills theory. Then we reproduce the violation of physical unitarity in a transparent way. This paper is a preliminary work to the subsequent papers in which we present a nonperturbative framework to propose a possible scenario of restoring the physical unitarity in the Curci-Ferrari model.
Some Comments on the String Singularity of the Yang-Mills-Higgs Theory
Lim, Kok-Geng; Teh, Rosy
2010-07-07
We are going to make use of the regulated polar angle which had been introduced by Boulware et al.. to show that in the SU(2) Yang-Mills-Higgs theory when the magnetic monopole is carried by the gauge field, the Higgs field does not carry the monopole and vice versa. In the Yang-Mills-Higgs theory, our solution shows that when the parameter {epsilon} {ne} 0, the monopole is carried by the gauge field and there is a string singularity in the gauge field. When the parameter {epsilon} {yields} 0, the monopole is transferred from the gauge field to the Higgs field and the string singularity disappeared. The solution is only singular at the origin, that is at r = 0 as it becomes the Wu-Yang monopole.
Hedgehogs in Wilson loops and phase transition in SU(2) Yang Mills theory
NASA Astrophysics Data System (ADS)
Belavin, V. A.; Chernodub, M. N.; Kozlov, I. E.
2006-08-01
We suggest that the gauge-invariant hedgehog-like structures in the Wilson loops are physically interesting degrees of freedom in the Yang-Mills theory. The trajectories of these "hedgehog loops" are closed curves corresponding to center-valued (untraced) Wilson loops and are characterized by the center charge and winding number. We show numerically in the SU(2) Yang-Mills theory that the density of hedgehog structures in the thermal Wilson-Polyakov line is very sensitive to the finite-temperature phase transition. The (additively normalized) hedgehog line density behaves like an order parameter: The density is almost independent of the temperature in the confinement phase and changes substantially as the system enters the deconfinement phase. In particular, our results suggest that the (static) hedgehog lines may be relevant degrees of freedom around the deconfinement transition and thus affect evolution of the quark-gluon plasma in high-energy heavy-ion collisions.
Quantum Metamorphosis of a Conformal Transformation in D3-Brane Yang-Mills Theory
Jevicki, A.; Kazama, Y.; Yoneya, T.
1998-12-01
We show how the linear special conformal transformation in four-dimensional N=4 super-Yang-Mills theory is metamorphosed into the nonlinear and field-dependent transformation for the collective coordinates of Dirichlet 3-branes, which agrees with the transformation law for the space-time coordinates in the anti{endash}de Sitter (AdS) space-time. Our result provides a new and strong support for the conjectured relation between AdS{sub 5}{times} S{sup 5} supergravity and super-Yang-Mills theory (SYM). Furthermore, our work sheds elucidating light on the nature of the AdS/SYM correspondence. {copyright} {ital 1998} {ital The American Physical Society}
Gauge Invariance and Gauge-Factor Group in Causal Yang-Mills Theory
NASA Astrophysics Data System (ADS)
Emmenegger, N.
2001-11-01
In the present work the gauge invariance of causal Yang-Mills theory will be proven with the aid of the gauge-factor group. For that purpose it must be shown, that the operator valued distributions T_n and D_n(ret) occurring in the causal S-matrix construction can be written, after applying the gauge variation d_Q, as a divergence. Since merely local terms lead to gauge destroying expressions, one has to focus on them exclusively. In the first part of the work the local gauge-factor group will be defined in the style of the concept of gauge cohomology theory. It will be shown, that every element out of the so defined factor group under the transformation d_Q leads to a divergence of the entire operator valued distribution d_Q(T_n). In the second part all local terms arising in causal Yang-Mills theory are systematically investigated. Without further restrictions there can be proven, that every local operator valued distribution is an element of the gauge factor group or equal to zero. This concludes the demonstration of gauge invariance of causal Yang-Mills theory.
Four-loop dressing phase of N=4 super-Yang-Mills theory
Beisert, N.; McLoughlin, T.; Roiban, R.
2007-08-15
We compute the dilatation generator in the su(2) sector of planar N=4 super-Yang-Mills theory at four loops. We use the known world-sheet scattering matrix to constrain the structure of the generator. The remaining few coefficients can be computed directly from Feynman diagrams. This allows us to confirm previous conjectures for the leading contribution to the dressing phase which is proportional to {zeta}(3)
Euclidean wormhole solutions of Einstein-Yang-Mills theory in diverse dimensions
Yoshida, K.; Hirenzaki, S. ); Shiraishi, K. )
1990-09-15
We solve the Euclidean Einstein equations with non-Abelian gauge fields of sufficiently large symmetry in various dimensions. In higher-dimensional spaces, we find the solutions which are similar to so-called scalar wormholes. In four-dimensional space-time, we find singular wormhole solutions with infinite Euclidean action. Wormhole solutions in the three-dimensional Einstein-Yang-Mills theory with a Chern-Simons term are also constructed.
NASA Astrophysics Data System (ADS)
Bassetto, Antonio; DePol, Giancarlo; Torrielli, Alessandro; Vian, Federica
2005-05-01
We present an investigation on the invariance properties of noncommutative Yang-Mills theory in two dimensions under area preserving diffeomorphisms. Stimulated by recent remarks by Ambjorn, Dubin and Makeenko who found a breaking of such an invariance, we confirm both on a fairly general ground and by means of perturbative analytical and numerical calculations that indeed invariance under area preserving diffeomorphisms is lost. However a remnant survives, namely invariance under linear unimodular tranformations.
Exact Spectrum of Planar N=4 Supersymmetric Yang-Mills Theory: Konishi Dimension at Any Coupling
NASA Astrophysics Data System (ADS)
Gromov, Nikolay; Kazakov, Vladimir; Vieira, Pedro
2010-05-01
We compute the full dimension of the Konishi operator in planar N=4 super Yang-Mills theory for a wide range of couplings, from weak to strong coupling regime, and predict the subleading terms in its strong coupling asymptotics. For this purpose we solve numerically the integral form of the AdS/CFT Y-system equations for the exact energies of excited states proposed by us and A. Kozak.
Integrability and maximally helicity violating diagrams in n=4 supersymmetric yang-mills theory.
Brandhuber, Andreas; Penante, Brenda; Travaglini, Gabriele; Young, Donovan
2015-02-20
We apply maximally helicity violating (MHV) diagrams to the derivation of the one-loop dilatation operator of N=4 supersymmetric Yang-Mills theory in the SO(6) sector. We find that in this approach the calculation reduces to the evaluation of a single MHV diagram in dimensional regularization. This provides the first application of MHV diagrams to an off-shell quantity. We also discuss other applications of the method and future directions. PMID:25763951
Yang-Mills Theory at 60: Milestones, Landmarks and Interesting Questions
NASA Astrophysics Data System (ADS)
Chau, Ling-Lie
On the auspicious occasion of celebrating the 60th anniversary of the Yang-Mills theory, and Professor Yang's many other important contributions to physics and mathematics, I will highlight the impressive milestones and landmarks that have been established in the last 60 years, as well as some interesting questions that are worthy of answers from future researches. The paper is written (without equations) for the interest of non-scientists as well as of scientists.
Yang-Mills theory at 60: Milestones, landmarks and interesting questions
NASA Astrophysics Data System (ADS)
Chau, Ling-Lie
2015-12-01
On the auspicious occasion of celebrating the 60th anniversary of the Yang-Mills theory, and Professor Yang’s many other important contributions to physics and mathematics, I will highlight the impressive milestones and landmarks that have been established in the last 60 years, as well as some interesting questions that still lie before us. The paper is written (without equations) for the interest of non-scientists as well as of scientists.
On the stability of dyons and dyonic black holes in Einstein-Yang-Mills theory
NASA Astrophysics Data System (ADS)
Nolan, Brien C.; Winstanley, Elizabeth
2016-02-01
We investigate the stability of four-dimensional dyonic soliton and black hole solutions of {su}(2) Einstein-Yang-Mills theory in anti-de Sitter space. We prove that, in a neighbourhood of the embedded trivial (Schwarzschild-)anti-de Sitter solution, there exist non-trivial dyonic soliton and black hole solutions of the field equations which are stable under linear, spherically symmetric, perturbations of the metric and non-Abelian gauge field.
Asymptotically flat, stable black hole solutions in Einstein-Yang-Mills-Chern-Simons theory.
Brihaye, Yves; Radu, Eugen; Tchrakian, D H
2011-02-18
We construct finite mass, asymptotically flat black hole solutions in d=5 Einstein-Yang-Mills-Chern-Simons theory. Our results indicate the existence of a second order phase transition between Reissner-Nordström solutions and the non-Abelian black holes which generically are thermodynamically preferred. Some of the non-Abelian configurations are also stable under linear, spherically symmetric perturbations. PMID:21405506
Exact Spectrum of Planar N=4 Supersymmetric Yang-Mills Theory: Konishi Dimension at Any Coupling
Gromov, Nikolay; Kazakov, Vladimir; Vieira, Pedro
2010-05-28
We compute the full dimension of the Konishi operator in planar N=4 super Yang-Mills theory for a wide range of couplings, from weak to strong coupling regime, and predict the subleading terms in its strong coupling asymptotics. For this purpose we solve numerically the integral form of the AdS/CFT Y-system equations for the exact energies of excited states proposed by us and A. Kozak.
Solving the ghost-gluon system of Yang-Mills theory on GPUs
NASA Astrophysics Data System (ADS)
Hopfer, Markus; Alkofer, Reinhard; Haase, Gundolf
2013-04-01
We solve the ghost-gluon system of Yang-Mills theory using graphics processing units (GPUs). Working in the Landau gauge, we use the Dyson-Schwinger formalism for the mathematical description, as this approach is well suited to directly benefit from the computing power of the GPUs. With the help of a Chebyshev expansion for the dressing functions and a subsequent appliance of a Newton-Raphson method, the non-linear system of coupled integral equations is linearized. The resulting Newton matrix is generated in parallel using OpenMPI and CUDA™. Our results show that it is possible to cut down the run time by two orders of magnitude as compared to a sequential version of the code. This makes the proposed techniques well suited for Dyson-Schwinger calculations on more complicated systems where the Yang-Mills sector of QCD serves as a starting point. In addition, the computation of Schwinger functions using GPU devices is studied.
N=4 supersymmetric Yang-Mills theory in soft-collinear effective theory
Chay, Junegone; Lee, Jae Yong
2011-01-01
We formulate N=4 supersymmetric Yang-Mills theory in terms of soft-collinear effective theory. The effective Lagrangian in soft-collinear effective theory is developed according to the power counting by a small parameter {eta}{approx}p{sub perpendicular}/Q. All the particles in this theory are in the adjoint representation of the SU(N) gauge group, and we derive the collinear gauge-invariant Lagrangian in the adjoint and fundamental representations, respectively. We consider collinear and ultrasoft Wilson lines in this theory, and show the ultrasoft factorization of the collinear Lagrangian by redefining the collinear fields with the use of the ultrasoft Wilson lines. The vertex correction for a vector fermion current at one loop is explicitly presented as an example to illustrate how the computation is performed in the effective theory.
Gauss' law and nonlinear plane waves for Yang-Mills theory
NASA Astrophysics Data System (ADS)
Tsapalis, A.; Politis, E. P.; Maintas, X. N.; Diakonos, F. K.
2016-04-01
We investigate nonlinear plane-wave solutions of the classical Minkowskian Yang-Mills (YM) equations of motion. By imposing a suitable ansatz which solves Gauss' law for the SU(3) theory, we derive solutions which consist of Jacobi elliptic functions depending on an enumerable set of elliptic modulus values. The solutions represent periodic anharmonic plane waves which possess arbitrary nonzero mass and are exact extrema of the nonlinear YM action. Among them, a unique harmonic plane wave with a nontrivial pattern in phase, spin, and color is identified. Similar solutions are present in the SU(4) case, while they are absent from the SU(2) theory.
The Hamiltonian analysis for Yang-Mills theory on R×S
NASA Astrophysics Data System (ADS)
Agarwal, Abhishek; Nair, V. P.
2009-07-01
Pure Yang-Mills theory on R×S is analyzed in a gauge-invariant Hamiltonian formalism. Using a suitable coordinatization for the sphere and a gauge-invariant matrix parametrization for the gauge potentials, we develop the Hamiltonian formalism in a manner that closely parallels previous analysis on R. The volume measure on the physical configuration space of the gauge theory, the nonperturbative mass-gap and the leading term of the vacuum wave functional are discussed using a point-splitting regularization. All the results carry over smoothly to known results on R in the limit in which the sphere is de-compactified to a plane.
Cold-atom quantum simulator for SU(2) Yang-Mills lattice gauge theory.
Zohar, Erez; Cirac, J Ignacio; Reznik, Benni
2013-03-22
Non-Abelian gauge theories play an important role in the standard model of particle physics, and unfold a partially unexplored world of exciting physical phenomena. In this Letter, we suggest a realization of a non-Abelian lattice gauge theory-SU(2) Yang-Mills in (1 + 1) dimensions, using ultracold atoms. Remarkably, and in contrast to previous proposals, in our model gauge invariance is a direct consequence of angular momentum conservation and thus is fundamental and robust. Our proposal may serve as well as a starting point for higher-dimensional realizations. PMID:25166817
Five-Loop Four-Point Amplitude of N=4 Super-Yang-Mills Theory
NASA Astrophysics Data System (ADS)
Bern, Z.; Carrasco, J. J. M.; Johansson, H.; Roiban, R.
2012-12-01
Using the method of maximal cuts, we construct the complete D-dimensional integrand of the five-loop four-point amplitude of N=4 super-Yang-Mills theory, including nonplanar contributions. In the critical dimension where this amplitude becomes ultraviolet divergent, we present a compact explicit expression for the nonvanishing ultraviolet divergence in terms of three vacuum integrals. This construction provides a crucial step towards obtaining the corresponding amplitude of N=8 supergravity required to resolve the general ultraviolet behavior of supergravity theories.
On the deconfining limit in (2+1)-dimensional Yang-Mills theory
NASA Astrophysics Data System (ADS)
Abe, Yasuhiro
2010-03-01
We consider (2+1)-dimensional Yang-Mills theory on S×S×R in the framework of a Hamiltonian approach developed by Karabali, Kim and Nair. The deconfining limit in the theory can be discussed in terms of one of the S radii of the torus ( S×S), while the other radius goes to infinity. We find that the limit agrees with the previously known result for a dynamical propagator mass of a gluon. We also make comparisons with numerical data.
Gravity and Yang-Mills Amplitude Relations in Field Theory
NASA Astrophysics Data System (ADS)
Søndergaard, Thomas
2011-07-01
We review some recent work in the famous Kawai-Lewellen-Tye (KLT) relations. Especially we present a compact way of writing down the general n-point relation. We also look at an extra feature of these relations which were only very recently realized, and leads to new relations among gauge-theory amplitudes.
Amplitudes in N = 4 Super-Yang-Mills Theory
NASA Astrophysics Data System (ADS)
Spradlin, Marcus
These lecture notes provide a lightning introduction to some aspects of scattering amplitudes in maximally supersymmetric theory, aimed at the audience of students attending the 2014 TASI summer school "Journeys Through the Precision Frontier: Amplitudes for Colliders". Emphasis is placed on explaining modern terminology so that students needing to delve further may more easily access the available literature.
Lower Dimension Vacuum Defects in Lattice Yang-Mills Theory
Zakharov, V.I.
2005-04-01
We overview lattice data on d = 0, 1, 2, 3 dimensional vacuum defects in lattice four-dimensional SU(2) (SU(3)) gluodynamics. In all the cases, defects have a total volume which scales in physical units (with zero fractal dimension). In the case of d = 1, 2, the defects are distinguished by ultraviolet divergent non-Abelian action as well. This sensitivity to the ultraviolet scale allows us to derive strong constraints from the continuum theory on the properties of the defects, which turn out to be satisfied by the lattice data. We discuss a classification scheme of the defects which allows us to (at least) visualize the defect properties in a simple and unified way. A not-yet-checked relation of the defects to the spontaneous chiral symmetry breaking is suggested by the scheme. Finally, we present some arguments that the defects considered could become fundamental variables of a dual formulation of the theory.
Reformulations of the Yang-Mills theory toward quark confinement and mass gap
NASA Astrophysics Data System (ADS)
Kondo, Kei-Ichi; Kato, Seikou; Shibata, Akihiro; Shinohara, Toru
2016-01-01
We propose the reformulations of the SU (N) Yang-Mills theory toward quark confinement and mass gap. In fact, we have given a new framework for reformulating the SU (N) Yang-Mills theory using new field variables. This includes the preceding works given by Cho, Faddeev and Niemi, as a special case called the maximal option in our reformulations. The advantage of our reformulations is that the original non-Abelian gauge field variables can be changed into the new field variables such that one of them called the restricted field gives the dominant contribution to quark confinement in the gauge-independent way. Our reformulations can be combined with the SU (N) extension of the Diakonov-Petrov version of the non-Abelian Stokes theorem for the Wilson loop operator to give a gauge-invariant definition for the magnetic monopole in the SU (N) Yang-Mills theory without the scalar field. In the so-called minimal option, especially, the restricted field is non-Abelian and involves the non-Abelian magnetic monopole with the stability group U (N- 1). This suggests the non-Abelian dual superconductivity picture for quark confinement. This should be compared with the maximal option: the restricted field is Abelian and involves only the Abelian magnetic monopoles with the stability group U(1)N-1, just like the Abelian projection. We give some applications of this reformulation, e.g., the stability for the homogeneous chromomagnetic condensation of the Savvidy type, the large N treatment for deriving the dimensional transmutation and understanding the mass gap, and also the numerical simulations on a lattice which are given by Dr. Shibata in a subsequent talk.
Gluon scattering in N=4 super-Yang-Mills theory fromweak to strong coupling
Dixon, Lance J.; /SLAC
2008-03-25
I describe some recent developments in the understanding of gluon scattering amplitudes in N = 4 super-Yang-Mills theory in the large-N{sub c} limit. These amplitudes can be computed to high orders in the weak coupling expansion, and also now at strong coupling using the AdS/CFT correspondence. They hold the promise of being solvable to all orders in the gauge coupling, with the help of techniques based on integrability. They are intimately related to expectation values for polygonal Wilson loops composed of light-like segments.
Nonperturbative gluon and ghost propagators for d=3 Yang-Mills theory
Aguilar, A. C.; Binosi, D.; Papavassiliou, J.
2010-06-15
We study a manifestly gauge-invariant set of Schwinger-Dyson equations to determine the nonperturbative dynamics of the gluon and ghost propagators in d=3 Yang-Mills theory. The use of the well-known Schwinger mechanism, in the Landau gauge leads to the dynamical generation of a mass for the gauge boson (gluon in d=3), which, in turn, gives rise to an infrared finite gluon propagator and ghost dressing function. The propagators obtained from the numerical solution of these nonperturbative equations are in very good agreement with the results of SU(2) lattice simulations.
Z{sub 2} monopoles in SU(n) Yang-Mills-Higgs theories
Kneipp, Marco A. C.; Liebgott, Paulo J.
2010-02-15
Z{sub n} monopoles are important for the understanding of the Goddard-Nuyts-Olive duality when the scalar field is not in the adjoint representation. We analyze the Z{sub 2} monopole solutions in SU(n) Yang-Mills-Higgs theories spontaneously broken to Spin(n)/Z{sub 2} by a scalar in the nxn representation. We construct explicitly Z{sub 2} monopole asymptotic fields solutions for each of the weights of the defining representation of the dual algebra so(n){sup or.}
From decay to complete breaking: pulling the strings in SU(2) Yang-Mills theory.
Pepe, M; Wiese, U-J
2009-05-15
We study {2Q+1} strings connecting two static charges Q in (2+1)D SU(2) Yang-Mills theory. While the fundamental {2} string between two charges Q=1/2 is unbreakable, the adjoint {3} string connecting two charges Q=1 can break. When a {4} string is stretched beyond a critical length, it decays into a {2} string by gluon pair creation. When a {5} string is stretched, it first decays into a {3} string, which eventually breaks completely. The energy of the screened charges at the ends of a string is well described by a phenomenological constituent gluon model. PMID:19518940
Vacuum energy of two-dimensional N=(2,2) super Yang-Mills theory
Kanamori, Issaku
2009-06-01
We measure the vacuum energy of two-dimensional N=(2,2) super Yang-Mills theory using lattice simulation. The obtained vacuum energy density is E{sub 0}=0.09(9)((+10/-8))g{sup 2}, where the first error is the systematic and the second is the statistical one, measured in the dimensionful gauge coupling g which governs the scale of the system. The result is consistent with unbroken supersymmetry, although we cannot exclude a possible very small nonzero vacuum energy.
Supersymmetric Yang-Mills theory on conformal supergravity backgrounds in ten dimensions
NASA Astrophysics Data System (ADS)
de Medeiros, Paul; Figueroa-O'Farrill, José
2016-03-01
We consider bosonic supersymmetric backgrounds of ten-dimensional conformal supergravity. Up to local conformal isometry, we classify the maximally supersymmetric backgrounds, determine their conformal symmetry superalgebras and show how they arise as near-horizon geometries of certain half-BPS backgrounds or as a plane-wave limit thereof. We then show how to define Yang-Mills theory with rigid supersymmetry on any supersymmetric conformal supergravity background and, in particular, on the maximally supersymmetric backgrounds. We conclude by commenting on a striking resemblance between the supersymmetric backgrounds of ten-dimensional conformal supergravity and those of eleven-dimensional Poincaré supergravity.
Composite Operators in the Twistor Formulation of N =4 Supersymmetric Yang-Mills Theory
NASA Astrophysics Data System (ADS)
Koster, Laura; Mitev, Vladimir; Staudacher, Matthias; Wilhelm, Matthias
2016-07-01
We incorporate gauge-invariant local composite operators into the twistor-space formulation of N =4 super Yang-Mills theory. In this formulation, the interactions of the elementary fields are reorganized into infinitely many interaction vertices and we argue that the same applies to composite operators. To test our definition of the local composite operators in twistor space, we compute several corresponding form factors, thereby also initiating the study of form factors using the position twistor-space framework. Throughout this Letter, we use the composite operator built from two identical complex scalars as a pedagogical example; we treat the general case in a follow-up paper.
Composite Operators in the Twistor Formulation of N=4 Supersymmetric Yang-Mills Theory.
Koster, Laura; Mitev, Vladimir; Staudacher, Matthias; Wilhelm, Matthias
2016-07-01
We incorporate gauge-invariant local composite operators into the twistor-space formulation of N=4 super Yang-Mills theory. In this formulation, the interactions of the elementary fields are reorganized into infinitely many interaction vertices and we argue that the same applies to composite operators. To test our definition of the local composite operators in twistor space, we compute several corresponding form factors, thereby also initiating the study of form factors using the position twistor-space framework. Throughout this Letter, we use the composite operator built from two identical complex scalars as a pedagogical example; we treat the general case in a follow-up paper. PMID:27419558
A complete two-loop, five-gluon helicity amplitude in Yang-Mills theory
NASA Astrophysics Data System (ADS)
Badger, Simon; Mogull, Gustav; Ochirov, Alexander; O'Connell, Donal
2015-10-01
We compute the integrand of the full-colour, two-loop, five-gluon scattering amplitude in pure Yang-Mills theory with all helicities positive, using generalized unitarity cuts. Tree-level BCJ relations, satisfied by amplitudes appearing in the cuts, allow us to deduce all the necessary non-planar information for the full-colour amplitude from known planar data. We present our result in terms of irreducible numerators, with colour factors derived from the multi-peripheral colour decomposition. Finally, the leading soft divergences are checked to reproduce the expected infrared behaviour.
Towards a consistent noncommutative supersymmetric Yang-Mills theory: Superfield covariant analysis
Ferrari, A.F.; Girotti, H.O.; Ribeiro, A.A.; Gomes, M.; Rivelles, V.O.; Silva, A.J. da; Petrov, A.Yu.
2004-10-15
Commutative four dimensional supersymmetric Yang-Mills (SYM) theory is known to be renormalizable for N=1,2, and finite for N=4. However, in the noncommutative version of the model the UV/IR mechanism gives rise to infrared divergences which may spoil the perturbative expansion. In this work we pursue the study of the consistency of the N=1,2,4 noncommutative supersymmetric Yang-Mills theory with gauge group U(N) (NCSYM). We employ the covariant superfield framework to compute the one-loop corrections to the two- and three-point functions of the gauge superfield V. It is found that the cancellation of the harmful UV/IR infrared divergences only takes place in the fundamental representation of the gauge group. We argue that this is in agreement with the low energy limit of the open superstring in the presence of an external magnetic field. As expected, the planar sector of the two-point function of the V superfield exhibits UV divergences. They are found to cancel, in the Feynman gauge, for the maximally extended N=4 supersymmetric theory. This gives support to the belief that the N=4 NCSYM theory is UV finite.
More on Gribov copies and propagators in Landau-gauge Yang-Mills theory
Maas, Axel
2009-01-01
Fixing a gauge in the nonperturbative domain of Yang-Mills theory is a nontrivial problem due to the presence of Gribov copies. In particular, there are different gauges in the nonperturbative regime which all correspond to the same definition of a gauge in the perturbative domain. Gauge-dependent correlation functions may differ in these gauges. Two such gauges are the minimal Landau gauge and the absolute Landau gauge, both corresponding to the perturbative Landau gauge. These, and their numerical implementation, are described and presented in detail. Other choices will also be discussed. This investigation is performed, using numerical lattice gauge theory calculations, by comparing the propagators of gluons and ghosts for the minimal Landau gauge and the absolute Landau gauge in SU(2) Yang-Mills theory. It is found that the propagators are different in the far infrared and even at energy scales of the order of half a GeV. In particular, the finite-volume effects are also modified. This is observed in two and three dimensions. Some remarks on the four-dimensional case are provided as well.
Brandhuber, Andreas; Heslop, Paul; Travaglini, Gabriele; Young, Donovan
2015-10-01
It is known that the Yangian of PSU(2,2|4) is a symmetry of the tree-level S matrix of N=4 super Yang-Mills theory. On the other hand, the complete one-loop dilatation operator in the same theory commutes with the level-one Yangian generators only up to certain boundary terms found by Dolan, Nappi, and Witten. Using a result by Zwiebel, we show how the Yangian symmetry of the tree-level S matrix of N=4 super Yang-Mills theory implies precisely the Yangian invariance, up to boundary terms, of the one-loop dilatation operator. PMID:26551805
Deconfinement phase transition in the Hamiltonian approach to Yang-Mills theory in Coulomb gauge
NASA Astrophysics Data System (ADS)
Reinhardt, H.; Campagnari, D.; Heffner, J.
2014-04-01
Recent results obtained for the deconfinement phase transition within the Hamiltonian approach to Yang-Mills theory are reviewed. Assuming a quasiparticle picture for the grand canonical gluon ensemble the thermal equilibrium state is found by minimizing the free energy with respect to the quasi-gluon energy. The deconfinement phase transition is accompanied by a drastic change of the infrared exponents of the ghost and gluon propagators. Above the phase transition the ghost form factor remains infrared divergent but its infrared exponent is approximately halved. The gluon energy being infrared divergent in the confined phase becomes infrared finite in the deconfined phase. Furthermore, the effective potential of the order parameter for confinement is calculated for SU(N) Yang-Mills theory in the Hamiltonian approach by compactifying one spatial dimension and using a background gauge fixing. In the simplest truncation, neglecting the ghost and using the ultraviolet form of the gluon energy, we recover the Weiss potential. From the full non-perturbative potential (with the ghost included) we extract a critical temperature of the deconfinement phase transition of 269 MeV for the gauge group SU(2) and 283 MeV for SU(3).
Yangian symmetry of scattering amplitudes in Script N = 4 super Yang-Mills theory
NASA Astrophysics Data System (ADS)
Drummond, James; Henn, Johannes; Plefka, Jan
2009-05-01
Tree-level scattering amplitudes in Script N = 4 super Yang-Mills theory have recently been shown to transform covariantly with respect to a `dual' superconformal symmetry algebra, thus extending the conventional superconformal symmetry algebra psu(2,2|4) of the theory. In this paper we derive the action of the dual superconformal generators in on-shell superspace and extend the dual generators suitably to leave scattering amplitudes invariant. We then study the algebra of standard and dual symmetry generators and show that the inclusion of the dual superconformal generators lifts the psu(2,2|4) symmetry algebra to a Yangian. The non-local Yangian generators acting on amplitudes turn out to be cyclically invariant due to special properties of psu(2,2|4). The representation of the Yangian generators takes the same form as in the case of local operators, suggesting that the Yangian symmetry is an intrinsic property of planar Script N = 4 super Yang-Mills, at least at tree level.
Non-Gaussianities in the topological charge distribution of the SU(3) Yang-Mills theory
NASA Astrophysics Data System (ADS)
Cè, Marco; Consonni, Cristian; Engel, Georg P.; Giusti, Leonardo
2015-10-01
We study the topological charge distribution of the SU(3) Yang-Mills theory with high precision in order to be able to detect deviations from Gaussianity. The computation is carried out on the lattice with high statistics Monte Carlo simulations by implementing a naive discretization of the topological charge evolved with the Yang-Mills gradient flow. This definition is far less demanding than the one suggested from Neuberger's fermions and, as shown in this paper, in the continuum limit its cumulants coincide with those of the universal definition appearing in the chiral Ward identities. Thanks to the range of lattice volumes and spacings considered, we can extrapolate the results for the second and fourth cumulant of the topological charge distribution to the continuum limit with confidence by keeping finite volume effects negligible with respect to the statistical errors. Our best results for the topological susceptibility is t02χ =6.67 (7 )×1 0-4 , where t0 is a standard reference scale, while for the ratio of the fourth cumulant over the second, we obtain R =0.233 (45 ). The latter is compatible with the expectations from the large Nc expansion, while it rules out the θ behavior of the vacuum energy predicted by the dilute instanton model. Its large distance from 1 implies that, in the ensemble of gauge configurations that dominate the path integral, the fluctuations of the topological charge are of quantum nonperturbative nature.
Perturbative quantization of Yang-Mills theory with classical double as gauge algebra
NASA Astrophysics Data System (ADS)
Ruiz Ruiz, F.
2016-02-01
Perturbative quantization of Yang-Mills theory with a gauge algebra given by the classical double of a semisimple Lie algebra is considered. The classical double of a real Lie algebra is a nonsemisimple real Lie algebra that admits a nonpositive definite invariant metric, the indefiniteness of the metric suggesting an apparent lack of unitarity. It is shown that the theory is UV divergent at one loop and that there are no radiative corrections at higher loops. One-loop UV divergences are removed through renormalization of the coupling constant, thus introducing a renormalization scale. The terms in the classical action that would spoil unitarity are proved to be cohomologically trivial with respect to the Slavnov-Taylor operator that controls gauge invariance for the quantum theory. Hence they do not contribute gauge invariant radiative corrections to the quantum effective action and the theory is unitary.
Complex time solutions with nontrivial topology and multiparticle scattering in Yang-Mills theory
NASA Astrophysics Data System (ADS)
Gould, Thomas M.; R. Poppitz, Erich
1993-08-01
A classical solution in Yang-Mills thoery is given a new semiclassical interpretation in terms of particle scattering. It solves the complex time boundary value problem which arises in the semiclassical approximation to a multiparticle transition probability in the one-instanton sector at fixed energy. The imaginary part of the action of the solution on the complex time contour and its topological charge obey the same relation as the self-dual Euclidean configurations. Hence the solution is relevant for the problem of tunneling with fermion number violation in the electroweak theory. It describes transitions from an initial state with a smaller number of particles to a final state with a larger umber of particles. The implications of these results for multiparticle production in the electroweak theory are also discussed.
Exact spectrum of anomalous dimensions of planar N = 4 supersymmetric Yang-Mills theory.
Gromov, Nikolay; Kazakov, Vladimir; Vieira, Pedro
2009-09-25
We present a set of functional equations defining the anomalous dimensions of arbitrary local single trace operators in planar N = 4 supersymmetric Yang-Mills theory. It takes the form of a Y system based on the integrability of the dual superstring sigma model on the five-dimensional anti-de Sitter space (AdS_{5} x S;{5}) background. This Y system passes some very important tests: it incorporates the full asymptotic Bethe ansatz at large length of operator L, including the dressing factor, and it confirms all recently found wrapping corrections. The recently proposed AdS_{4}/three-dimensional conformal field theory duality is also treated in a similar fashion. PMID:19905502
Exact Spectrum of Anomalous Dimensions of Planar N=4 Supersymmetric Yang-Mills Theory
Gromov, Nikolay; Kazakov, Vladimir; Vieira, Pedro
2009-09-25
We present a set of functional equations defining the anomalous dimensions of arbitrary local single trace operators in planar N=4 supersymmetric Yang-Mills theory. It takes the form of a Y system based on the integrability of the dual superstring sigma model on the five-dimensional anti-de Sitter space (AdS{sub 5}xS{sup 5}) background. This Y system passes some very important tests: it incorporates the full asymptotic Bethe ansatz at large length of operator L, including the dressing factor, and it confirms all recently found wrapping corrections. The recently proposed AdS{sub 4}/three-dimensional conformal field theory duality is also treated in a similar fashion.
Correlation functions of three-dimensional Yang-Mills theory from Dyson-Schwinger equations
NASA Astrophysics Data System (ADS)
Huber, Markus Q.
2016-04-01
The two- and three-point functions and the four-gluon vertex of three-dimensional Yang-Mills theory are calculated from their Dyson-Schwinger equations and the three-particle irreducible effective action. Within a self-contained truncation, various effects of truncating Dyson-Schwinger equations are studied. Estimates for the errors induced by truncations are derived from comparisons between results from different equations, comparisons with lattice results, and varying higher Green functions. The results indicate that the two-loop diagrams are important in the gluon propagator, where they are explicitly calculated, but not for the vertices. Furthermore, the influence of the four-gluon vertex on lower Green functions is found to be small.
Thermal monopole condensation and confinement in finite temperature Yang-Mills theories
D'Alessandro, Alessio; D'Elia, Massimo; Shuryak, Edward V.
2010-05-01
We investigate the connection between color confinement and thermal Abelian monopoles populating the deconfined phase of SU(2) Yang-Mills theory, by studying how the statistical properties of the monopole ensemble change as the confinement/deconfinement temperature is approached from above. In particular, we study the distribution of monopole currents with multiple wrappings in the Euclidean time direction, corresponding to two or more particle permutations, and show that multiple wrappings increase as the deconfinement temperature is approached from above, in a way compatible with a condensation of such objects happening right at the deconfining transition. We also address the question of the thermal monopole mass, showing that different definitions give consistent results only around the transition, where the monopole mass goes down and becomes of the order of the critical temperature itself.
Spatial volume dependence for 2+1 dimensional SU(N) Yang-Mills theory
NASA Astrophysics Data System (ADS)
Pérez, Margarita García; González-Arroyo, Antonio; Okawa, Masanori
2013-09-01
We study the 2+1 dimensional SU(N) Yang-Mills theory on a finite two-torus with twisted boundary conditions. Our goal is to study the interplay between the rank of the group N , the length of the torus L and the Z N magnetic flux. After presenting the classical and quantum formalism, we analyze the spectrum of the theory using perturbation theory to one-loop and using Monte Carlo techniques on the lattice. In perturbation theory, results to all orders depend on the combination x = λ N L and an angle defined in terms of the magnetic flux (λ is `t Hooft coupling). Thus, fixing the angle, the system exhibits a form of volume independence ( N L dependence). The numerical results interpolate between our perturbative calculations and the confinement regime. They are consistent with x-scaling and provide interesting information about the k-string spectrum and effective string theories. The occurrence of tachyonic instabilities is also analysed. They seem to be avoidable in the large N limit with a suitable scaling of the magnetic flux.
The Analytic Structure of Scattering Amplitudes in N = 4 Super-Yang-Mills Theory
NASA Astrophysics Data System (ADS)
Litsey, Sean Christopher
We begin the dissertation in Chapter 1 with a discussion of tree-level amplitudes in Yang-. Mills theories. The DDM and BCJ decompositions of the amplitudes are described and. related to one another by the introduction of a transformation matrix. This is related to the. Kleiss-Kuijf and BCJ amplitude identities, and we conjecture a connection to the existence. of a BCJ representation via a condition on the generalized inverse of that matrix. Under. two widely-believed assumptions, this relationship is proved. Switching gears somewhat, we introduce the RSVW formulation of the amplitude, and the extension of BCJ-like features to residues of the RSVW integrand is proposed. Using the previously proven connection of BCJ representations to the generalized inverse condition, this extension is validated, including a version of gravitational double copy. The remainder of the dissertation involves an analysis of the analytic properties of loop. amplitudes in N = 4 super-Yang-Mills theory. Chapter 2 contains a review of the planar case, including an exposition of dual variables and momentum twistors, dual conformal symmetry, and their implications for the amplitude. After defining the integrand and on-shell diagrams, we explain the crucial properties that the amplitude has no poles at infinite momentum and that its leading singularities are dual-conformally-invariant cross ratios, and can therefore be normalized to unity. We define the concept of a dlog form, and show that it is a feature of the planar integrand as well. This leads to the definition of a pure integrand basis. The proceeding setup is connected to the amplituhedron formulation, and we put forward the hypothesis that the amplitude is determined by zero conditions. Chapter 3 contains the primary computations of the dissertation. This chapter treats. amplitudes in fully nonplanar N = 4 super-Yang-Mills, analyzing the conjecture that they. follow the pattern of having no poles at infinity, can be written in dlog
Constraints on the infrared behavior of the ghost propagator in Yang-Mills theories
Cucchieri, A.; Mendes, T.
2008-11-01
We present rigorous upper and lower bounds for the momentum-space ghost propagator G(p) of Yang-Mills theories in terms of the smallest nonzero eigenvalue (and of the corresponding eigenvector) of the Faddeev-Popov matrix. We apply our analysis to data from simulations of SU(2) lattice gauge theory in Landau gauge, using the largest lattice sizes to date. Our results suggest that, in three and in four space-time dimensions, the Landau gauge ghost propagator is not enhanced as compared to its tree-level behavior. This is also seen in plots and fits of the ghost dressing function. In the two-dimensional case, on the other hand, we find that G(p) diverges as p{sup -2-2{kappa}} with {kappa}{approx_equal}0.15, in agreement with A. Maas, Phys. Rev. D 75, 116004 (2007). We note that our discussion is general, although we make an application only to pure gauge theory in Landau gauge. Our simulations have been performed on the IBM supercomputer at the University of Sao Paulo.
Analytical study of Yang-Mills theory in the infrared from first principles
NASA Astrophysics Data System (ADS)
Siringo, Fabio
2016-06-01
Pure Yang-Mills SU(N) theory is studied in the Landau gauge and four dimensional space. While leaving the original Lagrangian unmodified, a double perturbative expansion is devised, based on a massive free-particle propagator. In dimensional regularization, all diverging mass terms cancel exactly in the double expansion, without the need to include mass counterterms that would spoil the symmetry of the Lagrangian. No free parameters are included that were not in the original theory, yielding a fully analytical approach from first principles. The expansion is safe in the infrared and is equivalent to the standard perturbation theory in the UV. At one-loop, explicit analytical expressions are given for the propagators and the running coupling and are found in excellent agreement with the data of lattice simulations. A universal scaling property is predicted for the inverse propagators and shown to be satisfied by the lattice data. Higher loops are found to be negligible in the infrared below 300 MeV where the coupling becomes small and the one-loop approximation is under full control.
Plane-wave matrix theory from N=4 super-Yang-Mills on R×S 3
NASA Astrophysics Data System (ADS)
Kim, Nakwoo; Klose, Thomas; Plefka, Jan
2003-11-01
Recently a mass deformation of the maximally supersymmetric Yang-Mills quantum mechanics has been constructed from the supermembrane action in eleven-dimensional plane-wave backgrounds. However, the origin of this plane-wave matrix theory in terms of a compactification of a higher-dimensional super-Yang-Mills model has remained obscure. In this paper we study the Kaluza-Klein reduction of D=4, N=4 super-Yang-Mills theory on a round three-sphere, and demonstrate that the plane-wave matrix theory arises through a consistent truncation to the lowest lying modes. We further explore the relation between the dilatation operator of the conformal field theory and the Hamiltonian of the quantum mechanics through perturbative calculations up to two-loop order. In particular, we find that the one-loop anomalous dimensions of pure scalar operators are completely captured by the plane-wave matrix theory. At two-loop level this property ceases to exist.
NASA Astrophysics Data System (ADS)
Bergner, G.; Langelage, J.; Philipsen, O.
2015-11-01
We consider a three-dimensional effective theory of Polyakov lines derived previously from lattice Yang-Mills theory and QCD by means of a resummed strong coupling expansion. The effective theory is useful for investigations of the phase structure, with a sign problem mild enough to allow simulations also at finite density. In this work we present a numerical method to determine improved values for the effective couplings directly from correlators of 4d Yang-Mills theory. For values of the gauge coupling up to the vicinity of the phase transition, the dominant short range effective coupling are well described by their corresponding strong coupling series. We provide numerical results also for the longer range interactions, Polyakov lines in higher representations as well as four-point interactions, and discuss the growing significance of non-local contributions as the lattice gets finer. Within this approach the critical Yang-Mills coupling β c is reproduced to better than one percent from a one-coupling effective theory on N τ = 4 lattices while up to five couplings are needed on N τ = 8 for the same accuracy.
Massive Yang-Mills theory based on the nonlinearly realized gauge group
Bettinelli, D.; Ferrari, R.; Quadri, A.
2008-02-15
We propose a subtraction scheme for a massive Yang-Mills theory realized via a nonlinear representation of the gauge group [here SU(2)]. It is based on the subtraction of the poles in D-4 of the amplitudes, in dimensional regularization, after a suitable normalization has been performed. Perturbation theory is in the number of loops, and the procedure is stable under iterative subtraction of the poles. The unphysical Goldstone bosons, the Faddeev-Popov ghosts, and the unphysical mode of the gauge field are expected to cancel out in the unitarity equation. The spontaneous symmetry breaking parameter is not a physical variable. We use the tools already tested in the nonlinear sigma model: hierarchy in the number of Goldstone boson legs and weak-power-counting property (finite number of independent divergent amplitudes at each order). It is intriguing that the model is naturally based on the symmetry SU(2){sub L} local x SU(2){sub R} global. By construction the physical amplitudes depend on the mass and on the self-coupling constant of the gauge particle and moreover on the scale parameter of the radiative corrections. The Feynman rules are in the Landau gauge.
S-duality in SU(3) Yang-Mills theory with non-abelian unbroken gauge group
NASA Astrophysics Data System (ADS)
Schroers, B. J.; Bais, F. A.
1998-12-01
It is observed that the magnetic charges of classical monopole solutions in Yang-Mills-Higgs theory with non-abelian unbroken gauge group H are in one-to-one correspondence with coherent states of a dual or magnetic group H˜. In the spirit of the Goddard-Nuyts-Olive conjecture this observation is interpreted as evidence for a hidden magnetic symmetry of Yang-Mills theory. SU(3) Yang-Mills-Higgs theory with unbroken gauge group U(2) is studied in detail. The action of the magnetic group on semi-classical states is given explicitly. Investigations of dyonic excitations show that electric and magnetic symmetry are never manifest at the same time: Non-abelian magnetic charge obstructs the realisation of electric symmetry and vice-versa. On the basis of this fact the charge sectors in the theory are classified and their fusion rules are discussed. Non-abelian electric-magnetic duality is formulated as a map between charge sectors. Coherent states obey particularly simple fusion rules, and in the set of coherent states S-duality can be formulated as an SL(2, Z) mapping between sectors which leaves the fusion rules invariant.
Yang-Mills field theory in an axial field-strength gauge
NASA Astrophysics Data System (ADS)
Tyburski, Lawrence
1984-02-01
We introduce what we call an axial field-strength gauge as an alternative to the conventional Coulomb gauge in the Yang-Mills field theory. This new gauge does not share the pathologies that were shown to exist in the Coulomb gauge by Gribov and Mandelstam. We apply this new gauge to the calculation, in two special cases, of the energy possessed by sources J1,20 interacting in the presence of a background field produced by a source J30, which is assumed to be of order g-1, in the limit g goes to zero, where g is the coupling constant. In the case in which the charge density J30 consists of two infinite uniform parallel plates bearing charge densities equal in magnitude but opposite in sign, we find that the potential energy possessed by two point particles bearing charge densities J1,20 grows linearly in proportion to the distance between them at large distances when the two particles are separated along a line parallel to the background field. This is a confining potential.
Non-intersecting Brownian walkers and Yang-Mills theory on the sphere
NASA Astrophysics Data System (ADS)
Forrester, Peter J.; Majumdar, Satya N.; Schehr, Grégory
2011-03-01
We study a system of N non-intersecting Brownian motions on a line segment [0,L] with periodic, absorbing and reflecting boundary conditions. We show that the normalized reunion probabilities of these Brownian motions in the three models can be mapped to the partition function of two-dimensional continuum Yang-Mills theory on a sphere respectively with gauge groups U(N), Sp(2N) and SO(2N). Consequently, we show that in each of these Brownian motion models, as one varies the system size L, a third order phase transition occurs at a critical value L=L(N)˜√{N} in the large N limit. Close to the critical point, the reunion probability, properly centered and scaled, is identical to the Tracy-Widom distribution describing the probability distribution of the largest eigenvalue of a random matrix. For the periodic case we obtain the Tracy-Widom distribution corresponding to the GUE random matrices, while for the absorbing and reflecting cases we get the Tracy-Widom distribution corresponding to GOE random matrices. In the absorbing case, the reunion probability is also identified as the maximal height of N non-intersecting Brownian excursions ("watermelons" with a wall) whose distribution in the asymptotic scaling limit is then described by GOE Tracy-Widom law. In addition, large deviation formulas for the maximum height are also computed.
Embedded monopoles in quark eigenmodes in SU(2) Yang-Mills theory
Chernodub, M. N.; Morozov, S. M.
2006-09-01
We study the embedded QCD monopoles ('quark monopoles') using low-lying eigenmodes of the overlap Dirac operator in zero- and finite-temperature SU(2) Yang-Mills theory on the lattice. These monopoles correspond to the gauge-invariant hedgehogs in the quark-antiquark condensates. The monopoles were suggested to be agents of the chiral symmetry restoration since their cores should suppress the chiral condensate. We study numerically the scalar, axial, and chirally invariant definitions of the embedded monopoles and show that the monopole densities are in fact globally anticorrelated with the density of the Dirac eigenmodes. We observe that the embedded monopoles corresponding to low-lying Dirac eigenvalues are dense in the chirally invariant (high temperature) phase and dilute in the chirally broken (low-temperature) phase. We find that the scaling of the scalar and axial monopole densities towards the continuum limit is similar to the scaling of the stringlike objects while the chirally invariant monopoles scale as membranes. The excess of gluon energy at monopole positions reveals that the embedded QCD monopole possesses a gluonic core which is, however, empty at the very center of the monopole.
Embedded monopoles in quark eigenmodes in SU(2) Yang-Mills theory
NASA Astrophysics Data System (ADS)
Chernodub, M. N.; Morozov, S. M.
2006-09-01
We study the embedded QCD monopoles (“quark monopoles”) using low-lying eigenmodes of the overlap Dirac operator in zero- and finite-temperature SU(2) Yang-Mills theory on the lattice. These monopoles correspond to the gauge-invariant hedgehogs in the quark-antiquark condensates. The monopoles were suggested to be agents of the chiral symmetry restoration since their cores should suppress the chiral condensate. We study numerically the scalar, axial, and chirally invariant definitions of the embedded monopoles and show that the monopole densities are in fact globally anticorrelated with the density of the Dirac eigenmodes. We observe that the embedded monopoles corresponding to low-lying Dirac eigenvalues are dense in the chirally invariant (high temperature) phase and dilute in the chirally broken (low-temperature) phase. We find that the scaling of the scalar and axial monopole densities towards the continuum limit is similar to the scaling of the stringlike objects while the chirally invariant monopoles scale as membranes. The excess of gluon energy at monopole positions reveals that the embedded QCD monopole possesses a gluonic core which is, however, empty at the very center of the monopole.
The Two-Loop Six-Point MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
Bern, Z.; Dixon, L.J.; Kosower, D.A.; Roiban, R.; Spradlin, M.; Vergu, C.; Volovich, A.
2008-03-12
We give a representation of the parity-even part of the planar two-loop six-gluon MHV amplitude of N = 4 super-Yang-Mills theory, in terms of loop-momentum integrals with simple dual conformal properties. We evaluate the integrals numerically in order to test directly the ABDK/BDS all-loop ansatz for planar MHV amplitudes. We find that the ansatz requires an additive remainder function, in accord with previous indications from strong-coupling and Regge limits. The planar six-gluon amplitude can also be compared with the hexagonal Wilson loop computed by Drummond, Henn, Korchemsky and Sokatchev in arXiv:0803.1466 [hep-th]. After accounting for differing singularities and other constants independent of the kinematics, we find that the Wilson loop and MHV-amplitude remainders are identical, to within our numerical precision. This result provides non-trivial confirmation of a proposed n-point equivalence between Wilson loops and planar MHV amplitudes, and suggests that an additional mechanism besides dual conformal symmetry fixes their form at six points and beyond.
An object oriented code for simulating supersymmetric Yang-Mills theories
NASA Astrophysics Data System (ADS)
Catterall, Simon; Joseph, Anosh
2012-06-01
We present SUSY_LATTICE - a C++ program that can be used to simulate certain classes of supersymmetric Yang-Mills (SYM) theories, including the well known N=4 SYM in four dimensions, on a flat Euclidean space-time lattice. Discretization of SYM theories is an old problem in lattice field theory. It has resisted solution until recently when new ideas drawn from orbifold constructions and topological field theories have been brought to bear on the question. The result has been the creation of a new class of lattice gauge theories in which the lattice action is invariant under one or more supersymmetries. The resultant theories are local, free of doublers and also possess exact gauge-invariance. In principle they form the basis for a truly non-perturbative definition of the continuum SYM theories. In the continuum limit they reproduce versions of the SYM theories formulated in terms of twisted fields, which on a flat space-time is just a change of the field variables. In this paper, we briefly review these ideas and then go on to provide the details of the C++ code. We sketch the design of the code, with particular emphasis being placed on SYM theories with N=(2,2) in two dimensions and N=4 in three and four dimensions, making one-to-one comparisons between the essential components of the SYM theories and their corresponding counterparts appearing in the simulation code. The code may be used to compute several quantities associated with the SYM theories such as the Polyakov loop, mean energy, and the width of the scalar eigenvalue distributions. Program summaryProgram title: SUSY_LATTICE Catalogue identifier: AELS_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AELS_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 9315 No. of bytes in distributed program
Radiating black holes in Einstein-Yang-Mills theory and cosmic censorship
Ghosh, Sushant G.; Dadhich, Naresh
2010-08-15
Exact nonstatic spherically symmetric black-hole solutions of the higher dimensional Einstein-Yang-Mills equations for a null dust with Yang-Mills gauge charge are obtained by employing Wu-Yang ansatz, namely, HD-EYM Vaidya solution. It is interesting to note that gravitational contribution of Yang-Mills (YM) gauge charge for this ansatz is indeed opposite (attractive rather than repulsive) that of Maxwell charge. It turns out that the gravitational collapse of null dust with YM gauge charge admits strong curvature shell focusing naked singularities violating cosmic censorship. However, there is significant shrinkage of the initial data space for a naked singularity of the HD-Vaidya collapse due to presence of YM gauge charge. The effect of YM gauge charge on structure and location of the apparent and event horizons is also discussed.
Berube, D.; Kroeger, H.; Lafrance, R.; Marleau, L. )
1991-02-15
We discuss properties of a noncompact formulation of gauge theories with fermions on a momentum ({ital k}) lattice. (a) This formulation is suitable to build in Fourier acceleration in a direct way. (b) The numerical effort to compute the action (by fast Fourier transform) goes essentially like log{ital V} with the lattice volume {ital V}. (c) For the Yang-Mills theory we find that the action conserves gauge symmetry and chiral symmetry in a weak sense: On a finite lattice the action is invariant under infinitesimal transformations with compact support. Under finite transformations these symmetries are approximately conserved and they are restored on an infinite lattice and in the continuum limit. Moreover, these symmetries also hold on a finite lattice under finite transformations, if the classical fields, instead of being {ital c}-number valued, take values from a finite Galois field. (d) There is no fermion doubling. (e) For the {phi}{sup 4} model we investigate the transition towards the continuum limit in lattice perturbation theory up to second order. We compute the two- and four-point functions and find local and Lorentz-invariant results. (f) In QED we compute a one-loop vacuum polarization and find in the continuum limit the standard result. (g) As a numerical application, we compute the propagator {l angle}{phi}({ital k}){phi}({ital k}{prime}){r angle} in the {phi}{sup 4} model, investigate Euclidean invariance, and extract {ital m}{sub {ital R}} as well as {ital Z}{sub {ital R}}. Moreover we compute {l angle}{ital F}{sub {mu}{nu}}({ital k}){ital F}{sub {mu}{nu}}({ital k}{prime}){r angle} in the SU(2) model.
Bonus Yangian Symmetry for the Planar S Matrix of N=4 Supersymmetric Yang-Mills Theory
Beisert, Niklas; Schwab, Burkhard U. W.
2011-06-10
Recent developments in the determination of the planar S matrix of N=4 super Yang-Mills are closely related to its Yangian symmetry. Here we provide evidence for a yet unobserved additional symmetry: the Yangian level-one helicity operator.
Self-dual solutions of Yang-Mills theory on Euclidean AdS space
Sarioglu, Oezguer; Tekin, Bayram
2009-05-15
We find nontrivial, time-dependent solutions of the (anti) self-dual Yang-Mills equations in the four-dimensional Euclidean anti-de Sitter space. In contrast to the Euclidean flat space, the action depends on the moduli parameters and the charge can take any noninteger value.
Comparing the drag force on heavy quarks in N=4 super-Yang-Mills theory and QCD
Gubser, Steven S.
2007-12-15
Computations of the drag force on a heavy quark moving through a thermal state of strongly coupled N=4 super-Yang-Mills theory have appeared recently. I compare the strength of this effect between N=4 gauge theory and QCD, using the static force between external quarks to normalize the 't Hooft coupling. Comparing N=4 and QCD at fixed energy density then leads to a relaxation time of roughly 2 fm/c for charm quarks moving through a quark-gluon plasma at T=250 MeV. This estimate should be regarded as preliminary because of the difficulties of comparing two such different theories.
Kovtun, Pavel; Uensal, Mithat; Yaffe, Laurence G.
2005-11-15
In previous work, we found that necessary and sufficient conditions for large N{sub c} equivalence between parent and daughter theories, for a wide class of orbifold projections of U(N{sub c}) gauge theories, are just the natural requirements that the discrete symmetry used to define the projection not be spontaneously broken in the parent theory, and the discrete symmetry permuting equivalent gauge group factors not be spontaneously broken in the daughter theory. In this paper, we discuss the application of this result to Z{sub k} projections of N=1 supersymmetric Yang-Mills theory in four dimensions, as well as various multiflavor generalizations. Z{sub k} projections with k>2 yielding chiral gauge theories violate the symmetry realization conditions needed for large N{sub c} equivalence, due to the spontaneous symmetry breaking of discrete chiral symmetry in the parent super-Yang-Mills theory. But for Z{sub 2} projections, we show that previous assertions of large N{sub c} inequivalence, in infinite volume, between the parent and daughter theories were based on incorrect mappings of vacuum energies, theta angles, or connected correlators between the two theories. With the correct identifications, there is no sign of any inconsistency. A subtle but essential feature of the connection between parent and daughter theories involves multivaluedness in the mapping of theta parameters from parent to daughter.
Emerging geometry from maximally super-symmetric Yang-Mills theory
NASA Astrophysics Data System (ADS)
Vazquez, Samuel Enrique
In this thesis, we explore the emergence of space-time geometry, and string theory physics from N = 4 supersymmetric Yang-Mills (SYM) theory with gauge group U(N). This is done in the context of the anti-de-Sitter/conformal field theory correspondence (AdS/CFT). The main results of this thesis are the following. First, we study single trace perturbations around generic 1/2 BPS states of the theory. We do this in the large N limit, and at one-loop in the 't-Hooft coupling. We show how these states can be mapped to dynamical lattices with boson statistics and periodic boundary conditions. By dynamical, we mean that the total boson occupation number is not conserved in general. Then, we show how to derive an effective sigma model for these systems which coincides with the Polyakov action of a probe string on a 1/2 BPS geometry (in the fast string limit). Secondly, we study non-supersymmetric perturbations of the vacuum which give rise to bosonic lattices with open boundary conditions. We also do this in the large N limit, and at one-loop in the 't-Hooft coupling. We show that these states are dual to open strings on D3-branes known as "Giant Gravitons". These lattice systems are also dynamical, but in some special cases, we show that we get an integrable spin chain with open boundary conditions. Next, we study single trace perturbations at strong coupling. We do this by taking a "dilute gas" approximation. We derive an all-loop result for the dispersion relation of the "magnons" which coincides with previous conjectures in the literature. What is more, we derive the geometrical picture of the so-called "giant magnon" string solution of Hofman and Maldacena, directly from the field theory. Finally, we explore the question of classical integrability of open strings on D-branes. In particular, we study the case of the giant gravitons, and compare the integrable structures on both sides of the AdS/CFT correspondence.
Classical Yang-Mills Theory with Fermions II:. DIRAC’S Observables
NASA Astrophysics Data System (ADS)
Lusanna, Luca
For pure Yang-Mills theory on Minkowski space-time, formulated in functional spaces where the covariant divergence is an elliptic operator without zero modes, and for a trivial principal bundle over the fixed time Euclidean space with a compact, semisimple, connected and simply connected structure Lie group, a Green function for the covariant divergence has been found. It allows one to solve the first class constraints associated with Gauss’ laws and to identify a connection-dependent coordinatization of the trivial principal bundle. In a neighborhood of the global identity section, by using canonical coordinates of the first kind on the fibers, one has a symplectic implementation of the Lie algebra of the small gauge transformations generated by Gauss’ laws and one can make a generalized Hodge decomposition of the gauge potential one-forms based on the BRST operator. This decomposition singles out a pure gauge background connection (the BRST ghost as Maurer-Cartan one-form on the group of gauge transformations) and a transverse gauge-covariant magnetic gauge potential. After an analogous decomposition of the electric field strength into the transverse and the longitudinal part, Dirac’s observables associated with the transverse electric and magnetic components are identified as their restriction to the global identity section of the trivial principal bundle. The longitudinal part of the electric field can be re-expressed in terms of these electric and magnetic transverse parts and of the constraints without Gribov ambiguity. The physical Lagrangian, Hamiltonian, non-Abelian and topological charges have been obtained in terms of transverse Dirac’s observables, also in the presence of fermion fields, after a symplectic decoupling of the gauge degrees of freedom; one has an explicit realization of the abstract “Riemannian metric” on the orbit space. Both the Lagrangian and the Hamiltonian are nonlocal and nonpolynomial; like in the Coulomb gauge they are
Supergravitons from one loop perturbative N=4 super Yang-Mills theory
Janik, Romuald A.; Trzetrzelewski, Maciej
2008-04-15
We determine the partition function of (1/16)BPS operators in N=4 super Yang-Mills (SYM) at weak coupling at the one-loop level in the planar limit. This partition function is significantly different from the one computed at zero coupling. We find that it coincides precisely with the partition function of a gas of (1/16)BPS supergravitons in AdS{sub 5}xS{sup 5}.
The construction of dual-trace factor in Yang-Mills theory
NASA Astrophysics Data System (ADS)
Du, Yi-Jian; Feng, Bo; Fu, Chih-Hao
2013-07-01
Recently, a BCJ dual of the color-ordered formula for Yang-Mills amplitude was proposed, where the dual-trace factor satisfies cyclic symmetry and KK-relation. In this paper, we present a systematic construction of the dual-trace factor based on its proposed relations to kinematic numerators in dual-DDM form. We show that the construction presented respects relabeling symmetry. In addition, we show that using relabeling symmetry as conditions, the same construction can be solved independently.
Effective metrics in the non-minimal Einstein-Yang-Mills-Higgs theory
Balakin, A.B. Dehnen, H. Zayats, A.E.
2008-09-15
We formulate a self-consistent non-minimal five-parameter Einstein-Yang-Mills-Higgs (EYMH) model and analyse it in terms of effective (associated, color and color-acoustic) metrics. We use a formalism of constitutive tensors in order to reformulate master equations for the gauge, scalar and gravitational fields and reconstruct in the algebraic manner the so-called associated metrics for the Yang-Mills field. Using WKB-approximation we find color metrics for the Yang-Mills field and color-acoustic metric for the Higgs field in the framework of five-parameter EYMH model. Based on explicit representation of these effective metrics for the EYMH system with uniaxial symmetry, we consider cosmological applications for Bianchi-I, FLRW and de Sitter models. We focus on the analysis of the obtained expressions for velocities of propagation of longitudinal and transversal color and color-acoustic waves in a (quasi)vacuum interacting with curvature; we show that curvature coupling results in time variations of these velocities. We show, that the effective metrics can be regular or can possess singularities depending on the choice of the parameters of non-minimal coupling in the cosmological models under discussion. We consider a physical interpretation of such singularities in terms of phase velocities of color and color-acoustic waves, using the terms 'wave stopping' and 'trapped surface'.
The Types of Axisymmetric Exact Solutions Closely Related to n-SOLITONS for Yang-Mills Theory
NASA Astrophysics Data System (ADS)
Zhong, Zai Zhe
In this letter, we point out that if a symmetric 2×2 real matrix M(ρ,z) obeys the Belinsky-Zakharov equation and |det(M)|=1, then an axisymmetric Bogomol'nyi field exact solution for the Yang-Mills-Higgs theory can be given. By using the inverse scattering technique, some special Bogomol'nyi field exact solutions, which are closely related to the true solitons, are generated. In particular, the Schwarzschild-like solution is a two-soliton-like solution.
Gao Zhifeng; Zhang Jing
2009-04-15
In this paper, we use the method of calculus of variations to establish the existence of energy-minimizing radially symmetric magnetic monopole solutions in the general (4p-1)-dimensional Yang-Mills gauge field theory developed recently by Radu and Tchrakian. We also show that these solutions are either self-dual or anti-self-dual and, hence, unique. Our study extends the existence work of Belavin, Polyakov, Schwartz, and Tyupin and the equivalence and uniqueness work of Maison in three dimensions and the work of Yang in seven dimensions to the situation of arbitrary (4p-1) dimensions.
NASA Astrophysics Data System (ADS)
Kondo, Kei-Ichi; Kato, Seikou; Shibata, Akihiro; Shinohara, Toru
2015-05-01
The purpose of this paper is to review the recent progress in understanding quark confinement. The emphasis of this review is placed on how to obtain a manifestly gauge-independent picture for quark confinement supporting the dual superconductivity in the Yang-Mills theory, which should be compared with the Abelian projection proposed by 't Hooft. The basic tools are novel reformulations of the Yang-Mills theory based on change of variables extending the decomposition of the SU(N) Yang-Mills field due to Cho, Duan-Ge and Faddeev-Niemi, together with the combined use of extended versions of the Diakonov-Petrov version of the non-Abelian Stokes theorem for the SU(N) Wilson loop operator. Moreover, we give the lattice gauge theoretical versions of the reformulation of the Yang-Mills theory which enables us to perform the numerical simulations on the lattice. In fact, we present some numerical evidences for supporting the dual superconductivity for quark confinement. The numerical simulations include the derivation of the linear potential for static interquark potential, i.e., non-vanishing string tension, in which the "Abelian" dominance and magnetic monopole dominance are established, confirmation of the dual Meissner effect by measuring the chromoelectric flux tube between quark-antiquark pair, the induced magnetic-monopole current, and the type of dual superconductivity, etc. In addition, we give a direct connection between the topological configuration of the Yang-Mills field such as instantons/merons and the magnetic monopole. We show especially that magnetic monopoles in the Yang-Mills theory can be constructed in a manifestly gauge-invariant way starting from the gauge-invariant Wilson loop operator and thereby the contribution from the magnetic monopoles can be extracted from the Wilson loop in a gauge-invariant way through the non-Abelian Stokes theorem for the Wilson loop operator, which is a prerequisite for exhibiting magnetic monopole dominance for quark
Towards the large N limit of pure Nu = 1 super Yang-Mills theory.
Maldacena, J; Nuñez, C
2001-01-22
We find the gravity solution corresponding to a large number of Neveu-Schwarz or D5-branes wrapped on a two sphere so that we have pure Nu = 1 super Yang-Mills in the IR. The supergravity solution is smooth, it shows confinement, and it breaks the U(1)(R) chiral symmetry in the appropriate way. When the gravity approximation is valid the masses of glueballs are comparable to the masses of Kaluza-Klein (KK) states on the 5-brane, but if we could quantize strings on this background it looks like we should be able to decouple the KK states. PMID:11177888
Infrared degrees of freedom of Yang-Mills theory in the Schroedinger representation
Forkel, Hilmar
2006-05-15
We set up a new calculational framework for the Yang-Mills vacuum transition amplitude in the Schroedinger representation. After integrating out hard-mode contributions perturbatively and performing a gauge-invariant gradient expansion of the ensuing soft-mode action, a manageable saddle-point expansion for the vacuum overlap can be formulated. In combination with the squeezed approximation to the vacuum wave functional this allows for an essentially analytical treatment of physical amplitudes. Moreover, it leads to the identification of dominant and gauge-invariant classes of gauge field orbits which play the role of gluonic infrared (IR) degrees of freedom. The latter emerge as a diverse set of saddle-point solutions and are represented by unitary matrix fields. We discuss their scale stability, the associated virial theorem and other general properties including topological quantum numbers and action bounds. We then find important saddle-point solutions (most of them solitons) explicitly and examine their physical impact. While some are related to tunneling solutions of the classical Yang-Mills equation, i.e. to instantons and merons, others appear to play unprecedented roles. A remarkable new class of IR degrees of freedom consists of Faddeev-Niemi type link and knot solutions, potentially related to glueballs.
Field-dependent BRST-antiBRST transformations in Yang-Mills and Gribov-Zwanziger theories
NASA Astrophysics Data System (ADS)
Moshin, Pavel Yu.; Reshetnyak, Alexander A.
2014-11-01
We introduce the notion of finite BRST-antiBRST transformations, both global and field-dependent, with a doublet λa, a=1,2, of anticommuting Grassmann parameters and find explicit Jacobians corresponding to these changes of variables in Yang-Mills theories. It turns out that the finite transformations are quadratic in their parameters. At the same time, exactly as in the case of finite field-dependent BRST transformations for the Yang-Mills vacuum functional, special field-dependent BRST-antiBRST transformations, with sa-potential parameters λa=saΛ induced by a finite even-valued functional Λ and by the anticommuting generators sa of BRST-antiBRST transformations, amount to a precise change of the gauge-fixing functional. This proves the independence of the vacuum functional under such BRST-antiBRST transformations. We present the form of transformation parameters that generates a change of the gauge in the path integral and evaluate it explicitly for connecting two arbitrary Rξ-like gauges. For arbitrary differentiable gauges, the finite field-dependent BRST-antiBRST transformations are used to generalize the Gribov horizon functional h, given in the Landau gauge, and being an additive extension of the Yang-Mills action by the Gribov horizon functional in the Gribov-Zwanziger model. This generalization is achieved in a manner consistent with the study of gauge independence. We also discuss an extension of finite BRST-antiBRST transformations to the case of general gauge theories and present an ansatz for such transformations. introduction of finite BRST-antiBRST transformations, being polynomial in powers of a constant Sp(2)-doublet of Grassmann-odd parameters λa and leaving the quantum action of the Yang-Mills theory invariant to all orders in λa; definition of finite field-dependent BRST-antiBRST transformations, being polynomial in powers of an Sp(2)-doublet of Grassmann-odd functionals λa(ϕ) depending on the classical Yang-Mills fields, the ghost
Perturbative tests for a large-N reduced model of {N} = {4} super Yang-Mills theory
NASA Astrophysics Data System (ADS)
Ishiki, Goro; Shimasaki, Shinji; Tsuchiya, Asato
2011-11-01
We study a non-perturbative formulation of {N} = {4} super Yang-Mills theory (SYM) on R × S 3 in the planar limit proposed in arXiv:0807.2352. This formulation is based on the large- N reduction, and the theory can be described as a particular large- N limit of the plane wave matrix model (PWMM), which is obtained by dimensionally reducing the original theory over S 3. In this paper, we perform some tests for this proposal. We construct an operator in the PWMM that corresponds to the Wilson loop in SYM in the continuum limit and calculate the vacuum expectation value of the operator for the case of the circular contour. We find that our result indeed agrees with the well-known result first obtained by Erickson, Semenoff and Zarembo. We also compute the beta function at the 1-loop level based on this formulation and see that it is indeed vanishing.
Perturbative tests for a large-N reduced model of mathcal{N} = {4} super Yang-Mills theory
NASA Astrophysics Data System (ADS)
Ishiki, Goro; Shimasaki, Shinji; Tsuchiya, Asato
2012-02-01
We study a non-perturbative formulation of mathcal{N} = {4} super Yang-Mills theory (SYM) on R × S 3 in the planar limit proposed in arXiv:0807.2352. This formulation is based on the large- N reduction, and the theory can be described as a particular large- N limit of the plane wave matrix model (PWMM), which is obtained by dimensionally reducing the original theory over S 3. In this paper, we perform some tests for this proposal. We construct an operator in the PWMM that corresponds to the Wilson loop in SYM in the continuum limit and calculate the vacuum expectation value of the operator for the case of the circular contour. We find that our result indeed agrees with the well-known result first obtained by Erickson, Semenoff and Zarembo. We also compute the beta function at the 1-loop level based on this formulation and see that it is indeed vanishing.
NASA Astrophysics Data System (ADS)
Balakin, Alexander B.; Lemos, José P. S.; Zayats, Alexei E.
2016-04-01
Alternative theories of gravity and their solutions are of considerable importance since, at some fundamental level, the world can reveal new features. Indeed, it is suspected that the gravitational field might be nonminimally coupled to the other fields at scales not yet probed, bringing into the forefront nonminimally coupled theories. In this mode, we consider a nonminimal Einstein-Yang-Mills theory with a cosmological constant. Imposing spherical symmetry and staticity for the spacetime and a magnetic Wu-Yang ansatz for the Yang-Mills field, we find expressions for the solutions of the theory. Further imposing constraints on the nonminimal parameters, we find a family of exact solutions of the theory depending on five parameters—two nonminimal parameters, the cosmological constant, the magnetic charge, and the mass. These solutions represent magnetic monopoles and black holes in magnetic monopoles with de Sitter, Minkowskian, and anti-de Sitter asymptotics, depending on the sign and value of the cosmological constant Λ . We classify completely the family of solutions with respect to the number and the type of horizons and show that the spacetime solutions can have, at most, four horizons. For particular sets of the parameters, these horizons can become double, triple, and quadruple. For instance, for a positive cosmological constant Λ , there is a critical Λc for which the solution admits a quadruple horizon, evocative of the Λc that appears for a given energy density in both the Einstein static and Eddington-Lemaître dynamical universes. As an example of our classification, we analyze solutions in the Drummond-Hathrell nonminimal theory that describe nonminimal black holes. Another application is with a set of regular black holes previously treated.
Correct effective potential of supersymmetric Yang-Mills theory on M{sup 4}xS{sup 1}
Haba, Naoyuki; Takenaga, Kazunori; Yamashita, Toshifumi
2005-01-15
We study an N=1 supersymmetric Yang-Mills theory defined on M{sup 4}xS{sup 1}. The vacuum expectation values for adjoint scalar field in vector multiplet, though important, have been overlooked in evaluating one-loop effective potential of the theory. We correctly take the vacuum expectation values into account in addition to the Wilson line phases to give an expression for the effective potential, and gauge symmetry breaking is discussed. In evaluating the potential, we employ the Scherk-Schwarz mechanism and introduce bare mass for gaugino in order to break supersymmetry. We also obtain masses for the scalars, the adjoint scalar, and the component gauge field for the S{sup 1} direction in the case of the SU(2) gauge group. We observe that large supersymmetry breaking gives larger mass for the scalar. This analysis is easily applied to the M{sup 4}xS{sup 1}/Z{sub 2} case.
Spacetime and flux tube S-matrices at finite coupling for N=4 supersymmetric Yang-Mills theory.
Basso, Benjamin; Sever, Amit; Vieira, Pedro
2013-08-30
We propose a nonperturbative formulation of planar scattering amplitudes in N=4 supersymmetric Yang-Mills theory, or, equivalently, polygonal Wilson loops. The construction is based on the operator product expansion approach and introduces a new decomposition of the Wilson loop in terms of fundamental building blocks named pentagon transitions. These transitions satisfy a simple relation to the worldsheet S matrix on top of the so-called Gubser-Klebanov-Polyakov vacuum which allows us to bootstrap them at any value of the coupling. In this Letter we present a subsector of the full solution which we call the gluonic part. We match our results with both weak and strong coupling data available in the literature. PMID:24033023
The Yang-Mills Mass Gap Solution
NASA Astrophysics Data System (ADS)
Yablon, Jay R.
2014-03-01
The Yang-Mills Mass Gap problem is solved by deriving SU(3)C Chromodynamics as a corollary theory from Yang-Mills gauge theory. The mass gap is filled from finite non-zero eigenvalues of a configuration space inverse perturbation tensor containing vacuum excitations. This results from carefully developing six equivalent views of Yang-Mills gauge theory as having: 1) non-commuting (non-Abelian) gauge fields; 2) gauge fields with non-linear self-interactions; 3) a ``steroidal'' minimal coupling; 4) perturbations; 5) curvature in the gauge space of connections; and 6) gauge fields related to source currents through an infinite recursive nesting. Based on combining classical Yang-Mills electric and magnetic source field equations into a single equation, confinement results from showing how magnetic monopoles of Yang-Mills gauge theory exhibit color confinement and meson flow and have all the color symmetries of baryons, from which we conclude that they are one and the same as baryons. Chiral symmetry breaking results from the recursive behavior of these monopoles coupled with viewing Dirac's gamma matrices as Hamiltonian quaternions extended into spacetime. Finally, with aid from the ``steroidal'' view, the recursive view of Yang-Mills enables polynomial gauge field terms in the Yang-Mills action to be stripped out and replaced by polynomial source current terms prior to path integration. This enables an exact analytical calculation of a non-linear path integral using a closed recursive kernel and yields a non-linear quantum amplitude also with a closed recursive kernel, thus proving the existence of a non-trivial relativistic quantum Yang-Mills field theory on R4 for any simple gauge group G.
Direct test of the AdS/CFT correspondence by Monte Carlo studies of super Yang-Mills theory
NASA Astrophysics Data System (ADS)
Honda, Masazumi; Ishiki, Goro; Kim, Sang-Woo; Nishimura, Jun; Tsuchiya, Asato
2013-11-01
We perform nonperturbative studies of super Yang-Mills theory by Monte Carlo simulation. In particular, we calculate the correlation functions of chiral primary operators to test the AdS/CFT correspondence. Our results agree with the predictions obtained from the AdS side that the SUSY non-renormalization property is obeyed by the three-point functions but not by the four-point functions investigated in this paper. Instead of the lattice regularization, we use a novel regularization of the theory based on an equivalence in the large- N limit between the SU( N) theory on R × S 3 and a one-dimensional SU( N) gauge theory known as the plane-wave (BMN) matrix model. The equivalence extends the idea of large- N reduction to a curved space and, at the same time, overcomes the obstacle related to the center symmetry breaking. The adopted regularization for S 3 preserves 16 SUSY, which is crucial in testing the AdS/CFT correspondence with the available computer resources. The only SUSY breaking effects, which come from the momentum cutoff Λ in R direction, are made negligible by using sufficiently large Λ.
Two-loop study of the deconfinement transition in Yang-Mills theories: SU(3) and beyond
NASA Astrophysics Data System (ADS)
Reinosa, U.; Serreau, J.; Tissier, M.; Wschebor, N.
2016-05-01
We study the confinement-deconfinement phase transition of pure Yang-Mills theories at finite temperature using a simple massive extension of standard background field methods. We generalize our recent next-to-leading-order perturbative calculation of the Polyakov loop and of the related background field effective potential for the SU(2) theory to any compact and connex Lie group with a simple Lie algebra. We discuss in detail the SU(3) theory, where the two-loop corrections yield improved values for the first-order transition temperature as compared to the one-loop result. We also show that certain one-loop artifacts of thermodynamical observables disappear at two-loop order, as was already the case for the SU(2) theory. In particular, the entropy and the pressure are positive for all temperatures. Finally, we discuss the groups SU(4) and Sp(2) which shed interesting light, respectively, on the relation between the (de)confinement of static matter sources in the various representations of the gauge group and on the use of the background field itself as an order parameter for confinement. In both cases, we obtain first-order transitions, in agreement with lattice simulations and other continuum approaches.
Faizal, Mir; Higuchi, Atsushi
2008-09-15
The propagators of the Faddeev-Popov (FP) ghosts for Yang-Mills theories and perturbative quantum gravity in the covariant gauge are infrared (IR) divergent in de Sitter spacetime. We point out, however, that the modes responsible for these divergences will not contribute to loop diagrams in computations of time-ordered products in either Yang-Mills theories or perturbative quantum gravity. Therefore, we propose that the IR-divergent FP-ghost propagator should be regularized by a small mass term that is sent to zero in the end of any perturbative calculations. This proposal is equivalent to using the effective FP-ghost propagators, which we present in an explicit form, obtained by removing the modes responsible for the IR divergences. We also make some comments on the corresponding propagators in anti-de Sitter spacetime.
NASA Astrophysics Data System (ADS)
García-Jiménez, I.; Novales-Sánchez, H.; Toscano, J. J.
2016-05-01
One-loop Standard Model observables produced by virtual heavy Kaluza-Klein fields play a prominent role in the minimal model of universal extra dimensions. Motivated by this aspect, we integrate out all the Kaluza-Klein heavy modes coming from the Yang-Mills theory set on a spacetime with an arbitrary number, n , of compact extra dimensions. After fixing the gauge with respect to the Kaluza-Klein heavy gauge modes in a covariant manner, we calculate a gauge-independent effective Lagrangian expansion containing multiple Kaluza-Klein sums that entail a bad divergent behavior. We use the Epstein-zeta function to regularize and characterize discrete divergences within such multiple sums, and then we discuss the interplay between the number of extra dimensions and the degree of accuracy of effective Lagrangians to generate or not divergent terms of discrete origin. We find that nonrenormalizable terms with mass dimension k are finite as long as k >4 +n . Multiple Kaluza-Klein sums of nondecoupling logarithmic terms, not treatable by Epstein-zeta regularization, are produced by four-dimensional momentum integration. On the grounds of standard renormalization, we argue that such effects are unobservable.
NASA Astrophysics Data System (ADS)
Silva, P. J.; Oliveira, O.
2016-06-01
The correlations between the modulus of the Polyakov loop, its phase θ , and the Landau gauge gluon propagator at finite temperature are investigated in connection with the center symmetry for pure Yang-Mills SU(3) theory. In the deconfined phase, where the center symmetry is spontaneously broken, the phase of the Polyakov loop per configuration is close to θ =0 , ±2 π /3 . We find that the gluon propagator form factors associated with θ ≈0 differ quantitatively and qualitatively from those associated to θ ≈±2 π /3 . This difference between the form factors is a property of the deconfined phase and a sign of the spontaneous breaking of the center symmetry. Furthermore, given that this difference vanishes in the confined phase, it can be used as an order parameter associated to the deconfinement transition. For simulations near the critical temperature Tc, the difference between the propagators associated to θ ≈0 and θ ≈±2 π /3 allows one to classify the configurations as belonging to the confined or deconfined phase. This establishes a selection procedure which has a measurable impact on the gluon form factors. Our results also show that the absence of the selection procedure can be erroneously interpreted as lattice artifacts.
Representations of Super Yang-Mills Algebras
NASA Astrophysics Data System (ADS)
Herscovich, Estanislao
2013-06-01
We study in this article the representation theory of a family of super algebras, called the super Yang-Mills algebras, by exploiting the Kirillov orbit method à la Dixmier for nilpotent super Lie algebras. These super algebras are an extension of the so-called Yang-Mills algebras, introduced by A. Connes and M. Dubois-Violette in (Lett Math Phys 61(2):149-158, 2002), and in fact they appear as a "background independent" formulation of supersymmetric gauge theory considered in physics, in a similar way as Yang-Mills algebras do the same for the usual gauge theory. Our main result states that, under certain hypotheses, all Clifford-Weyl super algebras {{Cliff}q(k) ⊗ Ap(k)}, for p ≥ 3, or p = 2 and q ≥ 2, appear as a quotient of all super Yang-Mills algebras, for n ≥ 3 and s ≥ 1. This provides thus a family of representations of the super Yang-Mills algebras.
Yang-Mills connections valued on the octonionic algebra
NASA Astrophysics Data System (ADS)
Restuccia, A.; Veiro, J. P.
2016-05-01
We consider a formulation of Yang-Mills theory where the gauge field is valued on an octonionic algebra and the gauge transformation is the group of automorphisms of it. We show, under mild assumptions, that the only possible gauge formulations are the usual su(2) or u(1) Yang-Mills theories.
Phase diagram of Script N = 4 super-Yang-Mills theory with R-symmetry chemical potentials
NASA Astrophysics Data System (ADS)
Yamada, Daisuke; Yaffe, Laurence G.
2006-09-01
The phase diagram of large Nc, weakly-coupled Script N = 4 supersymmetric Yang-Mills theory on a three-sphere with non-zero chemical potentials is examined. In the zero coupling limit, a transition line in the μ-T plane is found, separating a ``confined'' phase in which the Polyakov loop has vanishing expectation value from a ``deconfined'' phase in which this order parameter is non-zero. For non-zero but weak coupling, perturbative methods may be used to construct a dimensionally reduced effective theory valid for sufficiently high temperature. If the maximal chemical potential exceeds a critical value, then the free energy becomes unbounded below and no genuine equilibrium state exists. However, the deconfined plasma phase remains metastable, with a lifetime which grows exponentially with Nc (not Nc2). This metastable phase persists with increasing chemical potential until a phase boundary, analogous to a spinodal decomposition line, is reached. Beyond this point, no long-lived locally stable quasi-equilibrium state exists. The resulting picture for the phase diagram of the weakly coupled theory is compared with results believed to hold in the strongly coupled limit of the theory, based on the AdS/CFT correspondence and the study of charged black hole thermodynamics. The confinement/deconfinement phase transition at weak coupling is in qualitative agreement with the Hawking-Page phase transition in the gravity dual of the strongly coupled theory. The black hole thermodynamic instability line may be the counterpart of the spinodal decomposition phase boundary found at weak coupling, but no black hole tunneling instability, analogous to the instability of the weakly coupled plasma phase is currently known.
Bern, Zvi; Czakon, Michael; Dixon, Lance J.; Kosower, David A.; Smirnov, Vladimir A.
2006-11-15
We present an expression for the leading-color (planar) four-loop four-point amplitude of N = 4 supersymmetric Yang-Mills theory in 4-2{epsilon} dimensions, in terms of eight separate integrals. The expression is based on consistency of unitarity cuts and infrared divergences. We expand the integrals around {epsilon} = 0, and obtain analytic expressions for the poles from 1/{epsilon}{sup 8} through 1/{epsilon}{sup 4}. We give numerical results for the coefficients of the 1/{epsilon}{sup 3} and 1/e{sup 2} poles. These results all match the known exponentiated structure of the infrared divergences, at four separate kinematic points. The value of the 1/{epsilon}{sup 2} coefficient allows us to test a conjecture of Eden and Staudacher for the four-loop cusp (soft) anomalous dimension. We find that the conjecture is incorrect, although our numerical results suggest that a simple modification of the expression, flipping the sign of the term containing {zeta}{sub 3}{sup 2}, may yield the correct answer. Our numerical value can be used, in a scheme proposed by Kotikov, Lipatov and Velizhanin, to estimate the two constants in the strong-coupling expansion of the cusp anomalous dimension that are known from string theory. The estimate works to 2.6% and 5% accuracy, providing non-trivial evidence in support of the AdS/CFT correspondence. We also use the known constants in the strong-coupling expansion as additional input to provide approximations to the cusp anomalous dimension which should be accurate to under one percent for all values of the coupling. When the evaluations of the integrals are completed through the finite terms, it will be possible to test the iterative, exponentiated structure of the finite terms in the four-loop four-point amplitude, which was uncovered earlier at two and three loops.
Analytic Result for the Two-loop Six-point NMHV Amplitude in N = 4 Super Yang-Mills Theory
Dixon, Lance J.; Drummond, James M.; Henn, Johannes M.; /Humboldt U., Berlin /Princeton, Inst. Advanced Study
2012-02-15
We provide a simple analytic formula for the two-loop six-point ratio function of planar N = 4 super Yang-Mills theory. This result extends the analytic knowledge of multi-loop six-point amplitudes beyond those with maximal helicity violation. We make a natural ansatz for the symbols of the relevant functions appearing in the two-loop amplitude, and impose various consistency conditions, including symmetry, the absence of spurious poles, the correct collinear behavior, and agreement with the operator product expansion for light-like (super) Wilson loops. This information reduces the ansatz to a small number of relatively simple functions. In order to fix these parameters uniquely, we utilize an explicit representation of the amplitude in terms of loop integrals that can be evaluated analytically in various kinematic limits. The final compact analytic result is expressed in terms of classical polylogarithms, whose arguments are rational functions of the dual conformal cross-ratios, plus precisely two functions that are not of this type. One of the functions, the loop integral {Omega}{sup (2)}, also plays a key role in a new representation of the remainder function R{sub 6}{sup (2)} in the maximally helicity violating sector. Another interesting feature at two loops is the appearance of a new (parity odd) x (parity odd) sector of the amplitude, which is absent at one loop, and which is uniquely determined in a natural way in terms of the more familiar (parity even) x (parity even) part. The second non-polylogarithmic function, the loop integral {tilde {Omega}}{sup (2)}, characterizes this sector. Both {Omega}{sup (2)} and {tilde {Omega}}{sup (2)} can be expressed as one-dimensional integrals over classical polylogarithms with rational arguments.
Holographic Wilson loops in symmetric representations in {N} = {2}^{ast } super-Yang-Mills theory
NASA Astrophysics Data System (ADS)
Chen-Lin, Xinyi; Dekel, Amit; Zarembo, Konstantin
2016-02-01
We construct the D3-brane solution in the holographic dual of the {N} = {2}^{ast } theory that describes Wilson lines in symmetric representations of the gauge group. The results perfectly agree with the direct field-theory predictions based on localization.
Gravity as an internal Yang-Mills gauge field theory of the Poincaré group.
NASA Astrophysics Data System (ADS)
Hennig, Jörg; Nitsch, Jürgen
1981-10-01
In the framework of affine bundles we present gravity as an “internal” gauge field theory of the Poincaré group. The resulting geometry is a Riemann-Cartan space-time carrying torsion and curvature. In order to admit a nontrivial action of the translation group we formally extend the matter Lagrangian to affine field variables. Finally, we establish the relation of our approach with the formalism of Hehl et al.
Physical observables from boundary artifacts: scalar glueball in Yang-Mills theory
NASA Astrophysics Data System (ADS)
Chowdhury, Abhishek; Harindranath, A.; Maiti, Jyotirmoy
2016-02-01
By relating the functional averages of a generic scalar operator in simulations with Open (O) and Periodic (P) boundary conditions (BCs) respectively for SU(3) lattice gauge theory, we show that the scalar glueball mass and the glueball to vacuum matrix element can be extracted very efficiently from the former. Numerical results are compared with those extracted from the two point function of the time slice energy density (both PBC and OBC). The scaling properties of the mass and the matrix element are studied with the help of Wilson (gradient) flow.
The Framed Standard Model (I) -- A Physics Case for Framing the Yang-Mills Theory?
NASA Astrophysics Data System (ADS)
Chan, Hong-Mo; Tsou, Sheung Tsun
Introducing, in the underlying gauge theory of the Standard Model, the frame vectors in internal space as field variables (framons), in addition to the usual gauge boson and matter fermions fields, one obtains: * the standard Higgs scalar as the framon in the electroweak sector; * a global widetilde{su}(3) symmetry dual to colour to play the role of fermion generations. Renormalization via framon loops changes the orientation in generation space of the vacuum, hence also of the mass matrices of leptons and quarks, thus making them rotate with changing scale μ. From previous work, it is known already that a rotating mass matrix will lead automatically to: * CKM mixing and neutrino oscillations, * hierarchical masses for quarks and leptons, * a solution to the strong-CP problem transforming the theta-angle into a Kobayashi-Maskawa phase. Here in the framed standard model (FSM), the renormalization group equation has some special properties which explain the main qualitative features seen in experiment both for mixing matrices of quarks and leptons, and for their mass spectrum. Quantitative results will be given in Paper II. The present paper ends with some tentative predictions on Higgs decay, and with some speculations on the origin of dark matter...
The framed Standard Model (I) — A physics case for framing the Yang-Mills theory?
NASA Astrophysics Data System (ADS)
Chan, Hong-Mo; Tsou, Sheung Tsun
2015-10-01
Introducing, in the underlying gauge theory of the Standard Model, the frame vectors in internal space as field variables (framons), in addition to the usual gauge boson and matter fermions fields, one obtains: the standard Higgs scalar as the framon in the electroweak sector; a global su˜(3) symmetry dual to colour to play the role of fermion generations. Renormalization via framon loops changes the orientation in generation space of the vacuum, hence also of the mass matrices of leptons and quarks, thus making them rotate with changing scale μ. From previous work, it is known already that a rotating mass matrix will lead automatically to: CKM mixing and neutrino oscillations, hierarchical masses for quarks and leptons, a solution to the strong-CP problem transforming the theta-angle into a Kobayashi-Maskawa phase. Here in the framed standard model (FSM), the renormalization group equation has some special properties which explain the main qualitative features seen in experiment both for mixing matrices of quarks and leptons, and for their mass spectrum. Quantitative results will be given in Paper II. The present paper ends with some tentative predictions on Higgs decay, and with some speculations on the origin of dark matter.
NASA Astrophysics Data System (ADS)
Roche, Ph.
2016-03-01
We recall the relation between zeta function representation of groups and two-dimensional topological Yang-Mills theory through Mednikh formula. We prove various generalisations of Mednikh formulas and define generalization of zeta function representations of groups. We compute some of these functions in the case of the finite group GL(2, 𝔽q) and PGL(2, 𝔽q). We recall the table characters of these groups for any q, compute the Frobenius-Schur indicator of their irreducible representations, and give the explicit structure of their fusion rings.
NASA Astrophysics Data System (ADS)
Bourjaily, Jacob L.; Heslop, Paul; Tran, Vuong-Viet
2016-05-01
We use the soft-collinear bootstrap to construct the 8-loop integrand for the 4-point amplitude and 4-stress-tensor correlation function in planar maximally supersymmetric Yang-Mills theory. Both have a unique representation in terms of planar, conformal integrands grouped according to a hidden symmetry discovered for correlation functions. The answer we find exposes a fundamental tension between manifest locality and planarity with manifest conformality not seen at lower loops. For the first time, the integrand must include terms that are finite even on-shell and terms that are divergent even off-shell (so-called pseudoconformal integrals). We describe these novelties and their consequences in this Letter, and we make the full correlator and amplitude available as part of the Supplemental Material.
Bourjaily, Jacob L; Heslop, Paul; Tran, Vuong-Viet
2016-05-13
We use the soft-collinear bootstrap to construct the 8-loop integrand for the 4-point amplitude and 4-stress-tensor correlation function in planar maximally supersymmetric Yang-Mills theory. Both have a unique representation in terms of planar, conformal integrands grouped according to a hidden symmetry discovered for correlation functions. The answer we find exposes a fundamental tension between manifest locality and planarity with manifest conformality not seen at lower loops. For the first time, the integrand must include terms that are finite even on-shell and terms that are divergent even off-shell (so-called pseudoconformal integrals). We describe these novelties and their consequences in this Letter, and we make the full correlator and amplitude available as part of the Supplemental Material. PMID:27232016
Gravity as the square of Yang-Mills?
NASA Astrophysics Data System (ADS)
Borsten, L.; Duff, M. J.
2015-10-01
In these lectures we review how symmetries of gravitational theories may be regarded as originating from those of ‘Yang-Mills squared’. We begin by motivating the idea that certain aspects of gravitational theories can be captured by the product, in some sense, of two distinct Yang-Mills theories, particularly in the context of scattering amplitudes. We then introduce a concrete dictionary for the covariant fields of (super)gravity in terms of the product of two (super) Yang-Mills theories. The dictionary implies that the symmetries of each (super) Yang-Mills factor generate the symmetries of the corresponding (super)gravity theory: general covariance, p-form gauge invariance, local Lorentz invariance, local supersymmetry, R-symmetry and U-duality. Lecture delivered by M. J. Duff.
Yang-Mills for Historians and Philosophers
NASA Astrophysics Data System (ADS)
Crease, R. P.
The phrase "Yang-Mills" can be used (1) to refer to the specific theory proposed by Yang and Mills in 1954; or (2) as shorthand for any non-Abelian gauge theory. The 1954 version, physically speaking, had a famous show-stopping defect in the form of what might be called the "Pauli snag," or the requirement that, in the Lagrangian for non-Abelian gauge theory the mass term for the gauge field has to be zero. How, then, was it possible for (1) to turn into (2)? What unfolding sequence of events made this transition possible, and what does this evolution say about the nature of theories in physics? The transition between (1) and (2) illustrates what historians and philosophers a century from now might still find instructive and stimulating about the development of Yang-Mills theory.
NASA Astrophysics Data System (ADS)
Baxter, J. Erik
2016-02-01
We investigate dyonic black hole and dyon solutions of four-dimensional 𝔰𝔲(N) Einstein-Yang-Mills theory with a negative cosmological constant. We derive a set of field equations in this case, and prove the existence of non-trivial solutions to these equations for any integer N, with 2N - 2 gauge degrees of freedom. We do this by showing that solutions exist locally at infinity, and at the event horizon for black holes and the origin for solitons. We then prove that we can patch these solutions together regularly into global solutions that can be integrated arbitrarily far into the asymptotic regime. Our main result is to show that dyonic solutions exist in open sets in the parameter space, and hence that we can find non-trivial dyonic solutions in a number of regimes whose magnetic gauge fields have no zeros, which is likely important to the stability of the solutions.
NASA Astrophysics Data System (ADS)
Baxter, J. Erik; Winstanley, Elizabeth
2016-02-01
We investigate the stability of spherically symmetric, purely magnetic, soliton and black hole solutions of four-dimensional 𝔰𝔲(N) Einstein-Yang-Mills theory with a negative cosmological constant Λ. These solutions are described by N - 1 magnetic gauge field functions ωj. We consider linear, spherically symmetric, perturbations of these solutions. The perturbations decouple into two sectors, known as the sphaleronic and gravitational sectors. For any N, there are no instabilities in the sphaleronic sector if all the magnetic gauge field functions ωj have no zeros and satisfy a set of N - 1 inequalities. In the gravitational sector, we prove that there are solutions which have no instabilities in a neighbourhood of stable embedded 𝔰𝔲(2) solutions, provided the magnitude of the cosmological constant |" separators=" Λ | is sufficiently large.
Dyons and dyonic black holes in su (N ) Einstein-Yang-Mills theory in anti-de Sitter spacetime
NASA Astrophysics Data System (ADS)
Shepherd, Ben L.; Winstanley, Elizabeth
2016-03-01
We present new spherically symmetric, dyonic soliton and black hole solutions of the su (N ) Einstein-Yang-Mills equations in four-dimensional asymptotically anti-de Sitter spacetime. The gauge field has nontrivial electric and magnetic components and is described by N -1 magnetic gauge field functions and N -1 electric gauge field functions. We explore the phase space of solutions in detail for su (2 ) and su (3 ) gauge groups. Combinations of the electric gauge field functions are monotonic and have no zeros; in general the magnetic gauge field functions may have zeros. The phase space of solutions is extremely rich, and we find solutions in which the magnetic gauge field functions have more than fifty zeros. Of particular interest are solutions for which the magnetic gauge field functions have no zeros, which exist when the negative cosmological constant has sufficiently large magnitude. We conjecture that at least some of these nodeless solutions may be stable under linear, spherically symmetric, perturbations.
YANG-MILLS FIELDS AND THE LATTICE.
CREUTZ,M.
2004-05-18
The Yang-Mills theory lies at the heart of our understanding of elementary particle interactions. For the strong nuclear forces, we must understand this theory in the strong coupling regime. The primary technique for this is the lattice. While basically an ultraviolet regulator, the lattice avoids the use of a perturbative expansion. I discuss some of the historical circumstances that drove us to this approach, which has had immense success, convincingly demonstrating quark confinement and obtaining crucial properties of the strong interactions from first principles.
NASA Astrophysics Data System (ADS)
Duarte, Anthony G.; Oliveira, Orlando; Silva, Paulo J.
2016-07-01
The dependence of the Landau gauge two-point gluon and ghost correlation functions on the lattice spacing and on the physical volume are investigated for pure SU(3) Yang-Mills theory in four dimensions using lattice simulations. We present data from very large lattices up to 1284 and for two lattice spacings 0.10 fm and 0.06 fm corresponding to volumes of ˜(13 fm )4 and ˜(8 fm )4 , respectively. Our results show that, for sufficiently large physical volumes, both propagators have a mild dependence on the lattice volume. On the other hand, the gluon and ghost propagators change with the lattice spacing a in the infrared region, with the gluon propagator having a stronger dependence on a compared to the ghost propagator. In what concerns the strong coupling constant αs(p2), as defined from gluon and ghost two-point functions, the simulations show a sizeable dependence on the lattice spacing for the infrared region and for momenta up to ˜1 GeV .
Gauging Quantum Groups: Yang-Baxter Joining Yang-Mills
NASA Astrophysics Data System (ADS)
Wu, Yong-Shi
This review is an expansion of my talk at the conference on Sixty Years of Yang-Mills Theory. I review and explain the line of thoughts that lead to a recent joint work with Hu and Geer [Hu et al., arXiv:1502.03433] on the construction, exact solutions and ubiquitous properties of a class of quantum group gauge models on a honey-comb lattice. Conceptually the construction achieves a synthesis of the ideas of Yang-Baxter equations with those of Yang-Mills theory. Physically the models describe topological anyonic states in 2D systems.
Gauging quantum groups: Yang-Baxter joining Yang-Mills
NASA Astrophysics Data System (ADS)
Wu, Yong-Shi
2016-02-01
This review is an expansion of my talk at the conference on Sixty Years of Yang-Mills Theory. I review and explain the line of thoughts that lead to a recent joint work with Hu and Geer [Hu et al., arXiv:1502.03433] on the construction, exact solutions and ubiquitous properties of a class of quantum group gauge models on a honey-comb lattice. Conceptually the construction achieves a synthesis of the ideas of Yang-Baxter equations with those of Yang-Mills theory. Physically the models describe topological anyonic states in 2D systems.
Non-Abelian strings in supersymmetric Yang-Mills
Shifman, M.
2012-09-26
I give a broad review of novel phenomena discovered in certain Yang-Mills theories: non-Abelian strings and confined monopoles. Then I explain how these phenomena allow one to study strong dynamics of gauge theories in four dimensions from two-dimensional models emerging on the string world sheet.
Quantum Yang-Mills Dark Energy
NASA Astrophysics Data System (ADS)
Pasechnik, Roman
2016-02-01
In this short review, I discuss basic qualitative characteristics of quantum non-Abelian gauge dynamics in the non-stationary background of the expanding Universe in the framework of the standard Einstein--Yang--Mills formulation. A brief outlook of existing studies of cosmological Yang--Mills fields and their properties will be given. Quantum effects have a profound impact on the gauge field-driven cosmological evolution. In particular, a dynamical formation of the spatially-homogeneous and isotropic gauge field condensate may be responsible for both early and late-time acceleration, as well as for dynamical compensation of non-perturbative quantum vacua contributions to the ground state of the Universe. The main properties of such a condensate in the effective QCD theory at the flat Friedmann--Lema\\'itre--Robertson--Walker (FLRW) background will be discussed within and beyond perturbation theory. Finally, a phenomenologically consistent dark energy can be induced dynamically as a remnant of the QCD vacua compensation arising from leading-order graviton-mediated corrections to the QCD ground state.
Yang-Mills for historians and philosophers
NASA Astrophysics Data System (ADS)
Crease, R. P.
2016-01-01
The phrase “Yang-Mills” can be used (1) to refer to the specific theory proposed by Yang and Mills in 1954; or (2) as shorthand for any non-Abelian gauge theory. The 1954 version, physically speaking, had a famous show-stopping defect in the form of what might be called the “Pauli snag,” or the requirement that, in the Lagrangian for non-Abelian gauge theory the mass term for the gauge field has to be zero. How, then, was it possible for (1) to turn into (2)? What unfolding sequence of events made this transition possible, and what does this evolution say about the nature of theories in physics? The transition between (1) and (2) illustrates what historians and philosophers a century from now might still find instructive and stimulating about the development of Yang-Mills theory.
Wormhole solution in coupled Yang-Mills--axion system
Das, A. Department of Astronomy, University of Rochester, Rochester, New York 14627 ); Maharana, J. )
1990-01-15
We show that wormhole solutions arise naturally in the effective action, resulting from a heterotic string theory, in which Einstein gravity is coupled to the antisymmetric tensor and an SU(2) Yang-Mills field. The Peccei-Quinn scale in this case gets related to the string tension which is natural in any string compactification.
Dynamics of Higgs fields and a route to turbulence in the theory of SU(2) Yang-Mills fields
Lavkin, A.G.
1995-09-01
The dynamics of SU(2) Yancy-Mills (YM) fields, both free fields and fields interacting with Higgs bosons, is investigated by the Poincare surface-of-section method and the method of Lyapunov maximum exponents. As for free YM fields and YM fields interacting with a Higgs condensate, the route to turbulence in the system consisting of YM fields and Higgs particles lies through an infinite sequence of period-doubling bifurcations of the relevant phase trajectory. Prospects for future investigations in this field, such as constructing a consistent dynamical theory of second-order phase transitions on the basis of the analog between such transitions and the bifurcation transition to chaos, and taking into account the effects of the quark degrees of freedom of hadron matter and of thermal and quantum vacuum fluctuations on the scenario of the development of turbulence in the theory of YM fields, are also discussed. 14 refs., 1 fig.
(Super)Yang-Mills at finite heavy-quark density
NASA Astrophysics Data System (ADS)
Faedo, Antón F.; Kundu, Arnab; Mateos, David; Tarrío, Javier
2015-02-01
We study the gravitational duals of d-dimensional Yang-Mills theories with d ≤ 6 in the presence of an density of heavy quarks, with N the number of colors. For concreteness we focus on maximally supersymmetric Yang-Mills, but our results apply to a larger class of theories with or without supersymmetry. The gravitational solutions describe renormalization group flows towards infrared scaling geometries characterized by fixed dynamical and hyperscaling-violating exponents. The special case d = 5 yields an geometry upon uplifting to M-theory. We discuss the multitude of physical scales that separate different dynamical regimes along the flows, as well as the validity of the supergravity description. We also present exact black brane solutions that encode the low-temperature thermodynamics.
HYM-flation: Yang-Mills cosmology with Horndeski coupling
NASA Astrophysics Data System (ADS)
Davydov, E.; Gal'tsov, D.
2016-02-01
We propose new mechanism for inflation using classical SU (2) Yang-Mills (YM) homogeneous and isotropic field non-minimally coupled to gravity via Horndeski prescription. This is the unique generally and gauge covariant ghost-free YM theory with the curvature-dependent action leading to second-order gravity and Yang-Mills field equations. We show that its solution space contains de Sitter boundary to which the trajectories are attracted for some finite time, ensuring the robust inflation with a graceful exit. The theory can be generalized to include the Higgs field leading to two-steps inflationary scenario, in which the Planck-scale YM-generated inflation naturally prepares the desired initial conditions for the GUT-scale Higgs inflation.
Yang-Mills generalization of the geometrical collective model
NASA Astrophysics Data System (ADS)
Rosensteel, George; Sparks, Nick
2015-04-01
The geometrical or Bohr-Mottelson model is generalized and recast as a Yang-Mills theory. The gauge symmetry determines conservation of Kelvin circulation. The circulation commutes with the Hamiltonian when it is the sum of the kinetic energy and a potential that depends only on deformation. The conventional Bohr-Mottelson model is the special case of circulation zero, and wave functions are complex-valued. In the generalization, any quantized value of the circulation is allowed, and the wave functions are vector-valued. The Yang-Mills formulation introduces a new coupling between the geometrical and intrinsic degrees of freedom. The coupling appears in the covariant derivative term of the collective kinetic energy. This kind of coupling is sometimes called ``magnetic'' because of the analogy with electrodynamics.
Formation and decay of Einstein-Yang-Mills black holes
NASA Astrophysics Data System (ADS)
Rinne, Oliver
2014-12-01
We study various aspects of black holes and gravitational collapse in Einstein-Yang-Mills theory under the assumption of spherical symmetry. Numerical evolution on hyperboloidal surfaces extending to future null infinity is used. We begin by constructing colored and Reissner-Nordström black holes on surfaces of constant mean curvature and analyze their perturbations. These linearly perturbed black holes are then evolved into the nonlinear regime and the masses of the final Schwarzschild black holes are computed as a function of the initial horizon radius. We compare with an information-theoretic bound on the lifetime of unstable hairy black holes derived by Hod. Finally we study critical phenomena in gravitational collapse at the threshold between different Yang-Mills vacuum states of the final Schwarzschild black holes, where the n =1 colored black hole forms the critical solution. The work of Choptuik et al. [Phys. Rev. D 60, 124011 (1999)] is extended by using a family of initial data that includes another region in parameter space where the colored black hole with the opposite sign of the Yang-Mills potential forms the critical solution. We investigate the boundary between the two regions and discover that the Reissner-Nordström solution appears as a new approximate codimension-two attractor.
Fate of Yang-Mills black hole in early Universe
Nakonieczny, Lukasz; Rogatko, Marek
2013-02-21
According to the Big Bang Theory as we go back in time the Universe becomes progressively hotter and denser. This leads us to believe that the early Universe was filled with hot plasma of elementary particles. Among many questions concerning this phase of history of the Universe there are questions of existence and fate of magnetic monopoles and primordial black holes. Static solution of Einstein-Yang-Mills system may be used as a toy model for such a black hole. Using methods of field theory we will show that its existence and regularity depend crucially on the presence of fermions around it.
Gauge-covariant decomposition and magnetic monopole for G (2 ) Yang-Mills field
NASA Astrophysics Data System (ADS)
Matsudo, Ryutaro; Kondo, Kei-Ichi
2016-08-01
We provide a gauge-covariant decomposition of the Yang-Mills field with the exceptional gauge group G (2 ), which extends the field decomposition proposed by Cho, Duan-Ge, and Faddeev-Niemi for the S U (N ) Yang-Mills field. As an application of the decomposition, we derive a new expression of the non-Abelian Stokes theorem for the Wilson loop operator in an arbitrary representation of G (2 ). The resulting new form is used to define gauge-invariant magnetic monopoles in the G (2 ) Yang-Mills theory. Moreover, we obtain the quantization condition to be satisfied by the resulting magnetic charge. The method given in this paper is general enough to be applicable to any semisimple Lie group other than S U (N ) and G (2 ).
Orbifold singularities, Lie algebras of the third kind (LATKes), and pure Yang-Mills with matter
NASA Astrophysics Data System (ADS)
Friedmann, Tamar
2011-02-01
We discover the unique, simple Lie algebra of the third kind, or LATKe, that stems from codimension 6 orbifold singularities and gives rise to a new kind of Yang-Mills theory which simultaneously is pure and contains matter. The root space of the LATKe is one-dimensional and its Dynkin diagram consists of one point. The uniqueness of the LATKe is a vacuum selection mechanism. [ {c} {The World in a Point?}{Blow-up of} C^3/Z_3| {Dynkin diagram of the LATKe}bullet {Pure Yang-Mills with matter}
Combined study of the gluon and ghost condensates and <{epsilon}{sup abc}c{sup b}c{sup c}> in Euclidean SU(2) Yang-Mills theory in the Landau gauge
Capri, M.A.L.; Lemes, V.E.R.; Sobreiro, R.F.; Sorella, S.P.; Dudal, D.; Verschelde, H.; Gracey, J.A.
2006-01-01
The ghost condensate <{epsilon}{sup abc}c{sup b}c{sup c}> is considered together with the gluon condensate in SU(2) Euclidean Yang-Mills theories quantized in the Landau gauge. The vacuum polarization ceases to be transverse due to the nonvanishing condensate <{epsilon}{sup abc}c{sup b}c{sup c}>. The gluon propagator itself remains transverse. By polarization effects, this ghost condensate induces then a splitting in the gluon mass parameter, which is dynamically generated through . The obtained effective masses are real when is included in the analysis. In the absence of , the already known result that the ghost condensate induces effective tachyonic masses is recovered. At the one-loop level, we find that the effective diagonal mass becomes smaller than the off-diagonal one. This might serve as an indication for some kind of Abelian dominance in the Landau gauge, similar to what happens in the maximal Abelian gauge.
Yang-Mills vacuum: An attempt of lattice loop calculus
Furmanski, W.; Kolawa, A.
1985-01-01
An attempt is made to derive and to solve the Schrodinger equation in the low energy region (vacuum, first excitation, etc.) of the Yang-Mills theory on the lattice. The complete orthonormal basis in the physical Hilbert space is constructed by classifying independent solutions of Gauss's law. Loops of electric flux are chosen as elementary variables. The loop space Hamiltonian is derived, an ansatz is made for the low energy wave functionals and the Schrodinger equation is solved in the (truncated) loop basis. The resulting physical picture for the Yang-Mills vacuum in the cross-over region is that of, still quite dilute, gas of fluctuating loops. Definite candidate for the confining force emerges: the repulsive non-abelian loop-loop interaction (rather weak but persistent) generates an effective external field (''external pressure'') prohibiting unbounded loop size fluctuations. The negative sign (repulsion) is universal for all compact groups. Preliminary numerical results, so far mainly of illustrative character, are presented. 8 refs., 22 figs.
Massive Yang-Mills model and diffractive scattering
NASA Astrophysics Data System (ADS)
Forshaw, J. R.; Papavassiliou, J.; Parrinello, C.
1999-04-01
We argue that the massive Yang-Mills model of Kunimasa and Goto, Slavnov, and Cornwall, in which massive gauge vector bosons are introduced in a gauge-invariant way without resorting to the Higgs mechanism, may be useful for studying diffractive scattering of strongly interacting particles. With this motivation, we perform in this model explicit calculations of S-matrix elements between quark states, at the tree level, one loop, and two loops, and discuss issues of renormalizability and unitarity. In particular, it is shown that the S-matrix element for quark scattering is renormalizable at one-loop order, and is only logarithmically non-renormalizable at two loops. The discrepancies in the ultraviolet regime between the one-loop predictions of this model and those of massless QCD are discussed in detail. In addition, some of the similarities and differences between the massive Yang-Mills model and theories with a Higgs mechanism are analyzed at the level of the S matrix. Finally, we briefly discuss the high-energy behavior of the leading order amplitude for quark-quark elastic scattering in the diffractive region. The above analysis sets up the stage for carrying out a systematic computation of the higher order corrections to the two-gluon exchange model of the Pomeron using massive gluons inside quantum loops.
Construction of an effective Yang-Mills Lagrangian with manifest BCJ duality
NASA Astrophysics Data System (ADS)
Tolotti, Mathias; Weinzierl, Stefan
2013-07-01
The BCJ decomposition is a highly non-trivial property of gauge theories. In this paper we systematically construct an effective Lagrangian, whose Feynman rules automatically produce the BCJ numerators. The effective Lagrangian contains non-local terms. The difference between the standard Yang-Mills Lagrangian and the effective Lagrangian simplifies to zero.
Emergent 5-Dimensional Black Hole from Weakly Interacting 4-Dimensional Super Yang-Mills Gas
NASA Astrophysics Data System (ADS)
Rey, Soo-Jong
2005-12-01
We demonstrate five-dimensional anti-de Sitter black hole emerges as dual geometry holographic to weakly interacting N = 4 superconformal Yang-Mills theory. We first note that an ideal probe of the dual geometry is the Yang-Mills instanton, probing point by point in spacetime. We then study instanton moduli space at finite temperature by adopting Hitchin's proposal that geometry of the moduli space is definable by Fisher-Rao ``information geometry''. In Yang-Mills theory, the information metric is measured by a novel class of gauge-invariant, nonlocal operators in the instanton sector. We show that the moduli space metric exhibits (1) asymptotically anti-de Sitter, (2) horizon at radial distance set by the Yang-Mills temperature, and (3) after Wick rotation of the moduli space to the Lorentzian signature, a singularity at the origin. We argue that the dual geometry emerges even for rank of gauge groups of order unity and for weak 't Hooft coupling.
Emergent 5-Dimensional Black Hole from Weakly Interacting 4-Dimensional Super Yang-Mills Gas
Rey, Soo-Jong
2005-12-02
We demonstrate five-dimensional anti-de Sitter black hole emerges as dual geometry holographic to weakly interacting N = 4 superconformal Yang-Mills theory. We first note that an ideal probe of the dual geometry is the Yang-Mills instanton, probing point by point in spacetime. We then study instanton moduli space at finite temperature by adopting Hitchin's proposal that geometry of the moduli space is definable by Fisher-Rao 'information geometry'. In Yang-Mills theory, the information metric is measured by a novel class of gauge-invariant, nonlocal operators in the instanton sector. We show that the moduli space metric exhibits (1) asymptotically anti-de Sitter (2) horizon at radial distance set by the Yang-Mills temperature, and (3) after Wick rotation of the moduli space to the Lorentzian signature, a singularity at the origin. We argue that the dual geometry emerges even for rank of gauge groups of order unity and for weak 't Hooft coupling.
Galactic Rotation Curves from Yang-Mills Gravity
NASA Astrophysics Data System (ADS)
Katz, Daniel
2014-03-01
Yang-Mills Gravity (YMG) is a gauge field theory based on the T4 group in flat spacetime. In its macroscopic limit, it modifies the trajectories of classical objects such that it serves as an alternative to General Relativity (GR). Since YMG is relatively new and unknown, a brief review of the general theory is given and a more comprehensive list of references is provided. In the present work, we find that the Schwarzchild-like solution to YMG supports a term like αr with constant α. This translates into an r-term in the effective gravitational potential of classical objects. We use this modified potential to predict the shape of the rotation curves of spiral galaxies, and then use data from SDSS to constrain α, which seems to be a free parameter in YMG. This work was supported the NSF's GK12 Vibes and Waves Fellowship.
New insights on non-perturbative Yang-Mills
Aguilar, Arlene C.
2010-11-12
In this talk we review some recent results on the infrared properties of the gluon and ghost propagators in pure Yang-Mills theories. These results are obtained from the corresponding Schwinger-Dyson equation formulated in a special truncation scheme, which preserves gauge invariance. The presence of massless poles in the three gluon vertex triggers the generation of a dynamical gluon mass (Schwinger mechanism in d = 4), which gives rise to an infrared finite gluon propagator and ghost dressing function. As a byproduct of this analysis we calculate the Kugo-Ojima function, required for the definition of the non-perturbative QCD effective charge within the pinch technique framework. We show that the numerical solutions of these non-perturbative equations are in very good agreement with the results of SU(3) lattice simulations.
Polyakov loop and gluon quasiparticles in Yang-Mills thermodynamics
NASA Astrophysics Data System (ADS)
Ruggieri, M.; Alba, P.; Castorina, P.; Plumari, S.; Ratti, C.; Greco, V.
2012-09-01
We study the interpretation of lattice data about the thermodynamics of the deconfinement phase of SU(3) Yang-Mills theory, in terms of gluon quasiparticles propagating in a background of a Polyakov loop. A potential for the Polyakov loop, inspired by the strong coupling expansion of the QCD action, is introduced; the Polyakov loop is coupled to transverse gluon quasiparticles by means of a gaslike effective potential. This study is useful to identify the effective degrees of freedom propagating in the gluon medium above the critical temperature. A main general finding is that a dominant part of the phase transition dynamics is accounted for by the Polyakov loop dynamics; hence, the thermodynamics can be described without the need for diverging or exponentially increasing quasiparticle masses as T→Tc, at variance respect to standard quasiparticle models.
NASA Astrophysics Data System (ADS)
Lin, C.-J. David; Ogawa, Kenji; Ramos, Alberto
2015-12-01
We perform the step-scaling investigation of the running coupling constant, using the gradient-flow scheme, in SU(3) gauge theory with twelve massless fermions in the fundamental representation. The Wilson plaquette gauge action and massless unimproved staggered fermions are used in the simulations. Our lattice data are prepared at high accuracy, such that the statistical error for the renormalised coupling, g GF , is at the subpercentage level. To investigate the reliability of the continuum extrapolation, we employ two different lattice discretisations to obtain g GF . For our simulation setting, the corresponding gauge-field averaging radius in the gradient flow has to be almost half of the lattice size, in order to have this extrapolation under control. We can determine the renormalisation group evolution of the coupling up to g GF 2 ˜ 6, before the onset of the bulk phase structure. In this infrared regime, the running of the coupling is significantly slower than the two-loop perturbative prediction, although we cannot draw definite conclusion regarding possible infrared conformality of this theory. Furthermore, we comment on the issue regarding the continuum extrapolation near an infrared fixed point. In addition to adopting the fit ansätz a' la Symanzik for performing this task, we discuss a possible alternative procedure inspired by properties derived from low-energy scale invariance at strong coupling. Based on this procedure, we propose a finite-size scaling method for the renormalised coupling as a means to search for infrared fixed point. Using this method, it can be shown that the behaviour of the theory around g GF 2 ˜ 6 is still not governed by possible infrared conformality.
Scattering equations and matrices: from Einstein to Yang-Mills, DBI and NLSM
NASA Astrophysics Data System (ADS)
Cachazo, Freddy; He, Song; Yuan, Ellis Ye
2015-07-01
The tree-level S-matrix of Einstein's theory is known to have a representation as an integral over the moduli space of punctured spheres localized to the solutions of the scattering equations. In this paper we introduce three operations that can be applied on the integrand in order to produce other theories. Starting in d + M dimensions we use dimensional reduction to construct Einstein-Maxwell with gauge group U(1) M . The second operation turns gravitons into gluons and we call it "squeezing". This gives rise to a formula for all multi-trace mixed amplitudes in Einstein-Yang-Mills. Dimensionally reducing Yang-Mills we find the S-matrix of a special Yang-Mills-Scalar (YMS) theory, and by the squeezing operation we find that of a YMS theory with an additional cubic scalar vertex. A corollary of the YMS formula gives one for a single massless scalar with a ϕ 4 interaction. Starting again from Einstein's theory but in d + d dimensions we introduce a "generalized dimensional reduction" that produces the Born-Infeld theory or a special Galileon theory in d dimensions depending on how it is applied. An extension of Born-Infeld formula leads to one for the Dirac-Born-Infeld (DBI) theory. By applying the same operation to Yang-Mills we obtain the U( N ) non-linear sigma model (NLSM). Finally, we show how the Kawai-Lewellen-Tye relations naturally follow from our formulation and provide additional connections among these theories. One such relation constructs DBI from YMS and NLSM.
New perspectives on an old problem: The bending of light in Yang-Mills gravity
NASA Astrophysics Data System (ADS)
Cottrell, Kazuo Ota; Hsu, Jong-Ping
Yang-Mills gravity with electromagnetism predicts, in the geometric optics limit, a value for the deflection of light by the sun which agrees closely with the reanalysis of Eddington's 1919 optical measurements done in 1979. Einstein's General Theory of Relativity, on the other hand, agrees very closely with measurements of the deflection of electromagnetic waves made in the range of radio frequencies. Since both General Relativity and Yang-Mills gravity with electromagnetism in the geometric optics limit make predictions for the optical region which fall within experimental uncertainty, it becomes important to consider the possibility of the existence of a frequency dependence in the measurement results for the deflection of light, in order to determine which theory more closely describes nature...
A nonperturbative definition of N = 4 Super Yang-Mills by the plane wave matrix model
Shimasaki, Shinji
2008-11-23
We propose a nonperturbative definition of N = 4 Super Yang-Mills(SYM). We realize N = 4 SYM on RxS{sup 3} as the theory around a vacuum of the plane wave matrix model. Our regularization preserves 16 supersymmetries and the gauge symmetry. We perform the one-loop calculation to give evidence that in the continuum limit the superconformal symmetry is restored.
The Polarization Tensor of the Massless Mode in Yang-Mills Thermodynamics
Schwarz, Markus
2011-09-22
We discuss the constraints on energy-momentum transfers in local vertices in the effective theory for the deconfining phase of SU(2) Yang-Mills thermodynamics. Subsequently, we apply these constraints to the computation of the polarization tensor of the massless mode on the one-loop level. The resulting gap equation for the sought-after screening function is solved numerically. We discuss and interpret our results.
The Infrared Behaviour of the Pure Yang-Mills Green Functions
NASA Astrophysics Data System (ADS)
Boucaud, Ph.; Leroy, J. P.; Le Yaouanc, A.; Micheli, J.; Pène, O.; Rodríguez-Quintero, J.
2012-10-01
We review the infrared properties of the pure Yang-Mills correlators and discuss recent results concerning the two classes of low-momentum solutions for them reported in literature, i.e. decoupling and scaling solutions. We will mainly focus on the Landau gauge and pay special attention to the results inferred from the analysis of the Dyson-Schwinger equations of the theory and from " quenched" lattice QCD. The results obtained from properly interplaying both approaches are strongly emphasized.
String scattering in flat space and a scaling limit of Yang-Mills correlators
Okuda, Takuya; Penedones, Joao
2011-04-15
We use the flat space limit of the AdS/CFT correspondence to derive a simple relation between the 2{yields}2 scattering amplitude of massless string states in type IIB superstring theory on ten-dimensional Minkowski space and a scaling limit of the N=4 super Yang-Mills four-point functions. We conjecture that this relation holds nonperturbatively and at arbitrarily high energy.
Topologically massive Yang-Mills: A Hamilton-Jacobi constraint analysis
Bertin, M. C.; Pimentel, B. M.; Valcárcel, C. E.; Zambrano, G. E. R.
2014-04-15
We analyse the constraint structure of the topologically massive Yang-Mills theory in instant-form and null-plane dynamics via the Hamilton-Jacobi formalism. The complete set of hamiltonians that generates the dynamics of the system is obtained from the Frobenius’ integrability conditions, as well as its characteristic equations. As generators of canonical transformations, the hamiltonians are naturally linked to the generator of Lagrangian gauge transformations.
Recombination of H and He in Yang-Mills Gravity
NASA Astrophysics Data System (ADS)
Katz, Daniel
2015-07-01
We investigate some aspects of the thermal history of the early universe according to Yang-Mills Gravity (YMG); a gauge theory of gravity set in flat space-time. Specifically, equations for the ionization fractions of hydrogen and singly ionized helium during the recombination epoch are deduced analytically and then solved numerically. By considering several approximations, we find that the presence of primordial helium and its interaction with Lyman series photons has a much stronger effect on the overall free electron density in YMG than it does in the standard, General Relativity (GR)-based, model. Compared to the standard model, recombination happens over a much larger range of temperatures, although there is still a very sharp temperature of last scattering around 2000 K. The ionization history of the universe is not directly observable, but knowledge of it is necessary for CMB power spectrum calculations. Such calculations will provide another rigorous test of YMG and will be explored in detail in an upcoming paper.
Generalized Yang-Mills actions from Dirac operator determinants
NASA Astrophysics Data System (ADS)
Langmann, Edwin
2001-11-01
We consider the quantum effective action of Dirac fermions on four-dimensional flat Euclidean space coupled to external vector- and axial Yang-Mills fields, i.e., the logarithm of the (regularized) determinant of a Dirac operator on flat R4 twisted by generalized Yang-Mills fields. According to physics folklore, the logarithmic divergent part of this effective action in the pure vector case is proportional to the Yang-Mills action. We present a simple explicit computation proving this fact and extending it to the chiral case. We use an efficient computation method for quantum effective actions which is based on calculation rules for pseudo-differential operators and which yields an expansion of the logarithm of Dirac operators in local and quasi-gauge invariant polynomials of decreasing scaling dimension.
NASA Astrophysics Data System (ADS)
Isobe, Takeshi; Marini, Antonella
2012-06-01
In this paper, we complete the proof of the existence of multiple solutions (and, in particular, non minimal ones), to the ɛ-Dirichlet problem obtained as a variational problem for the SU(2)ɛ-Yang-Mills functional. This is equivalent to proving the existence of multiple solutions to the Dirichlet problem for the SU(2)-Yang-Mills functional with small boundary data. In the first paper of this series this non-compact variational problem is transformed into the finite-dimensional problem of finding the critical points of the function J_{ɛ }({q}), which is essentially the Yang-Mills functional evaluated on the approximate solutions, constructed via a gluing technique. In the present paper, we establish a Morse theory for J_{ɛ }({q}), by means of Ljusternik-Schnirelmann theory, thus complete the proofs of Theorems 1-3 given by Isobe and Marini ["Small coupling limit and multiple solutions to the Dirichlet Problem for Yang-Mills connections in 4 dimensions - Part I," J. Math. Phys. 53, 063706 (2012)], 10.1063/1.4728211.
Yang-Mills radiation in ultrarelativistic nuclear collisions
NASA Astrophysics Data System (ADS)
Gyulassy, M.; McLerran, L.
1997-10-01
The classical Yang-Mills radiation computed in the McLerran-Venugopalan model is shown to be equivalent to the gluon bremsstrahlung distribution to lowest (g6) order in pQCD. The classical distribution is also shown to match smoothly onto the conventional pQCD minijet distribution at a scale k2⊥~χ, characteristic of the initial parton transverse density of the system. The atomic number and energy dependence of χ is computed from available structure function information. The limits of applicability of the classical Yang-Mills description of nuclear collisions at RHIC and LHC energies are discussed.
Some remarks on representations of Yang-Mills algebras
NASA Astrophysics Data System (ADS)
Herscovich, Estanislao
2015-01-01
In this article, we present some new properties of representations of Yang-Mills algebras. We first show that any free Lie algebra with m generators is a quotient of the Yang-Mills algebra 𝔶𝔪(n) on n generators, for n ≥ 2m. We derive from this that any semisimple Lie algebra and even any affine Kac-Moody algebra is a quotient of 𝔶𝔪(n) for n ≥ 4. Combining this with previous results on representations of Yang-Mills algebras given in [Herscovich and Solotar, Ann. Math. 173(2), 1043-1080 (2011)], one may obtain solutions to the Yang-Mills equations by differential operators acting on sections of twisted vector bundles on the affine space of dimension n ≥ 4 associated to representations of any semisimple Lie algebra. We also show that this quotient property does not hold for n = 3, since any morphism of Lie algebras from 𝔶𝔪(3) to 𝔰𝔩(2, k) has in fact solvable image.
Symmetric blocking and renormalization in lattice N=4 super Yang-Mills
NASA Astrophysics Data System (ADS)
Giedt, Joel; Catterall, Simon
2015-04-01
The form of the long distance effective action of the twisted lattice N = 4 super Yang-Mills theory depends on having a real space renormalization group transformation that preserves the original lattice properties, both the symmetries and the geometric interpretation of the fields. We have found such a transformation and have exhibited its behavior through a preliminary Monte Carlo renormalization group calculation. Other results regarding the number of counterterms are also obtained by considering rescalings of the lattice fields. Supported by Department of Energy, Office of Science, Office of High Energy Physics Grants DE-FG02-08ER41575 and SC0009998.
Three-dimensional super Yang-Mills with compressible quark matter
NASA Astrophysics Data System (ADS)
Faedo, Antón F.; Kundu, Arnab; Mateos, David; Pantelidou, Christiana; Tarrío, Javier
2016-03-01
We construct the gravity dual of three-dimensional, SU(N c) super Yang-Mills theory with N f flavors of dynamical quarks in the presence of a non-zero quark density N q. The supergravity solutions include the backreaction of N c color D2-branes and N f flavor D6-branes with N q units of electric flux on their worldvolume. For massless quarks, the solutions depend non-trivially only on the dimensionless combination ρ = N c 2 N q/ λ 2 N f 4 , with λ = g YM 2 N c the 't Hooft coupling, and describe renormalization group flows between the super Yang-Mills theory in the ultraviolet and a non-relativistic theory in the infrared. The latter is dual to a hyperscaling-violating, Lifshitz-like geometry with dynamical and hyperscaling-violating exponents z = 5 and θ = 1, respectively. If ρ ≪ 1 then at intermediate energies there is also an approximate AdS4 region, dual to a conformal Chern-Simons-Matter theory, in which the flow exhibits quasi-conformal dynamics. At zero temperature we compute the chemical potential and the equation of state and extract the speed of sound. At low temperature we compute the entropy density and extract the number of low-energy degrees of freedom. For quarks of non-zero mass M q the physics depends non-trivially on ρ and M q N c /λ N f.
Gravity and Yang-Mills amplitude relations
Bjerrum-Bohr, N. E. J.; Damgaard, Poul H.; Soendergaard, Thomas; FengBo
2010-11-15
Using only general features of the S matrix and quantum field theory, we prove by induction the Kawai-Lewellen-Tye relations that link products of gauge theory amplitudes to gravity amplitudes at tree level. As a bonus of our analysis, we provide a novel and more symmetric form of these relations. We also establish an infinite tower of new identities between amplitudes in gauge theories.
Super Yang-Mills and θ-exact Seiberg-Witten map: absence of quadratic noncommutative IR divergences
NASA Astrophysics Data System (ADS)
Martin, Carmelo P.; Trampetic, Josip; You, Jiangyang
2016-05-01
We compute the one-loop 1PI contributions to all the propagators of the noncommutative (NC) N=1,2,4 super Yang-Mills (SYM) U(1) theories defined by the means of the θ-exact Seiberg-Witten (SW) map in the Wess-Zumino gauge. Then we extract the UV divergent contributions and the noncommutative IR divergences. We show that all the quadratic noncommutative IR divergences add up to zero in each propagator.
Iteration of Planar Amplitudes inMaximally Supersymmetric Yang-Mills Theoryat Three Loops
Bern, Zvi; Dixon, Lance J.; Smirnov, Vladimir A.; /Moscow State U.
2005-05-27
We compute the leading-color (planar) three-loop four-point amplitude of N = 4 supersymmetric Yang-Mills theory in 4 - 2{epsilon} dimensions, as a Laurent expansion about {epsilon} = 0 including the finite terms. The amplitude was constructed previously via the unitarity method, in terms of two Feynman loop integrals, one of which has been evaluated already. Here we use the Mellin-Barnes integration technique to evaluate the Laurent expansion of the second integral. Strikingly, the amplitude is expressible, through the finite terms, in terms of the corresponding one- and two-loop amplitudes, which provides strong evidence for a previous conjecture that higher-loop planar N = 4 amplitudes have an iterative structure. The infrared singularities of the amplitude agree with the predictions of Sterman and Tejeda-Yeomans based on resummation. Based on the four-point result and the exponentiation of infrared singularities, we give an exponentiated ansatz for the maximally helicity-violating n-point amplitudes to all loop orders. The 1/{epsilon}{sup 2} pole in the four-point amplitude determines the soft, or cusp, anomalous dimension at three loops in N = 4 supersymmetric Yang-Mills theory. The result confirms a prediction by Kotikov, Lipatov, Onishchenko and Velizhanin, which utilizes the leading-twist anomalous dimensions in QCD computed by Moch, Vermaseren and Vogt. Following similar logic, we are able to predict a term in the three-loop quark and gluon form factors in QCD.
NASA Astrophysics Data System (ADS)
Isobe, Takeshi; Marini, Antonella
2012-06-01
In this paper and its sequel (Part II), we analyze the space of solutions to the ɛ-Dirichlet problem for the Yang-Mills equations on the four-dimensional disk, for small values of the coupling constant ɛ. These are in 1-1 correspondence with solutions to the Dirichlet problem for Yang-Mills, for small boundary data ɛA0. We establish a Morse theory for this non-compact variational problem and prove the existence of multiple solutions, and, also, non minimal ones. Here, we describe the problem, state the main theorems and do the first part of the proof. This consists in making the problem finite dimensional, by seeking solutions approximated by the connected sum of a minimal solution with an instanton, plus a correction term due to the boundary. By introducing an auxiliary equation, we solve the problem orthogonally to the space of the approximate solutions.
The Yang-Mills Heat Semigroup on Three-Manifolds with Boundary
NASA Astrophysics Data System (ADS)
Charalambous, Nelia; Gross, Leonard
2013-02-01
Long time existence and uniqueness of solutions to the Yang-Mills heat equation is proven over a compact 3-manifold with smooth boundary. The initial data is taken to be a Lie algebra valued connection form in the Sobolev space H 1. Three kinds of boundary conditions are explored, Dirichlet type, Neumann type and Marini boundary conditions. The last is a nonlinear boundary condition, specified by setting the normal component of the curvature to zero on the boundary. The Yang-Mills heat equation is a weakly parabolic nonlinear equation. We use gauge symmetry breaking to convert it to a parabolic equation and then gauge transform the solution of the parabolic equation back to a solution of the original equation. Apriori estimates are developed by first establishing a gauge invariant version of the Gaffney-Friedrichs inequality. A gauge invariant regularization procedure for solutions is also established. Uniqueness holds upon imposition of boundary conditions on only two of the three components of the connection form because of weak parabolicity. This work is motivated by possible applications to quantum field theory.
Subleading terms in the collinear limit of Yang-Mills amplitudes
NASA Astrophysics Data System (ADS)
Stieberger, Stephan; Taylor, Tomasz R.
2015-11-01
For two massless particles i and j, the collinear limit is a special kinematic configuration in which the particles propagate with parallel four-momentum vectors, with the total momentum P distributed as pi = xP and pj = (1 - x) P, so that sij ≡(pi +pj) 2 =P2 = 0. In Yang-Mills theory, if i and j are among N gauge bosons participating in a scattering process, it is well known that the partial amplitudes associated to the (single trace) group factors with adjacent i and j are singular in the collinear limit and factorize at the leading order into (N - 1)-particle amplitudes times the universal, x-dependent Altarelli-Parisi factors. We give a precise definition of the collinear limit and show that at the tree level, the subleading, non-singular terms are related to the amplitudes with a single graviton inserted instead of two collinear gauge bosons. To that end, we argue that in one-graviton Einstein-Yang-Mills amplitudes, the graviton with momentum P can be replaced by a pair of collinear gauge bosons carrying arbitrary momentum fractions xP and (1 - x) P.
Yang-Mills condensate as dark energy: A nonperturbative approach
NASA Astrophysics Data System (ADS)
Donà, Pietro; Marcianò, Antonino; Zhang, Yang; Antolini, Claudia
2016-02-01
Models based on the Yang-Mills condensate (YMC) have been advocated for in the literature and claimed as successful candidates for explaining dark energy. Several variations on this simple idea have been considered, the most promising of which are reviewed here. Nevertheless, the previously attained results relied heavily on the perturbative approach to the analysis of the effective Yang-Mills action, which is only adequate in the asymptotically free limit, and were extended into a regime, the infrared limit, in which confinement is expected. We show that if a minimum of the effective Lagrangian in θ =-Fμν aFa μ ν/2 exists, a YMC forms that drives the Universe toward an accelerated de Sitter phase. The details of the models depend weakly on the specific form of the effective Yang-Mills Lagrangian. Using nonperturbative techniques mutated from the functional renormalization-group procedure, we finally show that the minimum in θ of the effective Lagrangian exists. Thus, a YMC can actually take place. The nonperturbative model has properties similar to the ones in the perturbative model. In the early stage of the Universe, the YMC equation of state has an evolution that resembles the radiation component, i.e., wy→1 /3 . However, in the late stage, wy naturally runs to the critical state with wy=-1 , and the Universe transitions from a matter-dominated into a dark energy dominated stage only at latest time, at a redshift whose value depends on the initial conditions that are chosen while solving the dynamical system.
Yang-Mills localization in warped space
Batell, Brian; Gherghetta, Tony
2007-01-15
We present a mechanism to localize zero mode non-Abelian gauge fields in a slice of AdS{sub 5}. As in the U(1) case, bulk and boundary mass terms allow for a massless mode with an exponential profile that can be localized anywhere in the bulk. However in the non-Abelian extension, the cubic and quartic zero-mode gauge couplings do not match, implying a loss of 4D gauge invariance. We show that the symmetry can be restored at the nonlinear level by considering brane-localized interactions, which are added in a gauge invariant way using boundary kinetic terms. Possible issues related to the scalar sector of the theory, such as strong coupling and ghosts, are also discussed. Our approach is then compared with other localization mechanisms motivated by dilaton gravity and deconstruction. Finally, we show how to localize the scalar component A{sub 5} zero mode anywhere in the bulk which could be relevant in gauge-Higgs unification models.
Yang-Mills solutions and Spin(7)-instantons on cylinders over coset spaces with G 2-structure
NASA Astrophysics Data System (ADS)
Haupt, Alexander S.
2016-03-01
We study {g} -valued Yang-Mills fields on cylinders Zleft(G/Hright)={R}× G/H , where G/H is a compact seven-dimensional coset space with G 2-structure, {g} is the Lie algebra of G, and Z(G/H) inherits a Spin(7)-structure. After imposing a general G-invariance condition, Yang-Mills theory with torsion on Z(G/H) reduces to Newtonian mechanics of a point particle moving in {{R}}^n under the influence of some quartic potential and possibly additional constraints. The kinematics and dynamics depends on the chosen coset space. We consider in detail three coset spaces with nearly parallel G 2-structure and four coset spaces with SU(3)-structure. For each case, we analyze the critical points of the potential and present a range of finite-energy solutions. We also study a higher-dimensional analog of the instanton equation. Its solutions yield G-invariant Spin(7)-instanton configurations on Z(G/H), which are special cases of Yang-Mills configurations with torsion.
Neumann domination for the Yang-Mills heat equation
NASA Astrophysics Data System (ADS)
Charalambous, Nelia; Gross, Leonard
2015-07-01
Long time existence and uniqueness of solutions to the Yang-Mills heat equation have been proven over a compact 3-manifold with boundary for initial data of finite energy. In the present paper, we improve on previous estimates by using a Neumann domination technique that allows us to get much better pointwise bounds on the magnetic field. As in the earlier work, we focus on Dirichlet, Neumann, and Marini boundary conditions. In addition, we show that the Wilson Loop functions, gauge invariantly regularized, converge as the parabolic time goes to infinity.
3D Virtual Reality Check: Learner Engagement and Constructivist Theory
ERIC Educational Resources Information Center
Bair, Richard A.
2013-01-01
The inclusion of three-dimensional (3D) virtual tools has created a need to communicate the engagement of 3D tools and specify learning gains that educators and the institutions, which are funding 3D tools, can expect. A review of literature demonstrates that specific models and theories for 3D Virtual Reality (VR) learning do not exist "per…
Gluon scattering in N = 4 Super Yang-Mills at finite temperature
Ito, Katsushi; Iwasaki, Koh; Nastase, Horatiu
2008-11-23
We extend the AdS/CFT prescription of Alday and Maldacena to finite temperature T, defining an amplitude for gluon scattering in N = 4 Super Yang-Mills at strong coupling from string theory. It is defined by a lightlike 'Wilson loop' living at the horizon of the T-dual to the black hole in AdS space. Unlike the zero temperature case, this is different from the Wilson loop contour defined at the boundary of the AdS black hole metric, thus at nonzero T there is no relation between gluon scattering amplitudes and the Wilson loop. We calculate a gauge theory observable that can be interpreted as the amplitude at strong coupling in both cut-off and generalized dimensional regularization.
Higher spin gravitational couplings: Ghosts in the Yang-Mills detour complex
Gover, A. R.; Hallowell, K.; Waldron, A.
2007-01-15
Gravitational interactions of higher spin fields are generically plagued by inconsistencies. There exists however, a simple framework that couples higher spins to a broad class of gravitational backgrounds (including Ricci flat and Einstein) consistently at the classical level. The model is the simplest example of a Yang-Mills detour complex and has broad mathematical applications, especially to conformal geometry. Even the simplest version of the theory, which couples gravitons, vectors and scalar fields in a flat background is rather rich, providing an explicit setting for detailed analysis of ghost excitations. Its asymptotic scattering states consist of a physical massless graviton, scalar, and massive vector along with a degenerate pair of zero norm photon excitations. Coherent states of the unstable sector do have positive norms, but their evolution is no longer unitary and amplitudes grow with time. The class of models proposed is extremely general and of considerable interest for ghost condensation and invariant theory.
Hadamard States for the Linearized Yang-Mills Equation on Curved Spacetime
NASA Astrophysics Data System (ADS)
Gérard, C.; Wrochna, M.
2015-07-01
We construct Hadamard states for the Yang-Mills equation linearized around a smooth, space-compact background solution. We assume the spacetime is globally hyperbolic and its Cauchy surface is compact or equal . We first consider the case when the spacetime is ultra-static, but the background solution depends on time. By methods of pseudodifferential calculus we construct a parametrix for the associated vectorial Klein-Gordon equation. We then obtain Hadamard two-point functions in the gauge theory, acting on Cauchy data. A key role is played by classes of pseudodifferential operators that contain microlocal or spectral type low-energy cutoffs. The general problem is reduced to the ultra-static spacetime case using an extension of the deformation argument of Fulling, Narcowich and Wald. As an aside, we derive a correspondence between Hadamard states and parametrices for the Cauchy problem in ordinary quantum field theory.
Color-kinematics duality for pure Yang-Mills and gravity at one and two loops
NASA Astrophysics Data System (ADS)
Bern, Zvi; Davies, Scott; Dennen, Tristan; Huang, Yu-tin; Nohle, Josh
2015-08-01
We provide evidence in favor of the conjectured duality between color and kinematics for the case of nonsupersymmetric pure Yang-Mills amplitudes by constructing a form of the one-loop four-point amplitude of this theory that makes the duality manifest. Our construction is valid in any dimension. We also describe a duality-satisfying representation for the two-loop four-point amplitude with identical four-dimensional external helicities. We use these results to obtain corresponding gravity integrands for a theory containing a graviton, dilaton, and antisymmetric tensor, simply by replacing color factors with specified diagram numerators. Using this, we give explicit forms of ultraviolet divergences at one loop in four, six, and eight dimensions, and at two loops in four dimensions.
Hydrodynamics of the Polyakov line in SU(Nc) Yang-Mills
NASA Astrophysics Data System (ADS)
Liu, Yizhuang; Warchoł, Piotr; Zahed, Ismail
2016-02-01
We discuss a hydrodynamical description of the eigenvalues of the Polyakov line at large but finite Nc for Yang-Mills theory in even and odd space-time dimensions. The hydro-static solutions for the eigenvalue densities are shown to interpolate between a uniform distribution in the confined phase and a localized distribution in the de-confined phase. The resulting critical temperatures are in overall agreement with those measured on the lattice over a broad range of Nc, and are consistent with the string model results at Nc = ∞. The stochastic relaxation of the eigenvalues of the Polyakov line out of equilibrium is captured by a hydrodynamical instanton. An estimate of the probability of formation of a Z (Nc) bubble using a piece-wise sound wave is suggested.
Realization of Center Symmetry in Two Adjoint Flavor Large-N Yang-Mills
Catterall, Simon; Galvez, Richard; Unsal, Mithat; /SLAC /Stanford U., Phys. Dept.
2010-08-26
We report on the results of numerical simulations of SU(N) lattice Yang Mills with two flavors of (light) Wilson fermion in the adjoint representation. We analytically and numerically address the question of center symmetry realization on lattices with {Lambda} sites in each direction in the large-N limit. We show, by a weak coupling calculation that, for massless fermions, center symmetry realization is independent of {Lambda}, and is unbroken. Then, we extend our result by conducting simulations at non zero mass and finite gauge coupling. Our results indicate that center symmetry is intact for a range of fermion mass in the vicinity of the critical line on lattices of volume 2{sup 4}. This observation makes it possible to compute infinite volume physical observables using small volume simulations in the limit N {yields} {infinity}, with possible applications to the determination of the conformal window in gauge theories with adjoint fermions.
NASA Astrophysics Data System (ADS)
Ebert, Dietmar; Plefka, Jan; Rodigast, Andreas
2009-02-01
We study the question of a modification of the running gauge coupling of Yang-Mills theories due to quantum gravitational effects in a compact large extra dimensional brane world scenario with a low energy quantum gravity scale. The ADD scenario is applied for a D = d+δ dimensional space-time in which gravitons freely propagate, whereas the non-abelian gauge fields are confined to a d-dimensional brane. The extra dimensions are taken to be toroidal and the transverse fluctuation modes (branons) of the brane are taken into account. On this basis we have calculated the one-loop corrections due to virtual Kaluza-Klein graviton and branon modes for the gluon two- and three-point functions in an effective field theory treatment. Applying momentum cut-off regularization we find that for a d = 4 brane the leading gravitational divergencies cancel irrespective of the number of extra dimensions δ, generalizing previous results in the absence of extra-dimensions. Hence, again the Yang-Mills β-function receives no gravitational corrections at one-loop. This is no longer true in a `universal' extra dimensional scenario with a d > 4 dimensional brane. Moreover, the subleading power-law gravitational divergencies induce higher-dimensional counterterms, which we establish in our scheme. Interestingly, for d = 4 these gravitationally induced counterterms are of the form recently considered in non-abelian Lee-Wick extensions of the standard model—now with a possible mass scale in the TeV range due to the presence of large extra dimensions.
Gravity duals for the Coulomb branch of marginally deformed Script N = 4 Yang-Mills
NASA Astrophysics Data System (ADS)
Hernández, Rafael; Sfetsos, Konstadinos; Zoakos, Dimitrios
2006-03-01
Supergravity backgrounds dual to a class of exactly marginal deformations of Script N = 4 supersymmetric Yang-Mills can be constructed through an SL(2,Bbb R) sequence of T-dualities and coordinate shifts. We apply this transformation to multicenter solutions and derive supergravity backgrounds describing the Coulomb branch of Script N = 1 theories at strong 't Hooft coupling as marginal deformations of Script N = 4 Yang-Mills. For concreteness we concentrate to cases with an SO(4) × SO(2) symmetry preserved by continuous distributions of D3-branes on a disc and on a three-dimensional spherical shell. We compute the expectation value of the Wilson loop operator and confirm the Coulombic behaviour of the heavy quark-antiquark potential in the conformal case. When the vev is turned on we find situations where a complete screening of the potential arises, as well as a confining regime where a linear or a logarithmic potential prevails depending on the ratio of the quark-antiquark separation to the typical vev scale. The spectra of massless excitations on these backgrounds are analyzed by turning the associated differential equations into Schrödinger problems. We find explicit solutions taking into account the entire tower of states related to the reduction of type-IIB supergravity to five dimensions, and hence we go beyond the s-wave approximation that has been considered before for the undeformed case. Arbitrary values of the deformation parameter give rise to the Heun differential equation and the related Inozemtsev integrable system, via a non-standard trigonometric limit as we explicitly demonstrate.
Self-dual Yang-Mills fields in an Einstein universe
Pavlov, A. )
1992-12-01
Instanton solutions of Yang-Mills fields in flat Euclidean space have importance in studying the guage field vacuum. The authors find exact solutions of the self-consistent Einstein-Yang-Mills system of equations. These solutions are self-dual Yang-Mills fields in I[sup 1] [times] S[sup 3] space-time. The self-dual solutions have trivial topology and do not belong to instatons. The results of this study may help in understanding the vacuum structure of the fields under consideration. 4 refs.
Madsen, N.; Steich, D.; Cook, G.; Eme, B.
1995-03-16
The DSI3D-RCS code is designed to numerically evaluate radar cross sections on complex objects by solving Maxwell`s curl equations in the time-domain and in three space dimensions. The code has been designed to run on the new parallel processing computers as well as on conventional serial computers. The DSI3D-RCS code is unique for the following reasons: Allows the use of unstructured non-orthogonal grids, allows a variety of cell or element types, reduces to be the Finite Difference Time Domain (FDTD) method when orthogonal grids are used, preserves charge or divergence locally (and globally), is conditionally stable, is non-dissipative, is accurate for non-orthogonal grids. This method is derived using a Discrete Surface Integration (DSI) technique. As formulated, the DSI technique can be used with essentially arbitrary unstructured grids composed of convex polyhedral cells. This implementation of the DSI algorithm allows the use of unstructured grids that are composed of combinations of non-orthogonal hexahedrons, tetrahedrons, triangular prisms and pyramids. This algorithm reduces to the conventional FDTD method when applied on a structured orthogonal hexahedral grid.
Conformally flat Einstein-Yang-Mills-Higgs solutions with spherical symmetry
Mondaini, R.P.; Santos, N.O.
1983-10-15
We solve the Einstein-Yang-Mills-Higgs equations in a conformally flat metric with spherical symmetry. Two solutions are obtained corresponding to magnetic monopoles in the Higgs vacuum and outside of it.
NASA Astrophysics Data System (ADS)
Grützmann, Melchior; Strobl, Thomas
2015-10-01
Starting with minimal requirements from the physical experience with higher gauge theories, i.e. gauge theories for a tower of differential forms of different form degrees, we discover that all the structural identities governing such theories can be concisely recombined into what is called a Q-structure or, equivalently, an L∞-algebroid. This has many technical and conceptual advantages: complicated higher bundles become just bundles in the category of Q-manifolds in this approach (the many structural identities being encoded in the one operator Q squaring to zero), gauge transformations are generated by internal vertical automorphisms in these bundles and even for a relatively intricate field content the gauge algebra can be determined in some lines and is given by what is called the derived bracket construction. This paper aims equally at mathematicians and theoretical physicists; each more physical section is followed by a purely mathematical one. While the considerations are valid for arbitrary highest form degree p, we pay particular attention to p = 2, i.e. 1- and 2-form gauge fields coupled nonlinearly to scalar fields (0-form fields). The structural identities of the coupled system correspond to a Lie 2-algebroid in this case and we provide different axiomatic descriptions of those, inspired by the application, including e.g. one as a particular kind of a vector-bundle twisted Courant algebroid.
Kinetic energy for the nuclear Yang-Mills collective model
NASA Astrophysics Data System (ADS)
Rosensteel, George; Sparks, Nick
2015-10-01
The Bohr-Mottelson-Frankfurt model of nuclear rotations and quadrupole vibrations is a foundational model in nuclear structure physics. The model, also called the geometrical collective model or simply GCM, has two hidden mathematical structures, one Lie group theoretic and the other differential geometric. Although the group structure has been understood for some time, the geometric structure is a new unexplored feature that shares the same mathematical origin as Yang-Mills, viz., a vector bundle with a non-abelian structure group and a connection. Using the de Rham Laplacian ▵ = * d * d from differential geometry for the kinetic energy extends significantly the physical scope of the GCM model. This Laplacian contains a ``magnetic'' term due to the coupling between base manifold rotational and fiber vorticity degrees of freedom. When the connection specializes to irrotational flow, the Laplacian reduces to the Bohr-Mottelson kinetic energy operator. More generally, the connection yields a moment of inertia that is intermediate between the extremes of irrotational flow and rigid body motion.
Towards a string bit formulation of Script N = 4 super Yang-Mills
NASA Astrophysics Data System (ADS)
Alday, Luis F.; David, Justin R.; Gava, Edi; Narain, Kumar S.
2006-04-01
We show that planar Script N = 4 Yang-Mills theory at zero 't Hooft coupling can be efficiently described in terms of 8 bosonic and 8 fermionic oscillators. We show that these oscillators can serve as world-sheet variables, the string bits, of a discretized string. There is a one to one correspondence between the on shell gauge invariant words of the free Y-M theory and the states in the oscillators' Hilbert space, obeying a local gauge and cyclicity constraints. The planar two-point functions and the three-point functions of all gauge invariant words are obtained by the simple delta-function overlap of the corresponding discrete string world sheet. At first order in the 't Hooft coupling, i.e. at one-loop in the Y-M theory, the logarithmic corrections of the planar two-point and the three-point functions can be incorporated by nearest neighbour interactions among the discretized string bits. In the SU(2) sub-sector we show that the one-loop corrections to the structure constants can be uniquely determined by the symmetries of the bit picture. For the SU(2) sub-sector we construct a gauged, linear, discrete world-sheet model for the oscillators, with only nearest neighbour couplings, which reproduces the anomalous dimension Hamiltonian up to two loops. This model also obeys BMN scaling to all loops.
Massive Yang-Mills for vector and axial-vector spectral functions at finite temperature
NASA Astrophysics Data System (ADS)
Hohler, Paul M.; Rapp, Ralf
2016-05-01
The hadronic mechanism which leads to chiral symmetry restoration is explored in the context of the ρπa1 system using Massive Yang-Mills, a hadronic effective theory which governs their microscopic interactions. In this approach, vector and axial-vector mesons are implemented as gauge bosons of a local chiral gauge group. We have previously shown that this model can describe the experimentally measured vector and axial-vector spectral functions in vacuum. Here, we carry the analysis to finite temperatures by evaluating medium effects in a pion gas and calculating thermal spectral functions. We find that the spectral peaks in both channels broaden along with a noticeable downward mass shift in the a1 spectral peak and negligible movement of the ρ peak. The approach toward spectral function degeneracy is accompanied by a reduction of chiral order parameters, i.e., the pion decay constant and scalar condensate. Our findings suggest a mechanism where the chiral mass splitting induced in vacuum is burned off. We explore this mechanism and identify future investigations which can further test it.
Chaotic dynamics of Yang-Mills field as source of particle couplings and masses
Goldfain, E.
1995-04-01
Dynamics of classical uniform Yang-Mills fields is explored from the viewpoint of universal route to chaos in nonlinear systems. The author shows how the path to nonintegrable behavior of the field is equivalent to the period doubling bifurcation of the logistic map. Universal scalings of the growth parameter yield the full set of Standard Model couplings. Hamiltonian formulation in action-angle variables leads to the physics of phase transitions in classical lattice models. The ground state phase diagram of the system with {open_quotes}antiferromagnetic{close_quotes} interaction is known to exhibit a devil`s staircase form. Linking the staircase attributes to the asymptotic freedom of the gauge coupling yields an universal mass equation. Critical exponent is found to depend on the number of field flavors. Further solving the model for various stability plateaus renders the spectrum of particle masses in the low energy framework. Agreement between theory and experimental results is confirmed for the photon/graviton pair, weak bosons, leptons and quarks. The approach offers an intriguing explanation of the dymanical origin of the physical mass and on the internal hierarchy of particle families.
Dynamics of Euclideanized Einstein-Yang-Mills systems with arbitrary gauge groups
Bertolami, O.; Picken, R.F. ); Maurao, J.M. ); Volobujev, I.P. )
1991-09-30
This paper describes the dynamics of euclideanized SO(4)-symmetric Einstein-Yang-Mills (EYM) systems with arbitrary compact gauge groups K. For the case of SO(n) and SU(n) gauge groups and simple embeddings of the isotropy group in K, the authors show that in the resulting dynamical system, the Friedmann equation decouples from the Yang-Mills equations. Furthermore, the latter can be reduced to a system of two second-order differential equations. This allows the authors to find a broad class of instanton (wormhole) solutions of the EYM equations. These solutions are not afflicted by the giant-wormhole catastrophe.
A Chern-Simons-Yang-Mills-Higgs system in 3+1 dimensions
NASA Astrophysics Data System (ADS)
Navarro-Lérida, Francisco; Radu, Eugen; Tchrakian, D. H.
2014-10-01
We study spherically symmetric solutions of an SO(5) Chern-Simons-Yang-Mills-Higgs system in 3+1 dimensions. The Chern-Simons densities are defined in terms of both Yang-Mills fields and a five-component isomultiplet Higgs. The SO(3) × SO(2) solutions are analyzed in a systematic way, by employing numerical methods. These finite energy configurations possess both electric and magnetic global charges, differing radically, however, from Julia-Zee dyons. When two or more of these Chern-Simons densities are present in the Lagrangian, solutions with vanishing electric charge but nonvanishing electrostatic potential may exist.
Strongly coupled large N spectrum of two matrices coupled via a Yang-Mills interaction
Cook, Martin N. H.; Rodrigues, Joao P.
2008-09-15
We consider the large N spectrum of the quantum mechanical Hamiltonian of two Hermitian matrices coupled via a Yang-Mills interaction. In a framework where one of the matrices is treated exactly and the other is treated as a creation operator impurity, the difference equation associated with the Yang-Mills interaction is derived and solved exactly for two impurities. In this case, the full string tension corrected spectrum depends on two momenta. For a specific value of one of these momenta, the spectrum has the same structure as that of giant magnon bound states. States with general number of impurities are also discussed.
- criticality of AdS black hole in the Einstein-Maxwell-power-Yang-Mills gravity
NASA Astrophysics Data System (ADS)
Zhang, Ming; Yang, Zhan-Ying; Zou, De-Cheng; Xu, Wei; Yue, Rui-Hong
2015-02-01
We study the - critical behaivor of N-dimensional AdS black holes in Einstein-Maxwell-power-Yang-Mills gravity. Our results show the existence of the Van der Waals like small-large black hole phase transitions when taking some special values of charges of the Maxwell and Yang-Mills fields. Further to calculate the critical exponents of the black holes at the critical point, we find that they are the same as those in the Van der Waals liquid-gas system.
5D radiating black holes in Einstein-Yang-Mills-Gauss-Bonnet gravity
NASA Astrophysics Data System (ADS)
Ghosh, S. G.
2011-10-01
We derive nonstatic spherically symmetric solutions of a null fluid, in five dimension (5D), to Einstein-Yang-Mills (EYM) equations with the coupling of Gauss-Bonnet (GB) combination of quadratic curvature terms, namely, 5D EYMGB radiating black hole solution. It is shown that, in the limit, we can recover known radiating black hole solutions. The spherically symmetric known 5D static black hole solutions are also retrieved. The effect of the GB term and Yang-Mills (YM) gauge charge on the structure and location of horizons, of the 5D radiating black hole, is also discussed.
3D RISM theory with fast reciprocal-space electrostatics
Heil, Jochen; Kast, Stefan M.
2015-03-21
The calculation of electrostatic solute-solvent interactions in 3D RISM (“three-dimensional reference interaction site model”) integral equation theory is recast in a form that allows for a computational treatment analogous to the “particle-mesh Ewald” formalism as used for molecular simulations. In addition, relations that connect 3D RISM correlation functions and interaction potentials with thermodynamic quantities such as the chemical potential and average solute-solvent interaction energy are reformulated in a way that calculations of expensive real-space electrostatic terms on the 3D grid are completely avoided. These methodical enhancements allow for both, a significant speedup particularly for large solute systems and a smoother convergence of predicted thermodynamic quantities with respect to box size, as illustrated for several benchmark systems.
3D RISM theory with fast reciprocal-space electrostatics.
Heil, Jochen; Kast, Stefan M
2015-03-21
The calculation of electrostatic solute-solvent interactions in 3D RISM ("three-dimensional reference interaction site model") integral equation theory is recast in a form that allows for a computational treatment analogous to the "particle-mesh Ewald" formalism as used for molecular simulations. In addition, relations that connect 3D RISM correlation functions and interaction potentials with thermodynamic quantities such as the chemical potential and average solute-solvent interaction energy are reformulated in a way that calculations of expensive real-space electrostatic terms on the 3D grid are completely avoided. These methodical enhancements allow for both, a significant speedup particularly for large solute systems and a smoother convergence of predicted thermodynamic quantities with respect to box size, as illustrated for several benchmark systems. PMID:25796231
NASA Astrophysics Data System (ADS)
Challifour, John L.; Timko, Edward J.
2016-06-01
Using a Krein indefinite metric in Fock space, the Hamiltonian for cut-off models of canonically quantized Higgs-Yang-Mills fields interpolating between the Gupta-Bleuler-Feynman and Landau gauges is shown to be essentially maximal accretive and essentially Krein selfadjoint.
Two-loop five-point all-plus helicity Yang-Mills amplitude
NASA Astrophysics Data System (ADS)
Dunbar, David C.; Perkins, Warren B.
2016-04-01
We recompute the recently derived two-loop five-point all-plus Yang-Mills amplitude using unitarity and recursion. Recursion requires augmented recursion to determine the subleading pole. Using these methods, the simplicity of this amplitude is understood.
3D weak lensing: Modified theories of gravity
NASA Astrophysics Data System (ADS)
Pratten, Geraint; Munshi, Dipak; Valageas, Patrick; Brax, Philippe
2016-05-01
Weak lensing (WL) promises to be a particularly sensitive probe of both the growth of large-scale structure as well as the fundamental relation between matter density perturbations and metric perturbations, thus providing a powerful tool with which we may constrain modified theories of gravity (MG) on cosmological scales. Future deep, wide-field WL surveys will provide an unprecedented opportunity to constrain deviations from General Relativity. Employing a 3D analysis based on the spherical Fourier-Bessel expansion, we investigate the extent to which MG theories will be constrained by a typical 3D WL survey configuration including noise from the intrinsic ellipticity distribution σɛ of source galaxies. Here, we focus on two classes of screened theories of gravity: (i) f (R ) chameleon models and (ii) environmentally dependent dilaton models. We use one-loop perturbation theory combined with halo models in order to accurately model the evolution of the matter power spectrum with redshift in these theories. Using a χ2 analysis, we show that for an all-sky spectroscopic survey, the parameter fR0 can be constrained in the range fR0<5 ×10-6(9 ×10-6) for n =1 (2 ) with a 3 σ confidence level. This can be achieved by using relatively low-order angular harmonics ℓ<100 . Higher-order harmonics ℓ>100 could provide tighter constraints but are subject to nonlinear effects, such as baryonic feedback, that must be accounted for. We also employ a Principal Component Analysis in order to study the parameter degeneracies in the MG parameters. The confusion from intrinsic ellipticity correlation and modification of the matter power spectrum at a small scale due to feedback mechanisms is briefly discussed.
Einstein gravity as a 3D conformally invariant theory
NASA Astrophysics Data System (ADS)
Gomes, Henrique; Gryb, Sean; Koslowski, Tim
2011-02-01
We give an alternative description of the physical content of general relativity that does not require a Lorentz invariant spacetime. Instead, we find that gravity admits a dual description in terms of a theory where local size is irrelevant. The dual theory is invariant under foliation-preserving 3-diffeomorphisms and 3D conformal transformations that preserve the 3-volume (for the spatially compact case). Locally, this symmetry is identical to that of Hořava-Lifshitz gravity in the high energy limit but our theory is equivalent to Einstein gravity. Specifically, we find that the solutions of general relativity, in a gauge where the spatial hypersurfaces have constant mean extrinsic curvature, can be mapped to solutions of a particular gauge fixing of the dual theory. Moreover, this duality is not accidental. We provide a general geometric picture for our procedure that allows us to trade foliation invariance for conformal invariance. The dual theory provides a new proposal for the theory space of quantum gravity.
NASA Astrophysics Data System (ADS)
Ivashchuk, V. D.; Melnikov, V. N.
2014-01-01
In the framework of 10-dimensional "Friedmann-Calabi-Yau" cosmology of superstring origin we show that the time variation of either Newton's gravitational constant or Yang-Mills one is unavoidable in the present epoch.
Nonperturbative construction of massive Yang-Mills fields without the Higgs field
NASA Astrophysics Data System (ADS)
Kondo, Kei-Ichi
2013-01-01
In order to understand the so-called decoupling solution for gluon and ghost propagators in QCD, we give a nonperturbative construction of a massive vector field describing a non-Abelian massive spin-one particle, which has the correct physical degrees of freedom and is invariant under a modified Becchi-Rouet-Stora-Tyutin transformation, in a massive Yang-Mills model without the Higgs field, i.e., the Curci-Ferrari model. The resulting non-Abelian massive vector boson field is written by using a nonlinear but local transformation from the original fields in the Curci-Ferrari model. As an application, we write down a local mass term for the Yang-Mills field and a dimension-two condensate, which are exactly invariant under the modified Becchi-Rouet-Stora-Tyutin transformation, Lorentz transformation, and color rotation.
Wang, L. C.
1980-01-01
Bäecklund Transformations (BT) and the derivation of local conservation laws are first reviewed in the classic case of the Sine-Gordon equation. The BT, conservation laws (local and nonlocal), and the inverse-scattering formulation are discussed for the chiral and the self-dual Yang-Mills fields. Their possible applications to the loop formulation for the Yang-Mills fields are mentioned. 55 references, 1 figure.
Number of gauge singlets in supersymmetric Yang-Mills quantum mechanics
Trzetrzelewski, Maciej
2007-10-15
We calculate generating functions for a number of U(N) (SU(N)) singlets in Fock space in several space dimensions. The motivation to find the explicit form of the functions is from the numerical approach applied to supersymmetric Yang-Mills quantum mechanics, based on Fock space. Incidentally the functions give many important insights into the quantum mechanical models based on U(N)(SU(N)) gauge group.
Critical Wavelike Behaviour in Stringy Gravity with Yang Mills Source and Cosmological Constant
Slagter, Reinoud J.; Masselink, Derk
2006-11-03
We investigate numerically the behaviour of the self-gravitating coupled Einstein-Yang-Mills system on an axially symmetric five dimensional space time, with and without the Gauss-Bonnet term. We observe that the critical behaviour at the threshold of black hole formation is present in the 5-dimensional model and depends critically on the value of the cosmological constant and the Gauss-Bonnet coupling.
Reductions of self-dual Yang-Mills fields and classical systems
NASA Astrophysics Data System (ADS)
Chakravarty, S.; Ablowitz, M. J.; Clarkson, P. A.
1990-08-01
One-dimensional reductions of the self-dual Yang-Mills equations yield various classical systems depending on the choice of the Lie algebra associated with the self-dual fields. Included are the Euler-Arnold equations for rigid bodies in n dimensions, the Kovalevskaya top, and a generalization of the Nahm equation which is related to a classical third-order differential equation possessing a movable natural boundary in the complex plane.
An instability of hyperbolic space under the Yang-Mills flow
Gegenberg, Jack; Day, Andrew C.; Liu, Haitao; Seahra, Sanjeev S.
2014-04-15
We consider the Yang-Mills flow on hyperbolic 3-space. The gauge connection is constructed from the frame-field and (not necessarily compatible) spin connection components. The fixed points of this flow include zero Yang-Mills curvature configurations, for which the spin connection has zero torsion and the associated Riemannian geometry is one of constant curvature. We analytically solve the linearized flow equations for a large class of perturbations to the fixed point corresponding to hyperbolic 3-space. These can be expressed as a linear superposition of distinct modes, some of which are exponentially growing along the flow. The growing modes imply the divergence of the (gauge invariant) perturbative torsion for a wide class of initial data, indicating an instability of the background geometry that we confirm with numeric simulations in the partially compactified case. There are stable modes with zero torsion, but all the unstable modes are torsion-full. This leads us to speculate that the instability is induced by the torsion degrees of freedom present in the Yang-Mills flow.
Galaxy clustering in 3D and modified gravity theories
NASA Astrophysics Data System (ADS)
Munshi, D.; Pratten, G.; Valageas, P.; Coles, P.; Brax, P.
2016-02-01
We study Modified Gravity (MG) theories by modelling the redshifted matter power spectrum in a spherical Fourier-Bessel basis. We use a fully non-linear description of the real-space matter power spectrum and include the lowest order redshift-space correction (Kaiser effect), taking into account some additional non-linear contributions. Ignoring relativistic corrections, which are not expected to play an important role for a shallow survey, we analyse two different MG scenarios, namely the generalized Dilaton scalar-tensor theories and the f (R) models in the large curvature regime. We compute the 3D power spectrum C^s_{ℓ}(k_1,k_2) for various such MG theories with and without redshift-space distortions, assuming precise knowledge of background cosmological parameters. Using an all-sky spectroscopic survey with Gaussian selection function \\varphi (r)∝ exp (-{r^2/r^2_0}), r_0=150h^{-1} Mpc, and number density of galaxies bar{N} =10^{-4}Mpc^{-3}, we use a χ2 analysis, and find that the lower order (ℓ ≤ 25) multipoles of C^s_ℓ (k,k^' }) (with radial modes restricted to k < 0.2 h Mpc-1) can constraint the parameter f_{R_0} at a level of 2 × 10-5(3 × 10-5) with 3σ confidence for n = 1(2). Combining constraints from higher ℓ > 25 modes can further reduce the error bars and thus in principle make cosmological gravity constraints competitive with Solar system tests. However this will require an accurate modelling of non-linear redshift-space distortions. Using a tomographic β(a)-m(a) parametrization we also derive constraints on specific parameters describing the Dilaton models of MG.
Structure constants of β deformed super Yang-Mills
NASA Astrophysics Data System (ADS)
David, Justin R.; Sadhukhan, Abhishake
2013-10-01
We study the structure constants of the beta deformed theory perturbatively and at strong coupling. We show that the planar one loop corrections to the structure constants of single trace gauge invariant operators in the scalar sector is determined by the anomalous dimension Hamiltonian. This result implies that 3 point functions of the chiral primaries of the theory do not receive corrections at one loop. We then studythe structure constants at strong coupling using the Lunin-Maldacena geometry. We explicitly construct the supergravity mode dual to the chiral primary with three equal U(1) R-charges in the Lunin-Maldacena geometry. We show that the 3 point function of this supergravity mode with semi-classical states representing two other similar chiral primary states but with large U(1) charges to be independent of the beta deformation and identical to that found in the AdS 5 × S 5 geometry. This together with the one-loop result indicate that these structure constants are protected by a non-renormalization theorem. We also show that three point function of U(1) R-currents with classical massive strings is proportional to the R-charge carried by the string solution. This is in accordance with the prediction of the R-symmetry Ward identity.
Roiban, R.; Tseytlin, A. A.
2008-03-15
We consider folded (S,J) spinning strings in AdS{sub 5}xS{sup 5} (with one spin component in AdS{sub 5} and a one in S{sup 5}) corresponding to the Tr(D{sup S}{phi}{sup J}) operators in the sl(2) sector of the N=4 super Yang-Mills theory in the special scaling limit in which both the string mass {approx}{radical}({lambda})lnS and J are sent to infinity with their ratio fixed. Expanding in the parameter l=(J/{radical}({lambda})lnS) we compute the 2-loop string sigma-model correction to the string energy and show that it agrees with the expression proposed by Alday and Maldacena [J. High Energy Phys. 11 (2007) 019]. We suggest that a resummation of the logarithmic l{sup 2}ln{sup n}l terms is necessary in order to establish an interpolation to the weakly coupled gauge-theory results. In the process, we set up a general framework for the calculation of higher loop corrections to the energy of multispin string configurations. In particular, we find that in addition to the direct 2-loop term in the string energy there is a contribution from lower loop order due to a finite 'renormalization' of the relation between the parameters of the classical solution and the fixed spins, i.e., the charges of the SO(2,4)xSO(6) symmetry.
A New Reduction of the Self-Dual Yang-Mills Equations and its Applications
NASA Astrophysics Data System (ADS)
Zhang, Yufeng; Wang, Yan
2016-07-01
Through imposing on space-time symmetries, a new reduction of the self-dual Yang-Mills equations is obtained for which a Lax pair is established. By a proper exponent transformation, we transform the Lax pair to get a new Lax pair whose compatibility condition gives rise to a set of partial differential equations (PDEs). We solve such PDEs by taking different Lax matrices; we develop a new modified Burgers equation, a generalised type of Kadomtsev-Petviasgvili equation, and the Davey-Stewartson equation, which also generalise some results given by Ablowitz, Chakravarty, Kent, and Newman.
Attractor Solution in Coupled Yang-Mills Field Dark Energy Models
NASA Astrophysics Data System (ADS)
Zhao, Wen
We investigate the attractor solution in the coupled Yang-Mills field dark energy models with the general interaction term, and obtain the constraint equations for the interaction if the attractor solution exists. The research also shows that, if the attractor solution exists, the equation of state of dark energy must evolve from wy > 0 to wy ≤ -1, which is slightly suggested by the observation. At the same time, the total equation of state in the attractor solution is wtot = -1, the universe is a de Sitter expansion, and the cosmic big rip is naturally avoided. These features are all independent of the interacting forms.
One-loop amplitudes in Script N = 4 super Yang-Mills and anomalous dual conformal symmetry
NASA Astrophysics Data System (ADS)
Brandhuber, Andreas; Heslop, Paul; Travaglini, Gabriele
2009-08-01
We discuss what predictions can be made for one-loop superamplitudes in maximally supersymmetric Yang-Mills theory by using anomalous dual conformal symmetry. We show that the anomaly coefficient is a specific combination of two-mass hard and one-mass supercoefficients which appears in the supersymmetric on-shell recursion relations and equals the corresponding tree-level superamplitude. We discuss further novel relations among supercoefficients imposed by the remaining non-anomalous part of the symmetry. In particular, we find that all one-loop supercoefficients, except the four-mass box coefficients, can be expressed as linear combinations of three-mass box coefficients and a particular symmetric combination of two-mass hard coefficients. We check that our equations are explicitly satisfied in the case of one-loop n-point MHV and NMHV amplitudes. As a bonus, we prove the covariance of the NMHV superamplitudes at an arbitrary number of points, extending previous results at n <= 9.
3D Winding Number: Theory and Application to Medical Imaging
Becciu, Alessandro; Fuster, Andrea; Pottek, Mark; van den Heuvel, Bart; ter Haar Romeny, Bart; van Assen, Hans
2011-01-01
We develop a new formulation, mathematically elegant, to detect critical points of 3D scalar images. It is based on a topological number, which is the generalization to three dimensions of the 2D winding number. We illustrate our method by considering three different biomedical applications, namely, detection and counting of ovarian follicles and neuronal cells and estimation of cardiac motion from tagged MR images. Qualitative and quantitative evaluation emphasizes the reliability of the results. PMID:21317978
NASA Astrophysics Data System (ADS)
Yablon, Jay R.
2013-10-01
Evidence is summarized from four recent papers that baryons including protons and neutrons are magnetic monopoles of non-commuting Yang-Mills gauge theories: 1) Protons and neutrons are ``resonant cavities'' with binding energies determined strictly by the masses of the quarks they contain. This is proven true at parts-per million accuracy for each of the 2H, 3H,3He, 4He binding energies and the neutron minus proton mass difference. 2) Respectively, each free proton and neutron contains 7.64 MeV and 9.81 MeV of mass/energy used to confine its quarks. When these nucleons bind, some, never all, of this energy is released and the mass deficit goes into binding. The balance continues to confine quarks. 56Fe releases 99.8429% of this energy for binding, more than any other nuclide. 3) Once we consider the Fermi vev one also finds an entirely theoretical explanation of proton and neutron masses, which also connects within experimental errors to the CKM quark mixing angles. 4) A related GUT explains fermion generation replication based on generator loss during symmetry breaking, and answers Rabi's question ``who ordered this?'' 5) Nuclear physics is governed by combining Maxwell's two classical equations into one equation using non-commuting gauge fields in view of Dirac theory and Fermi-Dirac-Pauli Exclusion. 6) Atoms themselves are core magnetic charges (nucleons) paired with orbital electric charges (electrons and elusive neutrinos), with the periodic table itself revealing an electric/magnetic symmetry of Maxwell's equations often pondered but heretofore unrecognized for a century and a half.
Phase transitions of an anisotropic N=4 super Yang-Mills plasma via holography
NASA Astrophysics Data System (ADS)
Banks, Elliot
2016-07-01
Black hole solutions of type IIB supergravity were previously found that are dual to N=4 supersymmetric Yang-Mills plasma with an anisotropic spatial deformation. In the zero temperature limit, these black holes approach a Liftshitz like scaling solution in the IR. It was recently shown that these black holes are unstable, and at low temperatures there is a new class of black hole solutions that are thermodynamically preferred. We extend this analysis, by considering consistent truncations of the Kaluza-Klein reduction of IIB supergravity on a five-sphere that preserves multiple scalar and U(1) gauge fields. We show that the previously constructed black holes become unstable at low temperatures, and construct new classes of exotic black hole solutions. We study the DC thermo-electric conductivity of these U(1) charged black holes, and find a diverging DC conductivity at zero temperature due to the divergence of the gauge field coupling.
A new phase for the anisotropic N=4 super Yang-Mills plasma
NASA Astrophysics Data System (ADS)
Banks, Elliot; Gauntlett, Jerome P.
2015-09-01
Black hole solutions of type IIB supergravity have been previously constructed that describe the N=4 supersymmetric Yang-Mills plasma with an anisotropic spatial deformation. The zero temperature limit of these black holes approach a Lifshitz-like scaling solution in the infrared. We show that these black holes become unstable at low temperature and we construct a new class of black hole solutions which are thermodynamically preferred. The phase transition is third order and incorporates a spontaneous breaking of the SO(6) global symmetry down to SO(4) × SO(2). The critical exponents for the phase transition are given by ( α, β, γ, δ) = (-1, 1, 1, 2) which differ from the standard mean-field exponents usually seen in holography. At low temperatures the black holes approach a novel kind of scaling behaviour in the far IR with spatial anisotropy and hyperscaling violation. We show that the new ground states are thermal insulators in the direction of the anisotropy.
Pion in the Holographic Model with 5D Yang-Mills Fields
Grigoryan, Hovhannes; Radyushkin, Anatoly
2008-12-01
We study pion in the holographic model of Hirn and Sanz which contains two Yang-Mills fields defined in the background of the sliced AdS space. The infrared boundary conditions imposed on these fields generate the spontaneous breaking of the chiral symmetry down to its vector subgroup. Within the framework of this model, we get an analytic expression for the pion form factor and a compact result for its radius. We also extend the holographic model to include Chern-Simons term which is required to reproduce the appropriate axial anomaly of QCD. As a result, we calculate the anomalous form factor of the pion and predict its Q^2-slope for the kinematics when one of the photons is almost on-shell. We also observe that the anomalous form factor with one real and one virtual photon is given by the same analytic expression as the electromagnetic form factor of a charged pion.
Anisotropic N=4 Super-Yang-Mills Plasma and Its Instabilities
Mateos, David; Trancanelli, Diego
2011-09-02
We present a type-IIB supergravity solution dual to a spatially anisotropic finite-temperature N=4 super-Yang-Mills plasma. The solution is static and completely regular. The full geometry can be viewed as a renormalization group flow from an ultraviolet anti-de Sitter geometry to an infrared Lifshitz-like geometry. The anisotropy can be equivalently understood as resulting from a position-dependent {theta} term or from a nonzero number density of dissolved D7-branes. The holographic stress tensor is conserved and anisotropic. The presence of a conformal anomaly plays an important role in the thermodynamics. The phase diagram exhibits homogeneous and inhomogeneous (i.e., mixed) phases. In some regions the homogeneous phase displays instabilities reminiscent of those of weakly coupled plasmas. We comment on similarities with QCD at finite baryon density and with the phenomenon of cavitation.
Dark energy as a fixed point of the Einstein Yang-Mills Higgs equations
NASA Astrophysics Data System (ADS)
Rinaldi, Massimiliano
2015-10-01
We study the Einstein Yang-Mills Higgs equations in the SO(3) representation on a isotropic and homogeneous flat Universe, in the presence of radiation and matter fluids. We map the equations of motion into an autonomous dynamical system of first-order differential equations and we find the equilibrium points. We show that there is only one stable fixed point that corresponds to an accelerated expanding Universe in the future. In the past, instead, there is an unstable fixed point that implies a stiff-matter domination. In between, we find three other unstable fixed points, corresponding, in chronological order, to radiation domination, to matter domination, and, finally, to a transition from decelerated expansion to accelerated expansion. We solve the system numerically and we confirm that there are smooth trajectories that correctly describe the evolution of the Universe, from a remote past dominated by radiation to a remote future dominated by dark energy, passing through a matter-dominated phase.
Kinematic numerators and a double-copy formula for N=4 super-Yang-Mills residues
NASA Astrophysics Data System (ADS)
Litsey, Sean; Stankowicz, James
2014-07-01
Recent work by Cachazo et al.arXiv:1309.0885 shows that connected prescription residues obey the global identities of N=4 super-Yang-Mills amplitudes. In particular, they obey the Bern-Carrasco-Johansson (BCJ) amplitude identities. Here we offer a new way of interpreting this result via objects that we call residue numerators. These objects behave like the kinematic numerators introduced by BCJ except that they are associated with individual residues. In particular, these new objects satisfy a double-copy formula relating them to the residues appearing in recently discovered analogs of the connected prescription integrals for N=8 supergravity. Along the way, we show that the BCJ amplitude identities are equivalent to the consistency condition that allows kinematic numerators to be expressed as amplitudes using a generalized inverse.
Spherically symmetric self-dual Yang-Mills instantons on curved backgrounds in all even dimensions
Radu, Eugen; Tchrakian, D. H.; Yang Yisong
2008-02-15
We present several different classes of self-dual Yang-Mills instantons in all even d-dimensional backgrounds with Euclidean signature. In d=4p+2 the only solutions we found are on constant curvature dS (de Sitter) and AdS (anti-de Sitter) backgrounds and are evaluated in closed form. In d=4p an interesting class of instantons are given on black hole backgrounds. One class of solutions are (Euclidean) time-independent and spherically symmetric in d-1 dimensions, and the other class are spherically symmetric in all d dimensions. Some of the solutions in the former class are evaluated numerically, all the rest being given in closed form. Analytic proofs of existence covering all numerically evaluated solutions are given. All instantons studied have finite action and vanishing energy momentum tensor and do not disturb the geometry.
Exact solutions of (n+1)-dimensional Yang-Mills equations in curved space-time
Sanchez-Monroy, J.A.; Quimbay, C.J.
2012-09-15
In the context of a semiclassical approach where vectorial gauge fields can be considered as classical fields, we obtain exact static solutions of the SU(N) Yang-Mills equations in an (n+1)-dimensional curved space-time, for the cases n=1,2,3. As an application of the results obtained for the case n=3, we consider the solutions for the anti-de Sitter and Schwarzschild metrics. We show that these solutions have a confining behavior and can be considered as a first step in the study of the corrections of the spectra of quarkonia in a curved background. Since the solutions that we find in this work are valid also for the group U(1), the case n=2 is a description of the (2+1) electrodynamics in the presence of a point charge. For this case, the solution has a confining behavior and can be considered as an application of the planar electrodynamics in a curved space-time. Finally we find that the solution for the case n=1 is invariant under a parity transformation and has the form of a linear confining solution. - Highlights: Black-Right-Pointing-Pointer We study exact static confining solutions of the SU(N) Yang-Mills equations in an (n+1)-dimensional curved space-time. Black-Right-Pointing-Pointer The solutions found are a first step in the study of the corrections on the spectra of quarkonia in a curved background. Black-Right-Pointing-Pointer A expression for the confinement potential in low dimensionality is found.
MOM3D method of moments code theory manual
NASA Astrophysics Data System (ADS)
Shaeffer, John F.
1992-03-01
MOM3D is a FORTRAN algorithm that solves Maxwell's equations as expressed via the electric field integral equation for the electromagnetic response of open or closed three dimensional surfaces modeled with triangle patches. Two joined triangles (couples) form the vector current unknowns for the surface. Boundary conditions are for perfectly conducting or resistive surfaces. The impedance matrix represents the fundamental electromagnetic interaction of the body with itself. A variety of electromagnetic analysis options are possible once the impedance matrix is computed including backscatter radar cross section (RCS), bistatic RCS, antenna pattern prediction for user specified body voltage excitation ports, RCS image projection showing RCS scattering center locations, surface currents excited on the body as induced by specified plane wave excitation, and near field computation for the electric field on or near the body.
MOM3D method of moments code theory manual
NASA Technical Reports Server (NTRS)
Shaeffer, John F.
1992-01-01
MOM3D is a FORTRAN algorithm that solves Maxwell's equations as expressed via the electric field integral equation for the electromagnetic response of open or closed three dimensional surfaces modeled with triangle patches. Two joined triangles (couples) form the vector current unknowns for the surface. Boundary conditions are for perfectly conducting or resistive surfaces. The impedance matrix represents the fundamental electromagnetic interaction of the body with itself. A variety of electromagnetic analysis options are possible once the impedance matrix is computed including backscatter radar cross section (RCS), bistatic RCS, antenna pattern prediction for user specified body voltage excitation ports, RCS image projection showing RCS scattering center locations, surface currents excited on the body as induced by specified plane wave excitation, and near field computation for the electric field on or near the body.
NASA Astrophysics Data System (ADS)
Stoecker, Horst; Zhou, Kai; Schramm, Stefan; Senzel, Florian; Greiner, Carsten; Beitel, Maxim; Gallmeister, Kai; Gorenstein, Mark; Mishustin, Igor; Vasak, David; Steinheimer, Jan; Struckmeier, Juergen; Vovchenko, Volodymyr; Satarov, Leonid; Xu, Zhe; Zhuang, Pengfei; Csernai, Laszlo P.; Sinha, Bikash; Raha, Sibaji; Sándor Biró, Tamás; Panero, Marco
2016-08-01
The early stage of a high multiplicity pp, pA and AA collisions is represented by a nearly quarkless, hot, deconfined pure gluon plasma. According to pure Yang-Mills lattice gauge theory, this hot pure glue matter undergoes, at a high temperature, {T}c=270 {{MeV}}, a first-order phase transition into a confined Hagedorn glueball fluid. This new scenario should be characterized by a suppression of high p T photons and dileptons, baryon suppression and enhanced strange meson production. We propose to observe this newly predicted class of events at the Large Hadron Collider and the Relativistic Heavy-Ion Collider.
Some initial theory and practice exploration for 3D digital sea-route
NASA Astrophysics Data System (ADS)
Sui, Haigang; Zhang, Anmin; Wang, Juan; Hua, Li
2005-10-01
The safe navigation of Yangtse River is one of important system engineering. Traditional 2D electronic river map is very effective to ensure safe navigation. However, it is not visual and many kinds of complex analysis are difficult in 2D environment and they only can be processed in 3D situation. So the 3D digital sea-route is very important and urgent to realize digital and intelligent safe navigation. Aiming at this, a whole framework for 3D digital sea-route is first introduced. Under this framework, integrated services from sea-route data colleting, data storing, data management, data processing, data query and analysis, to data distribution and application are illustrated. And some key theory and techniques including automatic sounding creation and processing techniques, the sea-route 3D model production art based on GIS & CAD, the organization and management techniques of multi-source, multi-type, multi-scale data, the 3D dynamic visualization techniques for huge data, the 2D & 3D mutually display and analysis techniques are discussed in detail. Based on these theory and techniques, a system named TEAVIS for 3D digital sea-route is developed. This system is applied in the Marine Safety Administration Bureau of Tianjin City and the Yangtse River Sea-route Bureau and obtained good evaluation.
Daniel Heineman Prize: QCD, strings and black holes: A duality between gravity and field theory
NASA Astrophysics Data System (ADS)
Maldacena, Juan
2007-04-01
We discuss Yang Mills theory with a large number of colors. In this limit it becomes a theory of strings. We describe the string theory associated to the most supersymmetric version of Yang Mills theory. These strings live in a ten dimensional curved space. Thus supersymmetric Yang Mills theory is related to the ordinary ten dimensional superstring theory which describes quantum gravity. We will review some results in this area and discuss some recent developments. We will also discuss the implications for black hole entropy and the black hole information puzzle.
Rodrigues, Joao P.; Zaidi, Alia
2010-10-15
We derive a planar sector of the large N nonsupersymmetric background of the quantum mechanical Hamiltonian of two Hermitian matrices coupled via a Yang-Mills interaction, in terms of the density of eigenvalues of one of the matrices. This background satisfies an implicit nonlinear integral equation, with a perturbative small coupling expansion and a solvable large coupling solution, which is obtained. The energy of system and the expectation value of several correlators are obtained in this strong coupling limit. They are free of infrared divergences.
Two-loop five-point amplitudes of super Yang-Mills and supergravity in pure spinor superspace
NASA Astrophysics Data System (ADS)
Mafra, Carlos R.; Schlotterer, Oliver
2015-10-01
Supersymmetric integrands for the two-loop five-point amplitudes in tendimensional super Yang-Mills and type II supergravity are proposed. The kinematic numerators are manifestly local and satisfy the duality between color and kinematics described by Bern, Carrasco and Johansson. Our results are expected to reproduce the integrated two-loop amplitudes in dimensions D < 7. The UV divergence in the critical dimension D = 7 matches the low-energy limit of the corresponding superstring amplitudes and is written in terms of SYM tree amplitudes.
Dynamic scattering theory for dark-field electron holography of 3D strain fields.
Lubk, Axel; Javon, Elsa; Cherkashin, Nikolay; Reboh, Shay; Gatel, Christophe; Hÿtch, Martin
2014-01-01
Dark-field electron holography maps strain in crystal lattices into reconstructed phases over large fields of view. Here we investigate the details of the lattice strain-reconstructed phase relationship by applying dynamic scattering theory both analytically and numerically. We develop efficient analytic linear projection rules for 3D strain fields, facilitating a straight-forward calculation of reconstructed phases from 3D strained materials. They are used in the following to quantify the influence of various experimental parameters like strain magnitude, specimen thickness, excitation error and surface relaxation. PMID:24012934
Infrared analysis of propagators and vertices of Yang-Mills theory in Landau and Coulomb gauge
Schleifenbaum, W.; Leder, M.; Reinhardt, H.
2006-06-15
The infrared behavior of gluon and ghost propagators, ghost-gluon vertex, and three-gluon vertex is investigated for both the covariant Landau and the noncovariant Coulomb gauge. Assuming infrared ghost dominance, we find a unique infrared exponent in the d=4 Landau gauge, while in the d=3+1 Coulomb gauge we find two different infrared exponents. We also show that a finite dressing of the ghost-gluon vertex has no influence on the infrared exponents. Finally, we determine the infrared behavior of the three-gluon vertex analytically and calculate it numerically at the symmetric point in the Coulomb gauge.
Renormalization of composite operators in Yang-Mills theories using a general covariant gauge
Collins, J.C.; Scalise, R.J. )
1994-09-15
Essential to QCD applications of the operator product expansion, etc., is a knowledge of those operators that mix with gauge-invariant operators. A standard theorem asserts that the renormalization matrix is triangular: Gauge-invariant operators have alien'' gauge-variant operators among their counterterms, but, with a suitably chosen basis, the necessary alien operators have only themselves as counterterms. Moreover, the alien operators are supposed to vanish in physical matrix elements. A recent calculation by Hamberg and van Neerven apparently contradicts these results. By explicit calculations with the energy-momentum tensor, we show that the problems arise because of subtle infrared singularities that appear when gluonic matrix elements are taken on shell at zero momentum transfer.
Pomeron Eigenvalue at Three Loops in N=4 Supersymmetric Yang-Mills Theory.
Gromov, Nikolay; Levkovich-Maslyuk, Fedor; Sizov, Grigory
2015-12-18
We obtain an analytical expression for the next-to-next-to-leading order of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) Pomeron eigenvalue in planar N=4 SYM using quantum spectral curve (QSC) integrability-based method. The result is verified with more than 60-digit precision using the numerical method developed by us in a previous paper [N. Gromov, F. Levkovich-Maslyuk, and G. Sizov, arXiv:1504.06640]. As a by-product, we developed a general analytic method of solving the QSC perturbatively. PMID:26722913
On the Infrared Behaviour of Landau Gauge Yang-Mills Theory with Differently Charged Scalar Fields
Alkofer, Reinhard; Maas, Axel; Macher, Veronika; Fister, Leonard
2011-05-23
Recently it has been argued that infrared singularities of the quark-gluon vertex of Landau gauge QCD can confine static quarks via a linear potential. It is demonstrated that the same mechanism also may confine fundamental scalar fields. This opens the possibility that within functional approaches static confinement is an universal property of the gauge sector even though it is formally represented in the functional equations of the matter sector. The colour structure of Dyson-Schwinger equations for fundamental and adjoint scalar fields is determined for the gauge groups SU(N) and G(2) exhibiting interesting cancellations purely due to colour algebra.
Lattice evidence for the family of decoupling solutions of Landau gauge Yang-Mills theory
NASA Astrophysics Data System (ADS)
Sternbeck, André; Müller-Preussker, Michael
2013-10-01
We show that the low-momentum behavior of the lattice Landau-gauge gluon and ghost propagators is sensitive to the lowest non-trivial eigenvalue (λ1) of the Faddeev-Popov operator. If the gauge fixing favors Gribov copies with small λ1 the ghost dressing function rises more rapidly towards zero momentum than on copies with large λ1. This effect is seen for momenta below 1 GeV, and interestingly also for the gluon propagator at momenta below 0.2 GeV: For large λ1 the gluon propagator levels out to a lower value at zero momentum than for small λ1. For momenta above 1 GeV no dependence on Gribov copies is seen. Although our data is only for a single lattice size and spacing, a comparison to the corresponding (decoupling) solutions from the DSE/FRGE study of Fischer, Maas and Pawlowski (2009) [22] yields already a good qualitative agreement.
Quantification of Spatial Parameters in 3D Cellular Constructs Using Graph Theory
Lund, A. W.; Bilgin, C. C.; Hasan, M. A.; McKeen, L. M.; Stegemann, J. P.; Yener, B.; Zaki, M. J.; Plopper, G. E.
2009-01-01
Multispectral three-dimensional (3D) imaging provides spatial information for biological structures that cannot be measured by traditional methods. This work presents a method of tracking 3D biological structures to quantify changes over time using graph theory. Cell-graphs were generated based on the pairwise distances, in 3D-Euclidean space, between nuclei during collagen I gel compaction. From these graphs quantitative features are extracted that measure both the global topography and the frequently occurring local structures of the “tissue constructs.” The feature trends can be controlled by manipulating compaction through cell density and are significant when compared to random graphs. This work presents a novel methodology to track a simple 3D biological event and quantitatively analyze the underlying structural change. Further application of this method will allow for the study of complex biological problems that require the quantification of temporal-spatial information in 3D and establish a new paradigm in understanding structure-function relationships. PMID:19920859
NASA Astrophysics Data System (ADS)
Killingback, T. P.
1991-05-01
We define a two-dimensional topological Yang-Mills theory for an arbitrary compact simple Lie group. This theory is defined in terms of intersection theory on the moduli space of flat connections on a two-dimensional surface and corresponds physically to a two-dimensional reduction and truncation of four-dimensional topological Yang-Mills theory. Two-dimensional topological Yang-Mills theory defines a topological matter system and may be naturally coupled to two-dimensional topological gravity. This topological Yang-Mills theory is also closely related to Chern-Simons gauge theory in 2 + 1 dimensions. We also discuss a relation between SL (2, R) Chern-Simons theory and two-dimensional topological gravity.
On higher derivatives in 3D gravity and higher-spin gauge theories
Bergshoeff, Eric A. Hohm, Olaf Townsend, Paul K.
2010-05-15
The general second-order massive field equations for arbitrary positive integer spin in three spacetime dimensions, and their 'self-dual' limit to first-order equations, are shown to be equivalent to gauge-invariant higher-derivative field equations. We recover most known equivalences for spins 1 and 2, and find some new ones. In particular, we find a non-unitary massive 3D gravity theory with a 5th order term obtained by contraction of the Ricci and Cotton tensors; this term is part of an N=2 super-invariant that includes the 'extended Chern-Simons' term of 3D electrodynamics. We also find a new unitary 6th order gauge theory for 'self-dual' spin 3.
Equations on knot polynomials and 3d/5d duality
Mironov, A.; Morozov, A.
2012-09-24
We briefly review the current situation with various relations between knot/braid polynomials (Chern-Simons correlation functions), ordinary and extended, considered as functions of the representation and of the knot topology. These include linear skein relations, quadratic Plucker relations, as well as 'differential' and (quantum) A-polynomial structures. We pay a special attention to identity between the A-polynomial equations for knots and Baxter equations for quantum relativistic integrable systems, related through Seiberg-Witten theory to 5d super-Yang-Mills models and through the AGT relation to the q-Virasoro algebra. This identity is an important ingredient of emerging a 3d- 5d generalization of the AGT relation. The shape of the Baxter equation (including the values of coefficients) depend on the choice of the knot/braid. Thus, like the case of KP integrability, where (some, so far torus) knots parameterize particular points of the Universal Grassmannian, in this relation they parameterize particular points in the moduli space of many-body integrable systems of relativistic type.
Twisted 3D N=4 supersymmetric YM on deformed A{sub 3}{sup *} lattice
Saidi, El Hassan
2014-01-15
We study a class of twisted 3D N=4 supersymmetric Yang-Mills (SYM) theory on particular 3-dimensional lattice L{sub 3D} formally denoted as L{sub 3D}{sup su{sub 3}×u{sub 1}} and given by non-trivial fibration L{sub 1D}{sup u{sub 1}}×L{sub 2D}{sup su{sub 3}} with base L{sub 2D}{sup su{sub 3}}=A{sub 2}{sup *}, the weight lattice of SU(3). We first, develop the twisted 3D N=4 SYM in continuum by using superspace method where the scalar supercharge Q is manifestly exhibited. Then, we show how to engineer the 3D lattice L{sub 3D}{sup su{sub 3}×u{sub 1}} that host this theory. After that we build the lattice action S{sub latt} invariant under the following three points: (i) U(N) gauge invariance, (ii) BRST symmetry, (iii) the S{sub 3} point group symmetry of L{sub 3D}{sup su{sub 3}×u{sub 1}}. Other features such as reduction to twisted 2D supersymmetry with 8 supercharges living on L{sub 2D}≡L{sub 2D}{sup su{sub 2}×u{sub 1}}, the extension to twisted maximal 5D SYM with 16 supercharges on lattice L{sub 5D}≡L{sub 5D}{sup su{sub 4}×u{sub 1}} as well as the relation with known results are also given.
NASA Astrophysics Data System (ADS)
Mamo, Kiminad A.
2016-08-01
Using AdS /CFT correspondence, we find that a massless quark moving at the speed of light v =1 , in arbitrary direction, through a strongly coupled N =4 super Yang-Mills (SYM) vacuum at T =0 , in the presence of strong magnetic field B , loses its energy at a rate linearly dependent on B , i.e., d/E d t =-√{λ/} 6 π B . We also show that a heavy quark of mass M ≠0 moving at near the speed of light v2=v*2=1 -4/π2T2 B ≃1 , in arbitrary direction, through a strongly coupled N =4 SYM plasma at finite temperature T ≠0 , in the presence of strong magnetic field B ≫T2, loses its energy at a rate linearly dependent on B , i.e., d/E d t =-√{λ/}6 π B v*2≃-√{λ/}6 π B . Moreover, we argue that, in the strong magnetic field B ≫T2 (IR) regime, N =4 SYM and adjoint QCD theories (when the adjoint QCD theory has four flavors of Weyl fermions and is at its conformal IR fixed point λ =λ*) have the same microscopic degrees of freedom (i.e., gluons and lowest Landau levels of Weyl fermions) even though they have quite different microscopic degrees of freedom in the UV when we consider higher Landau levels. Therefore, in the strong magnetic field B ≫T2 (IR) regime, the thermodynamic and hydrodynamic properties of N =4 SYM and adjoint QCD plasmas, as well as the rates of energy loss of a quark moving through the plasmas, should be the same.
NASA Astrophysics Data System (ADS)
Bouta, Hara; Paraskeva, Fotini
2013-03-01
Research spanning two decades shows that there is a continuing development of 3D virtual worlds and investment in such environments for educational purposes. Research stresses the need for these environments to be well-designed and for suitable pedagogies to be implemented in the teaching practice in order for these worlds to be fully effective. To this end, we propose a pedagogical framework based on the cognitive apprenticeship for deriving principles and guidelines to inform the design, development and use of a 3D virtual environment. This study examines how the use of a 3D virtual world facilitates the teaching of mathematics in primary education by combining design principles and guidelines based on the Cognitive Apprenticeship Theory and the teaching methods that this theory introduces. We focus specifically on 5th and 6th grade students' engagement (behavioral, affective and cognitive) while learning fractional concepts over a period of two class sessions. Quantitative and qualitative analyses indicate considerable improvement in the engagement of the students who participated in the experiment. This paper presents the findings regarding students' cognitive engagement in the process of comprehending basic fractional concepts - notoriously hard for students to master. The findings are encouraging and suggestions are made for further research.
Kalnins, E.G.; Kress, J.M.; Miller, W. Jr.
2006-04-15
This article is one of a series that lays the groundwork for a structure and classification theory of second order superintegrable systems, both classical and quantum, in conformally flat spaces. In the first part of the article we study the Staeckel transform (or coupling constant metamorphosis) as an invertible mapping between classical superintegrable systems on different three-dimensional spaces. We show first that all superintegrable systems with nondegenerate potentials are multiseparable and then that each such system on any conformally flat space is Staeckel equivalent to a system on a constant curvature space. In the second part of the article we classify all the superintegrable systems that admit separation in generic coordinates. We find that there are eight families of these systems.
Transfer of learning between 2D and 3D sources during infancy: Informing theory and practice
Barr, Rachel
2010-01-01
The ability to transfer learning across contexts is an adaptive skill that develops rapidly during early childhood. Learning from television is a specific instance of transfer of learning between a 2-Dimensional (2D) representation and a 3-Dimensional (3D) object. Understanding the conditions under which young children might accomplish this particular kind of transfer is important because by 2 years of age 90% of US children are viewing television on a daily basis. Recent research shows that children can imitate actions presented on television using the corresponding real-world objects, but this same research also shows that children learn less from television than they do from live demonstrations until they are at least 3 years old; termed the video deficit effect. At present, there is no coherent theory to account for the video deficit effect; how learning is disrupted by this change in context is poorly understood. The aims of the present review are (1) to review the conditions under which children transfer learning between 2D images and 3D objects during early childhood, and (2) to integrate developmental theories of memory processing into the transfer of learning from media literature using Hayne’s (2004) developmental representational flexibility account. The review will conclude that studies on the transfer of learning between 2D and 3D sources have important theoretical implications for general developmental theories of cognitive development, and in particular the development of a flexible representational system, as well as policy implications for early education regarding the potential use and limitations of media as effective teaching tools during early childhood. PMID:20563302
Deconfinement Phase Transition in a 3D Nonlocal U(1) Lattice Gauge Theory
Arakawa, Gaku; Ichinose, Ikuo; Matsui, Tetsuo; Sakakibara, Kazuhiko
2005-06-03
We introduce a 3D compact U(1) lattice gauge theory having nonlocal interactions in the temporal direction, and study its phase structure. The model is relevant for the compact QED{sub 3} and strongly correlated electron systems like the t-J model of cuprates. For a power-law decaying long-range interaction, which simulates the effect of gapless matter fields, a second-order phase transition takes place separating the confinement and deconfinement phases. For an exponentially decaying interaction simulating matter fields with gaps, the system exhibits no signals of a second-order transition.
Structure Theory for Extended Kepler-Coulomb 3D Classical Superintegrable Systems
NASA Astrophysics Data System (ADS)
Kalnins, Ernie G.; Miller, Willard, Jr.
2012-06-01
The classical Kepler-Coulomb system in 3 dimensions is well known to be 2nd order superintegrable, with a symmetry algebra that closes polynomially under Poisson brackets. This polynomial closure is typical for 2nd order superintegrable systems in 2D and for 2nd order systems in 3D with nondegenerate (4-parameter) potentials. However the degenerate 3-parameter potential for the 3D extended Kepler-Coulomb system (also 2nd order superintegrable) is an exception, as its quadratic symmetry algebra doesn't close polynomially. The 3D 4-parameter potential for the extended Kepler-Coulomb system is not even 2nd order superintegrable. However, Verrier and Evans (2008) showed it was 4th order superintegrable, and Tanoudis and Daskaloyannis (2011) showed that in the quantum case, if a second 4th order symmetry is added to the generators, the double commutators in the symmetry algebra close polynomially. Here, based on the Tremblay, Turbiner and Winternitz construction, we consider a! n infinite class of classical extended Kepler-Coulomb 3- and 4-parameter systems indexed by a pair of rational numbers (k1,k2) and reducing to the usual systems when k1=k2=1. We show these systems to be superintegrable of arbitrarily high order and work out explicitly the structure of the symmetry algebras determined by the 5 basis generators we have constructed. We demonstrate that the symmetry algebras close rationally; only for systems admitting extra discrete symmetries is polynomial closure achieved. Underlying the structure theory is the existence of raising and lowering constants of the motion, not themselves polynomials in the momenta, that can be employed to construct the polynomial symmetries and their structure relations.
Renormalized Polyakov loop in the deconfined phase of SU(N) gauge theory and gauge-string duality.
Andreev, Oleg
2009-05-29
We use gauge-string duality to analytically evaluate the renormalized Polyakov loop in pure Yang-Mills theories. For SU(3), the result is in quite good agreement with lattice simulations for a broad temperature range. PMID:19519096
A dispersion minimizing scheme for the 3-D Helmholtz equation based on ray theory
NASA Astrophysics Data System (ADS)
Stolk, Christiaan C.
2016-06-01
We develop a new dispersion minimizing compact finite difference scheme for the Helmholtz equation in 2 and 3 dimensions. The scheme is based on a newly developed ray theory for difference equations. A discrete Helmholtz operator and a discrete operator to be applied to the source and the wavefields are constructed. Their coefficients are piecewise polynomial functions of hk, chosen such that phase and amplitude errors are minimal. The phase errors of the scheme are very small, approximately as small as those of the 2-D quasi-stabilized FEM method and substantially smaller than those of alternatives in 3-D, assuming the same number of gridpoints per wavelength is used. In numerical experiments, accurate solutions are obtained in constant and smoothly varying media using meshes with only five to six points per wavelength and wave propagation over hundreds of wavelengths. When used as a coarse level discretization in a multigrid method the scheme can even be used with down to three points per wavelength. Tests on 3-D examples with up to 108 degrees of freedom show that with a recently developed hybrid solver, the use of coarser meshes can lead to corresponding savings in computation time, resulting in good simulation times compared to the literature.
Symmetries of the 4D self-dual Yang-Mills equation and the reduction to the 2D KdV equation
HoSeong La )
1992-04-01
The Lie-point and the Lie-Baecklund symmetries of 4D self-dual Yang-Mills equation are investigated as those of differential equations. The Lie-point symmetry is nothing but the gauge symmetry at the level of field equation, but the Lie-Baecklund symmetries are new. In particular, by the symmetry reduction to KdV equation in 2D the corresponding Lie-Baecklund symmetries which reduce to the isospectral symmetries or to the nonisospectral symmetries are identified. Some speculations on the existence of the self-dual Yang-Mills hierarchy as well as the derivation of the 4D analogue of the string equation of the nonperturbative 2D quantum gravity are given.
NASA Astrophysics Data System (ADS)
Vacaru, Sergiu I.; Veliev, Elşen Veli; Yazici, Enis
2014-09-01
We show that geometric techniques can be elaborated and applied for constructing generic off-diagonal exact solutions in f(R, T)-modified gravity for systems of gravitational-Yang-Mills-Higgs equations. The corresponding classes of metrics and generalized connections are determined by generating and integration functions which depend, in general, on all space and time coordinates and may possess, or not, Killing symmetries. For nonholonomic constraints resulting in Levi-Civita configurations, we can extract solutions of the Einstein-Yang-Mills-Higgs equations. We show that the constructions simplify substantially for metrics with at least one Killing vector. Some examples of exact solutions describing generic off-diagonal modifications to black hole/ellipsoid and solitonic configurations are provided and analyzed.
Wilson loops in supersymmetric gauge theories
NASA Astrophysics Data System (ADS)
Pestun, Vasily
This thesis is devoted to several exact computations in four-dimensional supersymmetric gauge field theories. In the first part of the thesis we prove conjecture due to Erickson-Semenoff-Zarembo and Drukker-Gross which relates supersymmetric circular Wilson loop operators in the N = 4 supersymmetric Yang-Mills theory with a Gaussian matrix model. We also compute the partition function and give a new matrix model formula for the expectation value of a supersymmetric circular Wilson loop operator for the pure N = 2 and the N* = 2 supersymmetric Yang-Mills theory on a four-sphere. Circular supersymmetric Wilson loops in four-dimensional N = 2 superconformal gauge theory are treated similarly. In the second part we consider supersymmetric Wilson loops of arbitrary shape restricted to a two-dimensional sphere in the four-dimensional N = 4 supersymmetric Yang-Mills theory. We show that expectation value for these Wilson loops can be exactly computed using a two-dimensional theory closely related to the topological two-dimensional Higgs-Yang-Mills theory, or two-dimensional Yang-Mills theory for the complexified gauge group.
NASA Astrophysics Data System (ADS)
Navarro-Lérida, Francisco; Tchrakian, D. H.
2015-05-01
We study spherically symmetric finite energy solutions of two Higgs-Chern-Simons-Yang-Mills-Higgs (HCS-YMH) models in 3+1 dimensions, one with gauge group SO(5) and the other with SU(3). The Chern-Simons (CS) densities are defined in terms of both the Yang-Mills (YM) and Higgs fields and the choice of the two gauge groups is made so that they do not vanish. The solutions of the SO(5) model carry only electric charge and zero magnetic charge, while the solutions of the SU(3) model are dyons carrying both electric and magnetic charges like the Julia-Zee (JZ) dyon. Unlike the latter, however, the electric charge in both models receives an important contribution from the CS dynamics. We pay special attention to the relation between the energies and charges of these solutions. In contrast with the electrically charged JZ dyon of the Yang-Mills-Higgs (YMH) system, whose mass is larger than that of the electrically neutral (magnetic monopole) solutions, the masses of the electrically charged solutions of our HCS-YMH models can be smaller than their electrically neutral counterparts in some parts of the parameter space. To establish this is the main task of this work, which is performed by constructing the HCS-YMH solutions numerically. In the case of the SU(3) HCS-YMH, we have considered the question of angular momentum and it turns out that it vanishes.
Gale, Charles; Jeon, Sangyong; Schenke, Björn; Tribedy, Prithwish; Venugopalan, Raju
2013-01-01
Anisotropic flow coefficients v(1)-v(5) in heavy ion collisions are computed by combining a classical Yang-Mills description of the early time Glasma flow with the subsequent relativistic viscous hydrodynamic evolution of matter through the quark-gluon plasma and hadron gas phases. The Glasma dynamics, as realized in the impact parameter dependent Glasma (IP-Glasma) model, takes into account event-by-event geometric fluctuations in nucleon positions and intrinsic subnucleon scale color charge fluctuations; the preequilibrium flow of matter is then matched to the music algorithm describing viscous hydrodynamic flow and particle production at freeze-out. The IP-Glasma+MUSIC model describes well both transverse momentum dependent and integrated v(n) data measured at the Large Hadron Collider and the Relativistic Heavy Ion Collider. The model also reproduces the event-by-event distributions of v(2), v(3) and v(4) measured by the ATLAS Collaboration. The implications of our results for better understanding of the dynamics of the Glasma and for the extraction of transport properties of the quark-gluon plasma are outlined. PMID:23383781
NASA Astrophysics Data System (ADS)
Gale, Charles; Jeon, Sangyong; Schenke, Björn; Tribedy, Prithwish; Venugopalan, Raju
2013-01-01
Anisotropic flow coefficients v1-v5 in heavy ion collisions are computed by combining a classical Yang-Mills description of the early time Glasma flow with the subsequent relativistic viscous hydrodynamic evolution of matter through the quark-gluon plasma and hadron gas phases. The Glasma dynamics, as realized in the impact parameter dependent Glasma (IP-Glasma) model, takes into account event-by-event geometric fluctuations in nucleon positions and intrinsic subnucleon scale color charge fluctuations; the preequilibrium flow of matter is then matched to the music algorithm describing viscous hydrodynamic flow and particle production at freeze-out. The IP-Glasma+MUSIC model describes well both transverse momentum dependent and integrated vn data measured at the Large Hadron Collider and the Relativistic Heavy Ion Collider. The model also reproduces the event-by-event distributions of v2, v3 and v4 measured by the ATLAS Collaboration. The implications of our results for better understanding of the dynamics of the Glasma and for the extraction of transport properties of the quark-gluon plasma are outlined.
Ergodic theory and experimental visualization of chaos in 3D flows
NASA Astrophysics Data System (ADS)
Sotiropoulos, Fotis; Mezic, Igor
2000-11-01
In his motivation for the ergodic hypothesis Gibbs invoked an analogy with fluid mixing: “…Yet no fact is more familiar to us than that stirring tends to bring a liquid to a state of uniform mixture, or uniform densities of its components…”. Although proof of the ergodic hypothesis is possible only for the simplest of systems using methods from ergodic theory, the use of the hypothesis has led to many accurate predictions in statistical mechanics. The problem of fluid mixing, however, turned out to be considerably more complicated than Gibbs envisioned. Chaotic advection can indeed lead to efficient mixing even in non-turbulent flows, but many non-mixed islands are known to persist within well-mixed regions. In numerical studies, Poincaré maps can be used to reveal the structure of such islands but their visualization in the laboratory requires laborious experimental procedures and is possible only for certain types of flows. Here we propose the first non-intrusive, simple to implement, and generally applicable technique for constructing experimental Poincaré maps and apply it to a steady, 3D, vortex breakdown bubble. We employ standard laser-induced fluorescence (LIF) and construct Poincaré maps by time averaging a sufficiently long sequence of instantaneous LIF images. We also show that ergodic theory methods provide a rigorous theoretical justification for this approach whose main objective is to reveal the non-ergodic regions of the flow.
Perturbative and non-perturbative aspects of the two-dimensional string/Yang-Mills correspondence
NASA Astrophysics Data System (ADS)
Lelli, Simone; Maggiore, Michele; Rissone, Anna
2003-04-01
It is known that YM 2 with gauge group SU( N) is equivalent to a string theory with coupling gs=1/ N, order by order in the 1/ N expansion. We show how this result can be obtained from the bosonization of the fermionic formulation of YM 2, improving on results in the literature, and we examine a number of non-perturbative aspects of this string/YM correspondence. We find contributions to the YM 2 partition function of order exp{- kA/( πα' gs)} with k an integer and A the area of the target space, which would correspond, in the string interpretation, to D1-branes. Effects which could be interpreted as D0-branes are instead strictly absent, suggesting a non-perturbative structure typical of type 0B string theories. We discuss effects from the YM side that are interpreted in terms of the stringy exclusion principle of Maldacena and Strominger. We also find numerically an interesting phase structure, with a region where YM 2 is described by a perturbative string theory separated from a region where it is described by a topological string theory.
Zhang, Yachao; Yang, Yang; Jiang, Hong
2013-12-12
The 3d-4f exchange interaction plays an important role in many lanthanide based molecular magnetic materials such as single-molecule magnets and magnetic refrigerants. In this work, we study the 3d-4f magnetic exchange interactions in a series of Cu(II)-Gd(III) (3d(9)-4f(7)) dinuclear complexes based on the numerical atomic basis-norm-conserving pseudopotential method and density functional theory plus the Hubbard U correction approach (DFT+U). We obtain improved description of the 4f electrons by including the semicore 5s5p states in the valence part of the Gd-pseudopotential. The Hubbard U correction is employed to treat the strongly correlated Cu-3d and Gd-4f electrons, which significantly improve the agreement of the predicted exchange constants, J, with experiment, indicating the importance of accurate description of the local Coulomb correlation. The high efficiency of the DFT+U approach enables us to perform calculations with molecular crystals, which in general improve the agreement between theory and experiment, achieving a mean absolute error smaller than 2 cm(-1). In addition, through analyzing the physical effects of U, we identify two magnetic exchange pathways. One is ferromagnetic and involves an interaction between the Cu-3d, O-2p (bridge ligand), and the majority-spin Gd-5d orbitals. The other one is antiferromagnetic and involves Cu-3d, O-2p, and the empty minority-spin Gd-4f orbitals, which is suppressed by the planar Cu-O-O-Gd structure. This study demonstrates the accuracy of the DFT+U method for evaluating the 3d-4f exchange interactions, provides a better understanding of the exchange mechanism in the Cu(II)-Gd(III) complexes, and paves the way for exploiting the magnetic properties of the 3d-4f compounds containing lanthanides other than Gd. PMID:24274078
A unified viscous theory of lift and drag of 2-D thin airfoils and 3-D thin wings
NASA Technical Reports Server (NTRS)
Yates, John E.
1991-01-01
A unified viscous theory of 2-D thin airfoils and 3-D thin wings is developed with numerical examples. The viscous theory of the load distribution is unique and tends to the classical inviscid result with Kutta condition in the high Reynolds number limit. A new theory of 2-D section induced drag is introduced with specific applications to three cases of interest: (1) constant angle of attack; (2) parabolic camber; and (3) a flapped airfoil. The first case is also extended to a profiled leading edge foil. The well-known drag due to absence of leading edge suction is derived from the viscous theory. It is independent of Reynolds number for zero thickness and varies inversely with the square root of the Reynolds number based on the leading edge radius for profiled sections. The role of turbulence in the section induced drag problem is discussed. A theory of minimum section induced drag is derived and applied. For low Reynolds number the minimum drag load tends to the constant angle of attack solution and for high Reynolds number to an approximation of the parabolic camber solution. The parabolic camber section induced drag is about 4 percent greater than the ideal minimum at high Reynolds number. Two new concepts, the viscous induced drag angle and the viscous induced separation potential are introduced. The separation potential is calculated for three 2-D cases and for a 3-D rectangular wing. The potential is calculated with input from a standard doublet lattice wing code without recourse to any boundary layer calculations. Separation is indicated in regions where it is observed experimentally. The classical induced drag is recovered in the 3-D high Reynolds number limit with an additional contribution that is Reynold number dependent. The 3-D viscous theory of minimum induced drag yields an equation for the optimal spanwise and chordwise load distribution. The design of optimal wing tip planforms and camber distributions is possible with the viscous 3-D wing theory.
2D/1D approximations to the 3D neutron transport equation. I: Theory
Kelley, B. W.; Larsen, E. W.
2013-07-01
A new class of '2D/1D' approximations is proposed for the 3D linear Boltzmann equation. These approximate equations preserve the exact transport physics in the radial directions x and y and diffusion physics in the axial direction z. Thus, the 2D/1D equations are more accurate approximations of the 3D Boltzmann equation than the conventional 3D diffusion equation. The 2D/1D equations can be systematically discretized, to yield accurate simulation methods for 3D reactor core problems. The resulting solutions will be more accurate than 3D diffusion solutions, and less expensive to generate than standard 3D transport solutions. In this paper, we (i) show that the simplest 2D/1D equation has certain desirable properties, (ii) systematically discretize this equation, and (iii) derive a stable iteration scheme for solving the discrete system of equations. In a companion paper [1], we give numerical results that confirm the theoretical predictions of accuracy and iterative stability. (authors)
Dimension two condensates in the Gribov-Zwanziger theory in Coulomb gauge
NASA Astrophysics Data System (ADS)
Guimaraes, M. S.; Mintz, B. W.; Sorella, S. P.
2015-06-01
We investigate the dimension two condensate ⟨ϕ¯ia bϕia b-ω¯ia bωia b⟩ within the Gribov-Zwanziger approach to Euclidean Yang-Mills theories in the Coulomb gauge, in both 3 and 4 dimensions. An explicit calculation shows that, at the first order, the condensate ⟨ϕ¯i a bϕia b-ω¯i a bωia b⟩ is plagued by a nonintegrable IR divergence in 3 D , while in 4 D it exhibits a logarithmic UV divergence, being proportional to the Gribov parameter γ2. These results indicate that in 3D the transverse spatial Coulomb gluon two-point correlation function exhibits a scaling behavior, in agreement with Gribov's expression. In 4D, however, they suggest that, next to the scaling behavior, a decoupling solution might emerge too.
Perturbative gauge theory at null infinity
NASA Astrophysics Data System (ADS)
Adamo, Tim; Casali, Eduardo
2015-06-01
We describe a theory living on the null conformal boundary I of four-dimensional Minkowski space, the states of which include the radiative modes of Yang-Mills theory. The action of a Kac-Moody symmetry algebra on the correlators of these states leads to a Ward identity for asymptotic "large" gauge transformations which is equivalent to the soft gluon theorem. The subleading soft gluon behavior is also obtained from a Ward identity for charges acting as vector fields on the sphere of null generators of I . Correlation functions of the Yang-Mills states are shown to produce the full classical S-matrix of Yang-Mills theory. The model contains additional states arising from nonunitary gravitational degrees of freedom, indicating a relationship with the twistor string of Berkovits and Witten.
3D kinematics using dual quaternions: theory and applications in neuroscience
Leclercq, Guillaume; Lefèvre, Philippe; Blohm, Gunnar
2013-01-01
In behavioral neuroscience, many experiments are developed in 1 or 2 spatial dimensions, but when scientists tackle problems in 3-dimensions (3D), they often face problems or new challenges. Results obtained for lower dimensions are not always extendable in 3D. In motor planning of eye, gaze or arm movements, or sensorimotor transformation problems, the 3D kinematics of external (stimuli) or internal (body parts) must often be considered: how to describe the 3D position and orientation of these objects and link them together? We describe how dual quaternions provide a convenient way to describe the 3D kinematics for position only (point transformation) or for combined position and orientation (through line transformation), easily modeling rotations, translations or screw motions or combinations of these. We also derive expressions for the velocities of points and lines as well as the transformation velocities. Then, we apply these tools to a motor planning task for manual tracking and to the modeling of forward and inverse kinematics of a seven-dof three-link arm to show the interest of dual quaternions as a tool to build models for these kinds of applications. PMID:23443667
Possibility of gravitational quantization under the teleparallel theory of gravitation
NASA Astrophysics Data System (ADS)
Ming, Kian; Triyanta, Kosasih, J. S.
2016-03-01
Teleparallel gravity (TG) or tele-equivalent general relativity (TEGR) is an alternative gauge theory for gravity. In TG tetrad fields are defined to express gravitational fields and act like gauge potentials in standard gauge theory. The lagrangians for the gravitational field in TG and for the Yang-Mills field in standard gauge theory differ due to different indices that stick on the components of the corresponding fields: two external indices for tetrad field and internal and external indices for the Yang-Mills field. Different types of indices lead to different possible contractions and thus lead to different expression of the lagrangian for the Yang Mills field and for the tetrad field. As TG is a gauge theory it is then natural to quantize gravity in TG by applying the same procedure of quantization as in the standard gauge theory. Here we will discuss on the possibility to quantize gravity, canonically and functionally, under the framework of TG theory.
4d/3d reduction of s-confining theories: the role of the "exotic" D instantons
NASA Astrophysics Data System (ADS)
Amariti, Antonio
2016-02-01
The reduction of 4d Seiberg duality to 3d by compactification on a circle is possible if finite size effects are considered. These effects boil down to the contribution of KK monopole operators acting as instantons in 3d, and they are crucial to preserve the 4d duality in 3d. This mechanism has been reproduced in string theory by T-duality on the type IIA brane setup. In some cases the 4d dual "magnetic" theories are IR confined descriptions of the UV gauge theories. In these cases the monopoles are absent in the IR dynamics and the mechanism of reduction of the 4d duality has to be modified. In this paper we investigate such modification in the brane setup. The main observation behind our analysis is that in the 4d case the superpotential of the confined theories can been obtained also from the "exotic" contribution of a D0 brane, a stringy instanton. When considering these configurations we reproduce the field theory results in the brane setup. We study both the unitary and the symplectic case. As a further check we provide the interpretation of the mechanism in terms of localization.
ERIC Educational Resources Information Center
Bouta, Hara; Paraskeva, Fotini
2013-01-01
Research spanning two decades shows that there is a continuing development of 3D virtual worlds and investment in such environments for educational purposes. Research stresses the need for these environments to be well-designed and for suitable pedagogies to be implemented in the teaching practice in order for these worlds to be fully effective.…
Transfer of Learning between 2D and 3D Sources during Infancy: Informing Theory and Practice
ERIC Educational Resources Information Center
Barr, Rachel
2010-01-01
The ability to transfer learning across contexts is an adaptive skill that develops rapidly during early childhood. Learning from television is a specific instance of transfer of learning between a two-dimensional (2D) representation and a three-dimensional (3D) object. Understanding the conditions under which young children might accomplish this…
A 3-D PW ultrasonic Doppler flowmeter: theory and experimental characterization.
Calzolai, M; Capineri, L; Fort, A; Masotti, L; Rocchi, S; Scabia, M
1999-01-01
A complete 3-D ultrasonic pulsed Doppler system has been developed to measure quantitatively the velocity vector field of a fluid flow independently of the probe position. The probe consists of four 2.5 MHz piezocomposite ultrasonic transducers (one central transmitter and three receivers separated by 120 degrees ) to measure the velocity projections along three different directions. The Doppler shift of the three channels is calculated by analog phase and quadrature demodulation, then digitally processed to extract the mean velocity from the complex spectrum. The accuracy of the 3-D Doppler technique has been tested on a moving string phantom providing an error of about 4% for both amplitude and direction with an acquisition window of 100 ms. PMID:18238403
Wave optics theory and 3-D deconvolution for the light field microscope
Broxton, Michael; Grosenick, Logan; Yang, Samuel; Cohen, Noy; Andalman, Aaron; Deisseroth, Karl; Levoy, Marc
2013-01-01
Light field microscopy is a new technique for high-speed volumetric imaging of weakly scattering or fluorescent specimens. It employs an array of microlenses to trade off spatial resolution against angular resolution, thereby allowing a 4-D light field to be captured using a single photographic exposure without the need for scanning. The recorded light field can then be used to computationally reconstruct a full volume. In this paper, we present an optical model for light field microscopy based on wave optics, instead of previously reported ray optics models. We also present a 3-D deconvolution method for light field microscopy that is able to reconstruct volumes at higher spatial resolution, and with better optical sectioning, than previously reported. To accomplish this, we take advantage of the dense spatio-angular sampling provided by a microlens array at axial positions away from the native object plane. This dense sampling permits us to decode aliasing present in the light field to reconstruct high-frequency information. We formulate our method as an inverse problem for reconstructing the 3-D volume, which we solve using a GPU-accelerated iterative algorithm. Theoretical limits on the depth-dependent lateral resolution of the reconstructed volumes are derived. We show that these limits are in good agreement with experimental results on a standard USAF 1951 resolution target. Finally, we present 3-D reconstructions of pollen grains that demonstrate the improvements in fidelity made possible by our method. PMID:24150383
Ward identities and renormalization of general gauge theories
NASA Astrophysics Data System (ADS)
Grigore, D. R.
2004-02-01
We introduce the concept of general gauge theory which includes Yang-Mills models. We use the framework of the causal approach and show that the anomalies can appear only in the vacuum sector of the identities obtained from the gauge invariance condition by applying derivatives with respect to the basic fields. For the Yang-Mills model we provide these identities in the lowest orders of the perturbation theory and prove that they are valid. The investigation of higher orders of the perturbation theory is still an open problem.
Spinor helicity structures in higher spin theories
NASA Astrophysics Data System (ADS)
Ananth, Sudarshan
2012-11-01
It is shown that the coefficient of the cubic interaction vertex, in higher spin Lagrangians, has a very simple form when written in terms of spinor helicity products. The result for a higher-spin field, of spin λ, is equal to the corresponding Yang-Mills coefficient raised to the power λ. Among other things, this suggests perturbative ties, similar to the KLT relations, between higher spin theories and pure Yang-Mills. This result is obtained in four-dimensional flat spacetime.
New identities among gauge theory amplitudes
NASA Astrophysics Data System (ADS)
Bjerrum-Bohr, N. E. J.; Damgaard, Poul H.; Feng, Bo; Søndergaard, Thomas
2010-08-01
Color-ordered amplitudes in gauge theories satisfy non-linear identities involving amplitude products of different helicity configurations. We consider the origin of such identities and connect them to the Kawai-Lewellen-Tye (KLT) relations between gravity and gauge theory amplitudes. Extensions are made to one-loop order of the full N = 4 super Yang-Mills multiplet.
Deep inelastic scattering off a plasma with flavor from the D3-D7 brane model
Ballon Bayona, C. A.; Boschi-Filho, Henrique; Braga, Nelson R. F.
2010-04-15
We investigate the propagation of a spacelike flavor current in a strongly coupled N=2 super Yang-Mills plasma using the D3-D7 brane model at finite temperature. The partonic contribution to the plasma structure functions is obtained from the imaginary part of the retarded current-current commutator. At high temperatures we find a nonvanishing result, for a high energy current, indicating absorption of the flavor current by the quark constituents of the plasma. At low temperatures there is no quark contribution to the plasma structure functions.
3d-3d correspondence revisited
NASA Astrophysics Data System (ADS)
Chung, Hee-Joong; Dimofte, Tudor; Gukov, Sergei; Sułkowski, Piotr
2016-04-01
In fivebrane compactifications on 3-manifolds, we point out the importance of all flat connections in the proper definition of the effective 3d {N}=2 theory. The Lagrangians of some theories with the desired properties can be constructed with the help of homological knot invariants that categorify colored Jones polynomials. Higgsing the full 3d theories constructed this way recovers theories found previously by Dimofte-Gaiotto-Gukov. We also consider the cutting and gluing of 3-manifolds along smooth boundaries and the role played by all flat connections in this operation.
Morgan, F. Dale; Sogade, John
2004-12-14
This project was designed as a broad foundational study of spectral induced polarization (SIP) for characterization of contaminated sites. It encompassed laboratory studies of the effects of chemistry on induced polarization, development of 3D forward modeling and inversion codes, and investigations of inductive and capacitive coupling problems. In the laboratory part of the project a physico-chemical model developed in this project was used to invert laboratory IP spectra for the grain size and the effective grain size distribution of the sedimentary rocks as well as the formation factor, porosity, specific surface area, and the apparent fractal dimension. Furthermore, it was established that the IP response changed with the solution chemistry, the concentration of a given solution chemistry, valence of the constituent ions, and ionic radius. In the field part of the project, a 3D complex forward and inverse model was developed. It was used to process data acquired at two frequencies (1/16 Hz and 1/ 4Hz) in a cross-borehole configuration at the A-14 outfall area of the Savannah River Site (SRS) during March 2003 and June 2004. The chosen SRS site was contaminated with Tetrachloroethylene (TCE) and Trichloroethylene (PCE) that were disposed in this area for several decades till the 1980s. The imaginary conductivity produced from the inverted 2003 data correlated very well with the log10 (PCE) concentration derived from point sampling at 1 ft spacing in five ground-truth boreholes drilled after the data acquisition. The equivalent result for the 2004 data revealed that there were significant contaminant movements during the period March 2003 and June 2004, probably related to ground-truth activities and nearby remediation activities. Therefore SIP was successfully used to develop conceptual models of volume distributions of PCE/TCE contamination. In addition, the project developed non-polarizing electrodes that can be deployed in boreholes for years. A total of 28
Simplifying Multi-loop Integrands of Gauge Theory and Gravity Amplitudes
Bern, Z.; Carrasco, J.J.M.; Dixon, L.J.; Johansson, H.; Roiban, R.
2012-02-15
We use the duality between color and kinematics to simplify the construction of the complete four-loop four-point amplitude of N = 4 super-Yang-Mills theory, including the nonplanar contributions. The duality completely determines the amplitude's integrand in terms of just two planar graphs. The existence of a manifestly dual gauge-theory amplitude trivializes the construction of the corresponding N = 8 supergravity integrand, whose graph numerators are double copies (squares) of the N = 4 super-Yang-Mills numerators. The success of this procedure provides further nontrivial evidence that the duality and double-copy properties hold at loop level. The new form of the four-loop four-point supergravity amplitude makes manifest the same ultraviolet power counting as the corresponding N = 4 super-Yang-Mills amplitude. We determine the amplitude's ultraviolet pole in the critical dimension of D = 11/2, the same dimension as for N = 4 super-Yang-Mills theory. Strikingly, exactly the same combination of vacuum integrals (after simplification) describes the ultraviolet divergence of N = 8 supergravity as the subleading-in-1/N{sub c}{sup 2} single-trace divergence in N = 4 super-Yang-Mills theory.
Simplifying multiloop integrands and ultraviolet divergences of gauge theory and gravity amplitudes
NASA Astrophysics Data System (ADS)
Bern, Z.; Carrasco, J. J. M.; Dixon, L. J.; Johansson, H.; Roiban, R.
2012-05-01
We use the duality between color and kinematics to simplify the construction of the complete four-loop four-point amplitude of N=4 super-Yang-Mills theory, including the nonplanar contributions. The duality completely determines the amplitude’s integrand in terms of just two planar graphs. The existence of a manifestly dual gauge-theory amplitude trivializes the construction of the corresponding N=8 supergravity integrand, whose graph numerators are double copies (squares) of the N=4 super-Yang-Mills numerators. The success of this procedure provides further nontrivial evidence that the duality and double-copy properties hold at loop level. The new form of the four-loop four-point supergravity amplitude makes manifest the same ultraviolet power counting as the corresponding N=4 super-Yang-Mills amplitude. We determine the amplitude’s ultraviolet pole in the critical dimension of D=11/2, the same dimension as for N=4 super-Yang-Mills theory. Strikingly, exactly the same combination of vacuum integrals (after simplification) describes the ultraviolet divergence of N=8 supergravity as the subleading-in-1/Nc2 single-trace divergence in N=4 super-Yang-Mills theory.
A Quasi-3-D Theory for Impedance Eduction in Uniform Grazing Flow
NASA Technical Reports Server (NTRS)
Watson, W. R.; Jones, M. G.; Parrott, T. L.
2005-01-01
A 2-D impedance eduction methodology is extended to quasi-3-D sound fields in uniform or shearing mean flow. We introduce a nonlocal, nonreflecting boundary condition to terminate the duct and then educe the impedance by minimizing an objective function. The introduction of a parallel, sparse, equation solver significantly reduces the wall clock time for educing the impedance when compared to that of the sequential band solver used in the 2-D methodology. The accuracy, efficiency, and robustness of the methodology is demonstrated using two examples. In the first example, we show that the method reproduces the known impedance of a ceramic tubular test liner. In the second example, we illustrate that the approach educes the impedance of a four-segment liner where the first, second, and fourth segments consist of a perforated face sheet bonded to honeycomb, and the third segment is a cut from the ceramic tubular test liner. The ability of the method to educe the impedances of multisegmented liners has the potential to significantly reduce the amount of time and cost required to determine the impedance of several uniform liners by allowing them to be placed in series in the test section and to educe the impedance of each segment using a single numerical experiment. Finally, we probe the objective function in great detail and show that it contains a single minimum. Thus, our objective function is ideal for use with local, inexpensive, gradient-based optimizers.
NASA Astrophysics Data System (ADS)
Hsu, Jong-Ping
Within Yang-Mills gravity with translation group T(4) in flat space-time, the invariant action involving quadratic translation gauge-curvature leads to quadrupole radiations, which are shown to be consistent with experiments. The radiation power turns out to be the same as that in Einstein's gravity to the second-order approximation. We also discuss an interesting physical reason for the accelerated cosmic expansion based on the long-range Lee-Yang force of Ub(1) gauge field associated with the established conservation law of baryon number. We show that the Lee-Yang force can be related to a linear potential ∝ r, provided the gauge field satisfies a fourth-order differential equation in flat space-time. Furthermore, we consider an experimental test of the Lee-Yang force related to the accelerated cosmic expansion. The necessity of generalizing Lorentz transformations for accelerated frames of reference and accelerated Wu-Doppler effects are briefly discussed.
Vescovi, D.; Berzi, D.; Richard, P.
2014-05-15
We use existing 3D Discrete Element simulations of simple shear flows of spheres to evaluate the radial distribution function at contact that enables kinetic theory to correctly predict the pressure and the shear stress, for different values of the collisional coefficient of restitution. Then, we perform 3D Discrete Element simulations of plane flows of frictionless, inelastic spheres, sheared between walls made bumpy by gluing particles in a regular array, at fixed average volume fraction and distance between the walls. The results of the numerical simulations are used to derive boundary conditions appropriated in the cases of large and small bumpiness. Those boundary conditions are, then, employed to numerically integrate the differential equations of Extended Kinetic Theory, where the breaking of the molecular chaos assumption at volume fraction larger than 0.49 is taken into account in the expression of the dissipation rate. We show that the Extended Kinetic Theory is in very good agreement with the numerical simulations, even for coefficients of restitution as low as 0.50. When the bumpiness is increased, we observe that some of the flowing particles are stuck in the gaps between the wall spheres. As a consequence, the walls are more dissipative than expected, and the flows resemble simple shear flows, i.e., flows of rather constant volume fraction and granular temperature.
Comparison of 3D Classical Trajectory and Transition-State Theory Reaction Cross Sections
DOE R&D Accomplishments Database
Koeppl, G. W.; Karplus, Martin
1970-10-01
Although there is excellent agreement for a system such as H+H{sub 2} --> H{sub 2}+H, in which both the potential and the particle masses are symmetric, significant deviations occur for more asymmetric reactions. A detailed analysis show that the calculated differences are from the violation of two assumptions of transition-state theory.
A 3-D elasticity theory based model for acoustic radiation from multilayered anisotropic plates.
Shen, C; Xin, F X; Lu, T J
2014-05-01
A theoretical model built upon three-dimensional elasticity theory is developed to investigate the acoustic radiation from multilayered anisotropic plates subjected to a harmonic point force excitation. Fourier transform technique and stationary phase method are combined to predict the far-field radiated sound pressure of one-side water immersed plate. Compared to equivalent single-layer plate models, the present model based on elasticity theory can differentiate radiated sound pressure between dry-side and wet-side excited cases, as well as discrepancies induced by different layer sequences for multilayered anisotropic plates. These results highlight the superiority of the present theoretical model especially for handling multilayered anisotropic structures. PMID:24815294
Coulomb branches for rank 2 gauge groups in 3 d N=4 gauge theories
NASA Astrophysics Data System (ADS)
Hanany, Amihay; Sperling, Marcus
2016-08-01
The Coulomb branch of 3-dimensional N=4 gauge theories is the space of bare and dressed BPS monopole operators. We utilise the conformal dimension to define a fan which, upon intersection with the weight lattice of a GNO-dual group, gives rise to a collection of semi-groups. It turns out that the unique Hilbert bases of these semi-groups are a sufficient, finite set of monopole operators which generate the entire chiral ring. Moreover, the knowledge of the properties of the minimal generators is enough to compute the Hilbert series explicitly. The techniques of this paper allow an efficient evaluation of the Hilbert series for general rank gauge groups. As an application, we provide various examples for all rank two gauge groups to demonstrate the novel interpretation.
Gauge theories in anti-selfdual variables
NASA Astrophysics Data System (ADS)
Bochicchio, Marco; Pilloni, Alessandro
2013-09-01
Some years ago the Nicolai map, viewed as a change of variables from the gauge connection in a fixed gauge to the anti-selfdual part of the curvature, has been extended by the first named author to pure Yang-Mills from its original definition in = 1 supersymmetric Yang-Mills. We study here the perturbative one-particle irreducible effective action in the anti-selfdual variables of any gauge theory, in particular pure Yang-Mills, QCD and = 1 supersymmetric Yang-Mills. We prove that the one-loop one-particle irreducible effective action of a gauge theory mapped to the anti-selfdual variables in any gauge is identical to the one of the original theory. This is due to the conspiracy between the Jacobian of the change to the anti-selfdual variables and an extra functional determinant that arises from the non-linearity of the coupling of the anti-selfdual curvature to an external source in the Legendre transform that defines the one-particle irreducible effective action. Hence we establish the one-loop perturbative equivalence of the mapped and original theories on the basis of the identity of the one-loop one-particle irreducible effective actions. Besides, we argue that the identity of the perturbative one-particle irreducible effective actions extends order by order in perturbation theory.
Probing non-perturbative effects in M-theory on orientifolds
NASA Astrophysics Data System (ADS)
Okuyama, Kazumi
2016-01-01
Using holography, we study non-perturbative effects in M-theory on orientifolds from the analysis of the S 3 partition functions of dual field theories. We consider the S 3 partition functions of N=4 Yang-Mills theory with O( n) gauge symmetry coupled to one (anti)symmetric and N f fundamental hypermultiplets from the Fermi gas approach. In addition to the worldsheet instanton and membrane instanton corrections to the grand potential, which are also present in the U( n) Yang-Mills case, we find that there exist "half instanton" corrections coming from the effect of orientifold plane.
Localization of Gauge Theory on a Four-Sphere and Supersymmetric Wilson Loops
NASA Astrophysics Data System (ADS)
Pestun, Vasily
2012-07-01
We prove conjecture due to Erickson-Semenoff-Zarembo and Drukker-Gross which relates supersymmetric circular Wilson loop operators in the {N=4} supersymmetric Yang-Mills theory with a Gaussian matrix model. We also compute the partition function and give a new matrix model formula for the expectation value of a supersymmetric circular Wilson loop operator for the pure {N=2} and the {N=2^*} supersymmetric Yang-Mills theory on a four-sphere. A four-dimensional {N=2} superconformal gauge theory is treated similarly.
Lawrence, R.D.
1983-03-01
A nodal method is developed for the solution of the neutron-diffusion equation in two- and three-dimensional hexagonal geometries. The nodal scheme has been incorporated as an option in the finite-difference diffusion-theory code DIF3D, and is intended for use in the analysis of current LMFBR designs. The nodal equations are derived using higher-order polynomial approximations to the spatial dependence of the flux within the hexagonal-z node. The final equations, which are cast in the form of inhomogeneous response-matrix equations for each energy group, involved spatial moments of the node-interior flux distribution plus surface-averaged partial currents across the faces of the node. These equations are solved using a conventional fission-source iteration accelerated by coarse-mesh rebalance and asymptotic source extrapolation. This report describes the mathematical development and numerical solution of the nodal equations, as well as the use of the nodal option and details concerning its programming structure. This latter information is intended to supplement the information provided in the separate documentation of the DIF3D code.
The complete KLT-map between gravity and gauge theories
NASA Astrophysics Data System (ADS)
Damgaard, Poul H.; Huang, Rijun; Søndergaard, Thomas; Zhang, Yang
2012-08-01
We present the complete map of any pair of super Yang-Mills theories to supergravity theories as dictated by the KLT relations in four dimensions. Symmetries and the full set of associated vanishing identities are derived. A graphical method is introduced which simplifies counting of states, and helps in identifying the relevant set of symmetries.
NASA Astrophysics Data System (ADS)
Arsenault, Louis-François; Sémon, Patrick; Shastry, B. Sriram; Tremblay, A.-M. S.
2012-02-01
The Dynamical Mean-Field theory(DMFT) approach to the Hubbard model requires a method to solve the problem of a quantum impurity in a bath of non-interacting electrons. Iterated Perturbation Theory(IPT)[1] has proven its effectiveness as a solver in many cases of interest. Based on general principles and on comparisons with an essentially exact Continuous-Time Quantum Monte Carlo (CTQMC)[2], here we show that the standard implementation of IPT fails when the interaction is much larger than the bandwidth. We propose a slight modification to the IPT algorithm by requiring that double occupancy calculated with IPT gives the correct value. We call this method IPT-D. We show how this approximate impurity solver compares with respect to CTQMC. We consider a face centered cubic lattice(FCC) in 3d for different physical properties. We also use IPT-D to study the thermopower using two recently proposed approximations[3]S^* and SKelvin that do not require analytical continuation and show how thermopower is essentially the entropy per particle in the incoherent regime but not in the coherent one.[1]H.Kajueter et al. Phys. Rev. Lett. 77, 131(1996)[2]P. Werner, et al. Phys. Rev. Lett. 97, 076405(2006)[3]B.S. Sriram Shastry Rep. Prog. Phys. 72 016501(2009)
NASA Astrophysics Data System (ADS)
Leever, Karen; Oncken, Onno; Thorden Haug, Øystein
2015-04-01
For 2D critical taper theory to be applicable to 3D natural cases, cylindric deformation is a requirement. The assumption of cylindricity is violated in case of localized perturbations (subducting seamount, localized sedimentation) or due to a lateral change in decollement strength or depth. In natural accretionary wedges and fold-and-thrust belts, along strike changes may occur in a variety of ways: geometrical (due to a protruding indenter or a change in decollement depth), through a lateral change in basal friction (leading to laterally different tapers), or through a change in surface slope (by strongly localized fan sedimentation on accretionary wedges). Recent numerical modelling results (Ruh et al., 2013) have shown that lateral coupling preferentially occurs for relatively small perturbations, i.e. the horizontal shear stress caused by the perturbation is supported by the system. Lateral linking of the wedge in front of a protruding indenter to the wedge in front of the trailing edge of the back stop leads to curved thrust fronts and importantly it has been noted that even outside the curved zone, where the wedge front is again parallel to the direction of tectonic transport, the lateral effect is still evident: both tapers are different from the analytical prediction. We present results from a 3D analogue modelling parameter study to investigate this behavior more quantitatively, with the objective of empirically finding a lateral length scale of deformation in brittle contractional wedges. For a given wedge strength (angle of internal friction), we infer this to be a function of the size (width) of the perturbation and its magnitude (difference in basal friction). To this end we run different series of models in which we systematically vary the width and/or magnitude of a local perturbation. In the first series, the width of a zone of high basal friction is varied, in the second series we vary the width of an indenter and in the third series
NASA Astrophysics Data System (ADS)
Magic, Z.; Weiss, A.; Asplund, M.
2015-01-01
Aims: We investigate the relation between 1D atmosphere models that rely on the mixing length theory and models based on full 3D radiative hydrodynamic (RHD) calculations to describe convection in the envelopes of late-type stars. Methods: The adiabatic entropy value of the deep convection zone, sbot, and the entropy jump, Δs, determined from the 3D RHD models, were matched with the mixing length parameter, αMLT, from 1D hydrostatic atmosphere models with identical microphysics (opacities and equation-of-state). We also derived the mass mixing length parameter, αm, and the vertical correlation length of the vertical velocity, C[vz,vz], directly from the 3D hydrodynamical simulations of stellar subsurface convection. Results: The calibrated mixing length parameter for the Sun is α๏MLT (Sbot) = 1.98. . For different stellar parameters, αMLT varies systematically in the range of 1.7 - 2.4. In particular, αMLT decreases towards higher effective temperature, lower surface gravity and higher metallicity. We find equivalent results for α๏MLT (ΔS). In addition, we find a tight correlation between the mixing length parameter and the inverse entropy jump. We derive an analytical expression from the hydrodynamic mean-field equations that motivates the relation to the mass mixing length parameter, αm, and find that it qualitatively shows a similar variation with stellar parameter (between 1.6 and 2.4) with the solar value of α๏m = 1.83.. The vertical correlation length scaled with the pressure scale height yields 1.71 for the Sun, but only displays a small systematic variation with stellar parameters, the correlation length slightly increases with Teff. Conclusions: We derive mixing length parameters for various stellar parameters that can be used to replace a constant value. Within any convective envelope, αm and related quantities vary strongly. Our results will help to replace a constant αMLT. Appendices are available in electronic form at http
NASA Astrophysics Data System (ADS)
Ayissi, Raoul Domingo; Noutchegueme, Norbert; Etoua, Remy Magloire; Tchagna, Hugues Paulin Mbeutcha
2015-09-01
Recently in 2005, Briani and Rampazzo (Nonlinear Differ Equ Appl 12:71-91, 2005) gave, using results of Crandall and Lions (Ill J Math 31:665-688, 1987), Ishii (Indiana Univ Math J 33: 721-748, 1984, Bull Fac Sci Eng 28: 33-77, 1985) and Ley (Adv Diff Equ 6:547-576, 2001) a density approach to Hamilton-Jacobi equations with t-measurable Hamiltonians. In this paper we show, using an important result of Briani and Rampazzo (Nonlinear Differ Equ Appl 12:71-91, 2005) the existence and uniqueness of viscosity solutions to the one-body Liouville relativistic equation in Yang-Mills charged Bianchi space times with non-zero mass. To our knowledge, the method used here is original and thus, totally different from those used in Alves (C R Acad Sci Paris Sér A 278:1151-1154, 1975), Choquet-Bruhat and Noutchegueme (C R Acad Sci Paris Sér I 311, 1973), Choquet-Bruhat and Noutchegueme (Ann Inst Henri Poincaré 55:759-787, 1991), Choquet-Bruhat and Noutchegueme (Pitman Res Notes Math Ser 253:52-71, 1992), Noutchegueme and Noundjeu (Ann Inst Henri Poincaré 1:385-404, 2000), Wollman (J Math Anal Appl 127:103-121, 1987) and Choquet-Bruhat (Existence and uniqueness for the Einstein-Maxwell-Liouville system. Volume dedicated to Petrov, Moscow, 1971) who have studied the same equation.
Invariants from classical field theory
Diaz, Rafael; Leal, Lorenzo
2008-06-15
We introduce a method that generates invariant functions from perturbative classical field theories depending on external parameters. By applying our methods to several field theories such as Abelian BF, Chern-Simons, and two-dimensional Yang-Mills theory, we obtain, respectively, the linking number for embedded submanifolds in compact varieties, the Gauss' and the second Milnor's invariant for links in S{sup 3}, and invariants under area-preserving diffeomorphisms for configurations of immersed planar curves.
S-duality in 3D gravity with torsion
Mielke, Eckehard W. . E-mail: ekke@xanum.uam.mx; Maggiolo, Ali A. Rincon
2007-02-15
The deformation of the connection in three spacetime dimensions by the kinematically equivalent coframe is shown to induce a duality between the (Lorentz-) rotational and translational field momenta, for which the coupling to the deformation parameter is inverted. This new kind of strong/weak duality, pertinent to 3D, is instrumental for studying exact solutions of the 3D Poincare gauge field equations and the particle content of propagating modes on a background of constant curvature. For a topological Chern-Simons model of gravity, the propagating modes 'living' on an Anti-de Sitter (AdS) background correspond to real massive particles. Yang-Mills type generalizations and new cubic Lagrangians are found and completely classified in 3D. AdS or black hole type solutions with constant axial torsion emerge, also for these higher-order Lagrangians with new 'exotic' torsion-curvature couplings. Their pattern complies with our S-duality, with new repercussions for the field redefinition of the metric in 3D quantum gravity and the cosmological constant problem.
NASA Technical Reports Server (NTRS)
Wang, John T.; Pineda, Evan J.; Ranatunga, Vipul; Smeltzer, Stanley S.
2015-01-01
A simple continuum damage mechanics (CDM) based 3D progressive damage analysis (PDA) tool for laminated composites was developed and implemented as a user defined material subroutine to link with a commercially available explicit finite element code. This PDA tool uses linear lamina properties from standard tests, predicts damage initiation with an easy-to-implement Hashin-Rotem failure criteria, and in the damage evolution phase, evaluates the degradation of material properties based on the crack band theory and traction-separation cohesive laws. It follows Matzenmiller et al.'s formulation to incorporate the degrading material properties into the damaged stiffness matrix. Since nonlinear shear and matrix stress-strain relations are not implemented, correction factors are used for slowing the reduction of the damaged shear stiffness terms to reflect the effect of these nonlinearities on the laminate strength predictions. This CDM based PDA tool is implemented as a user defined material (VUMAT) to link with the Abaqus/Explicit code. Strength predictions obtained, using this VUMAT, are correlated with test data for a set of notched specimens under tension and compression loads.
NASA Astrophysics Data System (ADS)
Parisi, Laura; Ferreira, Ana M. G.
2016-04-01
The surface wave full ray theory (FRT) is an efficient tool to calculate synthetic waveforms of surface waves. It combines the concept of local modes with exact ray tracing as a function of frequency, providing a more complete description of surface wave propagation than the widely used great circle approximation (GCA). The purpose of this study is to evaluate the ability of the FRT approach to model teleseismic long-period surface waveforms (T ˜ 45-150 s) in the context of current 3-D Earth models to empirically assess its validity domain and its scope for future studies in seismic tomography. To achieve this goal, we compute vertical and horizontal component fundamental mode synthetic Rayleigh waveforms using the FRT, which are compared with calculations using the highly accurate spectral element method. We use 13 global earth models including 3-D crustal and mantle structure, which are derived by successively varying the strength and lengthscale of heterogeneity in current tomographic models. For completeness, GCA waveforms are also compared with the spectral element method. We find that the FRT accurately predicts the phase and amplitude of long-period Rayleigh waves (T ˜ 45-150 s) for almost all the models considered, with errors in the modelling of the phase (amplitude) of Rayleigh waves being smaller than 5 per cent (10 per cent) in most cases. The largest errors in phase and amplitude are observed for T ˜ 45 s and for the three roughest earth models considered that exhibit shear wave anomalies of up to ˜20 per cent, which is much larger than in current global tomographic models. In addition, we find that overall the GCA does not predict Rayleigh wave amplitudes well, except for the longest wave periods (T ˜ 150 s) and the smoothest models considered. Although the GCA accurately predicts Rayleigh wave phase for current earth models such as S20RTS and S40RTS, FRT's phase errors are smaller, notably for the shortest wave periods considered (T ˜ 45 s and
Using 1D theory to understand 3D stagnation of a wire-array Z pinch in the absence of radiation
NASA Astrophysics Data System (ADS)
Yu, Edmund
2015-11-01
Many high-energy-density systems implode towards the axis of symmetry, where it collides on itself, forming a hot plasma. However, experiments show these imploding plasmas develop three-dimensional (3D) structures. As a result, the plasma cannot completely dissipate its kinetic energy at stagnation, instead retaining significant 3D flow. A useful tool for understanding the effects of this residual flow is 3D simulation, but the amount and complexity of information can be daunting. To address this problem, we explore the connection between 3D simulation and one-dimensional (1D) theory. Such a connection, if it exists, is mutually beneficial: 1D theory can provide a clear picture of the underlying dynamics of 3D stagnation. On the other hand, deviations between theory and simulation suggest how 1D theory must be modified to account for 3D effects. In this work, we focus on a 3D, magnetohydrodynamic simulation of a compact wire-array Z pinch. To provide a simpler background against which to test our ideas, we artificially turn off radiation during the stagnation phase. Examination of the initial accumulation of mass on axis reveals oblique collision between jets, shock accretion, and vortex formation. Despite evidence for shock-dominated stagnation, a 1D shockless stagnation solution is more appropriate for describing the global dynamics, in that it reproduces the increase of on-axis density with time. However, the 1D solution must be modified to account for 3D effects: the flows suggest enhanced thermal transport as well as centrifugal force. Upon reaching peak compression, the stagnation transitions to a second phase, in which the high-pressure core on axis expands outward into the remaining imploding plasma. During this phase, a 1D shock solution describes the growth of the shock accretion region, as well as the decrease of on-axis density with time. However, the effect of 3D flows is still present: the on-axis temperature does not cool during expansion, which
NASA Technical Reports Server (NTRS)
Shih, T. I.-P.; Bailey, R. T.; Nguyen, H. L.; Roelke, R. J.
1990-01-01
modifications are needed in the grid generation part of the program. This technical memorandum describes the theory and method used in GRID2D/3D.
On skein relations in class S theories
NASA Astrophysics Data System (ADS)
Tachikawa, Yuji; Watanabe, Noriaki
2015-06-01
Loop operators of a class S theory arise from networks on the corresponding Riemann surface, and their operator product expansions are given in terms of the skein relations, that we describe in detail in the case of class S theories of type A. As two applications, we explicitly determine networks corresponding to dyonic loops of super Yang-Mills, and compute the superconformal index of a nontrivial network operator of the T 3 theory.
New set of 2D/3D thermodynamic indices for proteins. A formalism based on “ Molten Globule” theory
NASA Astrophysics Data System (ADS)
Ruiz-Blanco Yasser, B.; García, Y.; Sotomayor-Torres, C. M.; Yovani, Marrero-Ponce
We define eight new macromolecular indices, and several related descriptors for proteins. The coarse grained methodology used for its deduction ensures its fast execution and becomes a powerful potential tool to explore large databases of protein structures. The indices are intended for stability studies, predicting Φ-values, predicting folding rate constants, protein QSAR/QSPR as well as protein alignment studies. Also, these indices could be used as scoring function in protein-protein docking or 3D protein structure prediction algorithms and any others applications which need a numerical code for proteins and/or residues from 2D or 3D format.
Note on Gauge Theory on M4 × ZN with Auxiliary Field
NASA Astrophysics Data System (ADS)
Maekawa, T.; Taira, H.
1997-06-01
It is shown that the discrete gauge theory on ZN is well formulated with the auxiliary fields due to Chamseddine et al. and Okumura et al. together with the exterior algebra of Dimakis and Müller-Hoissen. A Lagrangian of the Yang-Mills-Higgs fields is also given.
The structure of the anomalies of gauge theories in the causal approach
NASA Astrophysics Data System (ADS)
Grigore, D. R.
2002-02-01
We consider the gauge invariance of the standard Yang-Mills model in the framework of the causal approach of Epstein-Glaser and Scharf and determine the generic form of the anomalies. The method used is based on the Epstein-Glaser approach to renormalization theory. In the case of quantum electrodynamics we obtain quite easily the absence of anomalies in all orders.
da Costa, L M; Hayaki, S; Stoyanov, S R; Gusarov, S; Tan, X; Gray, M R; Stryker, J M; Tykwinski, R; Carneiro, J Walkimar de M; Sato, H; Seidl, P R; Kovalenko, A
2012-03-21
We applied a multiscale modeling approach that involves the statistical-mechanical three-dimensional reference interaction site model with the Kovalenko-Hirata closure approximation (3D-RISM-KH molecular theory of solvation) as well as density functional theory (DFT) of electronic structure to study the role of water in aggregation of the asphaltene model compound 4,4'-bis(2-pyren-1-yl-ethyl)-2,2'-bipyridine (PBP) [X. Tan, H. Fenniri and M. R. Gray, Energy Fuels, 2008, 22, 715]. The solvation free energy and potential of mean force predicted by 3D-RISM-KH reveal favorable pathways for disaggregation of PBP dimers in pure versus water-saturated chloroform solvent. The water density distribution functions elucidate hydrogen bonding preferences and water bridge formation between PBP monomers. The ΔG(298) values of -5 to -7 kcal mol(-1) for transfer of water molecules in chloroform to a state interacting with PBP molecules are in agreement with experimental results. Geometry optimization and thermochemistry analysis of PBP dimers with and without water bridges using WB97Xd/6-31G(d,p) predict that both PBP dimerization and dimer stabilization by water bridges are spontaneous (ΔG(298) < 0). The (1)H NMR chemical shifts of PBP monomers and dimers predicted using the gauge-independent atomic orbital method and polarizable continuum model for solvation in chloroform are in an excellent agreement with the experimental results for dilute and concentrated PBP solutions in chloroform, respectively [X. Tan, H. Fenniri and M. R. Gray, Energy Fuels, 2009, 23, 3687]. The DFT calculations of PBP dimers with explicit water show that bridges containing 1-3 water molecules lead to stabilization of PBP dimers. Additional water molecules form hydrogen bonds with these bridges and de-shield the PBP protons, negating the effect of water on the (1)H(C3) NMR chemical shift of PBP, in agreement with experiment. The ΔG(298) results show that hydrogen bonding to water and water
Monopoles and knots in skyrme theory.
Cho, Y M
2001-12-17
We show that the Skyrme theory is actually a theory of monopoles which allows a new type of soliton, the topological knot made of the monopole-antimonopole pair, which is different from the well-known skyrmion. Furthermore, we derive a generalized Skyrme action from the Yang-Mills action of QCD, which we propose to be an effective action of QCD in the infrared limit. We discuss the physical implications of our results. PMID:11736568
Yang-Mills Magnetofluid Unification
Bambah, Bindu A.; Mahajan, Swadesh M.; Mukku, Chandrasekher
2006-08-18
We generalize the hybrid magnetofluid model of a charged fluid interacting with an electromagnetic field to the dynamics of a relativistic hot fluid interacting with a non-Abelian field. The fluid itself is endowed with a non-Abelian charge and the consequences of this generalization are worked out. Applications of this formalism to the quark gluon plasma are suggested.
Instantons in Lifshitz field theories
NASA Astrophysics Data System (ADS)
Fujimori, Toshiaki; Nitta, Muneto
2015-10-01
BPS instantons are discussed in Lifshitz-type anisotropic field theories. We consider generalizations of the sigma model/Yang-Mills instantons in renormalizable higher dimensional models with the classical Lifshitz scaling invariance. In each model, BPS instanton equation takes the form of the gradient flow equations for "the superpotential" defining "the detailed balance condition". The anisotropic Weyl rescaling and the coset space dimensional reduction are used to map rotationally symmetric instantons to vortices in two-dimensional anisotropic systems on the hyperbolic plane. As examples, we study anisotropic BPS baby Skyrmion 1+1 dimensions and BPS Skyrmion in 2+1 dimensions, for which we take Kähler 1-form and the Wess-Zumiono-Witten term as the superpotentials, respectively, and an anisotropic generalized Yang-Mills instanton in 4 + 1 dimensions, for which we take the Chern-Simons term as the superpotential.
Model of the N-quark potential in SU(N) gauge theory using gauge-string duality
NASA Astrophysics Data System (ADS)
Andreev, Oleg
2016-05-01
We use gauge-string duality to model the N-quark potential in pure Yang-Mills theories. For SU (3), the result agrees remarkably well with lattice simulations. The model smoothly interpolates between almost the Δ-law at short distances and the Y-law at long distances.
Scale invariance in the causal approach to renormalization theory
NASA Astrophysics Data System (ADS)
Grigore, Dan R.
2001-06-01
The dilation invariance is studied in the framework of Epstein-Glaser approach to renormalization theory. Some analogues of the Callan-Symanzik equations are found and they are applied to the scalar field theory and to Yang-Mills models. We find the interesting result that, if all fields of the theory have zero masses, then from purely cohomological consideration, one can obtain the anomalous terms of logarithmic type.
N=3 supersymmetric effective action of D2-branes in massive IIA string theory
NASA Astrophysics Data System (ADS)
Go, Gyungchoon; Kwon, O.-Kab; Tolla, D. D.
2012-01-01
We obtain a new type of N=3 Yang-Mills Chern-Simons theory from the Mukhi-Papageorgakis Higgs mechanism of the N=3 Gaiotto-Tomasiello theory. This theory has N=1 BPS fuzzy funnel solution, which is expressed in terms of the seven generators of SU(3), excluding T8. We propose that this is an effective theory of multiple D2-branes with D6- and D8-branes background in massive IIA string theory.
Uzunova, Ellie L
2011-03-01
The trioxide clusters with stoichiometry MO3, and the structural isomers with side-on and end-on bonded oxygen atoms, are studied by DFT with the B1LYP functional. For the first half of the 3d elements row (Sc to Cr), pyramidal or distorted pyramidal structures dominate among the trioxide and oxoperoxide ground states, while the remaining elements form planar trioxides, oxoperoxides, oxosuperoxides, and ozonides. Low-lying trioxide clusters are formed by Ti, V, Cr, and Mn, among which the distorted pyramidal VO3 in the (2)A'' state, the pyramidal CrO3 in the (1)A1 state, and the planar MnO3 in the (2)A1' state are global minima. With the exception of the middle-row elements Mn, Fe, and Co, the magnetic moment of the ground-state clusters is formed with a major contribution from unpaired electrons located at the oxygen atoms. The stability of trioxides and oxoperoxides toward release of molecular oxygen is significantly higher for Sc, Ti, and V than for the remaining elements of the row. A trend of increasing the capability to dissociate one oxygen molecule is observed from Cr to Cu, with the exception of OFe(O2) being more reactive than OCo(O2). A gradual increase of reactivity from Ti to Cu is observed for the complete fragmentation reaction M + O + O2. PMID:21299242
Planar Limit of Orientifold Field Theories and Emergent Center Symmetry
Armoni, Adi; Shifman, Mikhail; Unsal, Mithat
2007-12-05
We consider orientifold field theories (i.e. SU(N) Yang-Mills theories with fermions in the two-index symmetric or antisymmetric representations) on R{sub 3} x S{sub 1} where the compact dimension can be either temporal or spatial. These theories are planar equivalent to supersymmetric Yang-Mills. The latter has Z{sub N} center symmetry. The famous Polyakov criterion establishing confinement-deconfinement phase transition as that from Z{sub N} symmetric to Z{sub N} broken phase applies. At the Lagrangian level the orientifold theories have at most a Z{sub 2} center. We discuss how the full Z{sub N} center symmetry dynamically emerges in the orientifold theories in the limit N {yields} {infinity}. In the confining phase the manifestation of this enhancement is the existence of stable k-strings in the large-N limit of the orientifold theories. These strings are identical to those of supersymmetric Yang-Mills theories. We argue that critical temperatures (and other features) of the confinement-deconfinement phase transition are the same in the orientifold daughters and their supersymmetric parent up to 1/N corrections. We also discuss the Abelian and non-Abelian confining regimes of four-dimensional QCD-like theories.
Bending analysis of a general cross-ply laminate using 3D elasticity solution and layerwise theory
NASA Astrophysics Data System (ADS)
Yazdani Sarvestani, H.; Naghashpour, A.; Heidari-Rarani, M.
2015-12-01
In this study, the analytical solution of interlaminar stresses near the free edges of a general (symmetric and unsymmetric layups) cross-ply composite laminate subjected to pure bending loading is presented based on Reddy's layerwise theory (LWT) for the first time. First, the reduced form of displacement field is obtained for a general cross-ply composite laminate subjected to a bending moment by elasticity theory. Then, first-order shear deformation theory of plates and LWT is utilized to determine the global and local deformation parameters appearing in the displacement fields, respectively. One of the main advantages of the developed solution based on the LWT is exact prediction of interlaminar stresses at the boundary layer regions. To show the accuracy of this solution, three-dimensional elasticity bending problem of a laminated composite is solved for special set of boundary conditions as well. Finally, LWT results are presented for edge-effect problems of several symmetric and unsymmetric cross-ply laminates under the bending moment. The obtained results indicate high stress gradients of interlaminar stresses near the edges of laminates.
Hamoud Al-Tamimi, Mohammed Sabbih; Sulong, Ghazali; Shuaib, Ibrahim Lutfi
2015-07-01
Resection of brain tumors is a tricky task in surgery due to its direct influence on the patients' survival rate. Determining the tumor resection extent for its complete information via-à-vis volume and dimensions in pre- and post-operative Magnetic Resonance Images (MRI) requires accurate estimation and comparison. The active contour segmentation technique is used to segment brain tumors on pre-operative MR images using self-developed software. Tumor volume is acquired from its contours via alpha shape theory. The graphical user interface is developed for rendering, visualizing and estimating the volume of a brain tumor. Internet Brain Segmentation Repository dataset (IBSR) is employed to analyze and determine the repeatability and reproducibility of tumor volume. Accuracy of the method is validated by comparing the estimated volume using the proposed method with that of gold-standard. Segmentation by active contour technique is found to be capable of detecting the brain tumor boundaries. Furthermore, the volume description and visualization enable an interactive examination of tumor tissue and its surrounding. Admirable features of our results demonstrate that alpha shape theory in comparison to other existing standard methods is superior for precise volumetric measurement of tumor. PMID:25865822
Loop equation in D=4, N=4 super Yang-Mills theory and string field equation on AdS{sub 5}xS{sup 5}
Hata, Hiroyuki; Miwa, Akitsugu
2006-02-15
We consider the loop equation in four-dimensional N=4 SYM, which is a functional differential equation for the Wilson loop W(C) and expresses the propagation and the interaction of the string C. Our W(C) consists of the scalar and the gaugino fields as well as the gauge field. The loop C is specified by six bosonic coordinates y{sup i}(s) and two fermionic coordinates {zeta}(s) and {eta}(s) besides the four-dimensional spacetime coordinates x{sup {mu}}(s). We have successfully determined, to quadratic order in {zeta} and {eta}, the parameters in W(C) and the loop differential operator so that the equation of motion of SYM can be correctly reproduced to give the nonlinear term of W(C). We extract the most singular and linear part of our loop equation and compare it with the Hamiltonian constraint of the string propagating on AdS{sub 5}xS{sup 5} background.
Wong, Wilbur C K; So, Ronald W K; Chung, Albert C S
2012-04-01
We present an energy-minimization-based framework for locating the centerline and estimating the width of tubelike objects from their structural network with a nonparametric model. The nonparametric representation promotes simple modeling of nested branches and n -way furcations, i.e., structures that abound in an arterial network, e.g., a cerebrovascular circulation. Our method is capable of extracting the entire vascular tree from an angiogram in a single execution with a proper initialization. A succinct initial model from the user with arterial network inlets, outlets, and branching points is sufficient for complex vasculature. The novel method is based upon the theory of principal curves. In this paper, theoretical extension to grayscale angiography is discussed, and an algorithm to find an arterial network as principal curves is also described. Quantitative validation on a number of simulated data sets, synthetic volumes of 19 BrainWeb vascular models, and 32 Rotterdam Coronary Artery volumes was conducted. We compared the algorithm to a state-of-the-art method and further tested it on two clinical data sets. Our algorithmic outputs-lumen centers and flow channel widths-are important to various medical and clinical applications, e.g., vasculature segmentation, registration and visualization, virtual angioscopy, and vascular atlas formation and population study. PMID:22167625
Arooj, Mahreen; Thangapandian, Sundarapandian; John, Shalini; Hwang, Swan; Park, Jong Keun; Lee, Keun Woo
2011-01-01
Human chymase is a very important target for the treatment of cardiovascular diseases. Using a series of theoretical methods like pharmacophore modeling, database screening, molecular docking and Density Functional Theory (DFT) calculations, an investigation for identification of novel chymase inhibitors, and to specify the key factors crucial for the binding and interaction between chymase and inhibitors is performed. A highly correlating (r = 0.942) pharmacophore model (Hypo1) with two hydrogen bond acceptors, and three hydrophobic aromatic features is generated. After successfully validating “Hypo1”, it is further applied in database screening. Hit compounds are subjected to various drug-like filtrations and molecular docking studies. Finally, three structurally diverse compounds with high GOLD fitness scores and interactions with key active site amino acids are identified as potent chymase hits. Moreover, DFT study is performed which confirms very clear trends between electronic properties and inhibitory activity (IC50) data thus successfully validating “Hypo1” by DFT method. Therefore, this research exertion can be helpful in the development of new potent hits for chymase. In addition, the combinational use of docking, orbital energies and molecular electrostatic potential analysis is also demonstrated as a good endeavor to gain an insight into the interaction between chymase and inhibitors. PMID:22272131
NASA Astrophysics Data System (ADS)
Buchbinder, I. L.; Ivanov, E. A.; Pletnev, N. G.
2016-05-01
We review the current state of research on the construction of effective actions in supersymmetric quantum field theory. Special attention is paid to gauge models with extended supersymmetry in the superfield approach. The advantages of formulation of such models in harmonic superspace for the calculation of effective action are emphasized. Manifestly supersymmetric and manifestly gauge-invariant methods for constructing the low-energy effective actions and deriving the corrections to them are considered and the possibilities to obtain the exact solutions are discussed. The calculations of one-loop effective actions in N = 2 supersymmetric Yang-Mills theory with hypermultiplets and in N = 4 supersymmetric Yang-Mills theory are analyzed in detail. The relationship between the effective action in supersymmetric quantum field theory and the low-energy limit in superstring theory is discussed.
Dimensional Reduction of Gauge Theories, Spontaneous Compactification and Model Building
NASA Astrophysics Data System (ADS)
Kubyshin, Yura A.; Mourao, Jose M.; Rudolph, Gerd; Volobujev, Igor P.
This monograph presents in detail the reduction method for studying the unification of fundamental actions. The mathematical (differential geometrical) methods make extensive use of Lie Groups and the concept of homogeneous spaces. The main topic of the book is the dimensional reduction of pure Yang-Mills theories. A rather complete analysis of the structure of the scalar field potential is given and a general procedure for solving the equations of spontaneous compactification within Einstein-Yang-Mills systems is presented. The authors also discuss gravity and theories with fermions included and they review attempts to construct realistic models. The book presents the basic ideas and the calculations in detail and should be of interest to researchers and graduate students in mathematical physics.
N >= 4 Supergravity Amplitudes from Gauge Theory at One Loop
Bern, Z.; Boucher-Veronneau, C.; Johansson, H.; /Saclay
2011-08-19
We expose simple and practical relations between the integrated four- and five-point one-loop amplitudes of N {ge} 4 supergravity and the corresponding (super-)Yang-Mills amplitudes. The link between the amplitudes is simply understood using the recently uncovered duality between color and kinematics that leads to a double-copy structure for gravity. These examples provide additional direct confirmations of the duality and double-copy properties at loop level for a sample of different theories.
NASA Astrophysics Data System (ADS)
Chiodaroli, M.; Günaydin, M.; Johansson, H.; Roiban, R.
2016-07-01
We show that scattering amplitudes in magical, symmetric or homogeneous N =2 Maxwell-Einstein supergravities can be obtained as double copies of two gauge theories, using the framework of color-kinematics duality. The left-hand copy is N =2 super-Yang-Mills theory coupled to a hypermultiplet, whereas the right-hand copy is a nonsupersymmetric theory that can be identified as the dimensional reduction of a D -dimensional Yang-Mills theory coupled to P fermions. For generic D and P , the double copy gives homogeneous supergravities. For P =1 and D =7 , 8, 10, 14, it gives the magical supergravities. We compute explicit amplitudes, discuss their soft limits, and study the UV behavior at one loop.
Chiodaroli, M; Günaydin, M; Johansson, H; Roiban, R
2016-07-01
We show that scattering amplitudes in magical, symmetric or homogeneous N=2 Maxwell-Einstein supergravities can be obtained as double copies of two gauge theories, using the framework of color-kinematics duality. The left-hand copy is N=2 super-Yang-Mills theory coupled to a hypermultiplet, whereas the right-hand copy is a nonsupersymmetric theory that can be identified as the dimensional reduction of a D-dimensional Yang-Mills theory coupled to P fermions. For generic D and P, the double copy gives homogeneous supergravities. For P=1 and D=7, 8, 10, 14, it gives the magical supergravities. We compute explicit amplitudes, discuss their soft limits, and study the UV behavior at one loop. PMID:27419560
Quantum spectral curve of the N=6 supersymmetric Chern-Simons theory.
Cavaglià, Andrea; Fioravanti, Davide; Gromov, Nikolay; Tateo, Roberto
2014-07-11
Recently, it was shown that the spectrum of anomalous dimensions and other important observables in planar N=4 supersymmetric Yang-Mills theory are encoded into a simple nonlinear Riemann-Hilbert problem: the Pμ system or quantum spectral curve. In this Letter, we extend this formulation to the N=6 supersymmetric Chern-Simons theory introduced by Aharony, Bergman, Jafferis, and Maldacena. This may be an important step towards the exact determination of the interpolating function h(λ) characterizing the integrability of this model. We also discuss a surprising relation between the quantum spectral curves for the N=4 supersymmetric Yang-Mills theory and the N=6 supersymmetric Chern-Simons theory considered here. PMID:25062163
Quantum Spectral Curve of the N =6 Supersymmetric Chern-Simons Theory
NASA Astrophysics Data System (ADS)
Cavaglià, Andrea; Fioravanti, Davide; Gromov, Nikolay; Tateo, Roberto
2014-07-01
Recently, it was shown that the spectrum of anomalous dimensions and other important observables in planar N=4 supersymmetric Yang-Mills theory are encoded into a simple nonlinear Riemann-Hilbert problem: the Pμ system or quantum spectral curve. In this Letter, we extend this formulation to the N =6 supersymmetric Chern-Simons theory introduced by Aharony, Bergman, Jafferis, and Maldacena. This may be an important step towards the exact determination of the interpolating function h(λ) characterizing the integrability of this model. We also discuss a surprising relation between the quantum spectral curves for the N=4 supersymmetric Yang-Mills theory and the N=6 supersymmetric Chern-Simons theory considered here.
Studies in quantum field theory
NASA Astrophysics Data System (ADS)
Polmar, S. K.
The theoretical physics group at Washington University has been devoted to the solution of problems in theoretical and mathematical physics. All of the personnel on this task have a similar approach to their research in that they apply sophisticated analytical and numerical techniques to problems primarily in quantum field theory. Specifically, this group has worked on quantum chromodynamics, classical Yang-Mills fields, chiral symmetry breaking condensates, lattice field theory, strong-coupling approximations, perturbation theory in large order, nonlinear waves, 1/N expansions, quantum solitons, phase transitions, nuclear potentials, and early universe calculations.
NASA Astrophysics Data System (ADS)
Pletinckx, D.
2011-09-01
The current 3D hype creates a lot of interest in 3D. People go to 3D movies, but are we ready to use 3D in our homes, in our offices, in our communication? Are we ready to deliver real 3D to a general public and use interactive 3D in a meaningful way to enjoy, learn, communicate? The CARARE project is realising this for the moment in the domain of monuments and archaeology, so that real 3D of archaeological sites and European monuments will be available to the general public by 2012. There are several aspects to this endeavour. First of all is the technical aspect of flawlessly delivering 3D content over all platforms and operating systems, without installing software. We have currently a working solution in PDF, but HTML5 will probably be the future. Secondly, there is still little knowledge on how to create 3D learning objects, 3D tourist information or 3D scholarly communication. We are still in a prototype phase when it comes to integrate 3D objects in physical or virtual museums. Nevertheless, Europeana has a tremendous potential as a multi-facetted virtual museum. Finally, 3D has a large potential to act as a hub of information, linking to related 2D imagery, texts, video, sound. We describe how to create such rich, explorable 3D objects that can be used intuitively by the generic Europeana user and what metadata is needed to support the semantic linking.
Dualities in M-theory and Born-Infeld Theory
Brace, Daniel, M
2001-08-01
We discuss two examples of duality. The first arises in the context of toroidal compactification of the discrete light cone quantization of M-theory. In the presence of nontrivial moduli coming from the M-theory three form, it has been conjectured that the system is described by supersymmetric Yang-Mills gauge theory on a noncommutative torus. We are able to provide evidence for this conjecture, by showing that the dualities of this M-theory compactification, which correspond to T-duality in Type IIA string theory, are also dualities of the noncommutative supersymmetric Yang-Mills description. One can also consider this as evidence for the accuracy of the Matrix Theory description of M-theory in this background. The second type of duality is the self-duality of theories with U(1) gauge fields. After discussing the general theory of duality invariance for theories with complex gauge fields, we are able to find a generalization of the well known U(1) Born-Infeld theory that contains any number of gauge fields and which is invariant under the maximal duality group. We then find a supersymmetric extension of our results, and also show that our results can be extended to find Born-Infeld type actions in any even dimensional spacetime.
A New Lorentz Violating Nonlocal Field Theory From String-Theory
Ganor, Ori J.
2007-10-04
A four-dimensional field theory with a qualitatively new type of nonlocality is constructed from a setting where Kaluza-Klein particles probe toroidally compactified string theory with twisted boundary conditions. In this theory fundamental particles are not pointlike and occupy a volume proportional to their R-charge. The theory breaks Lorentz invariance but appears to preserve spatial rotations. At low energies, it is approximately N=4 Super Yang-Mills theory, deformed by an operator of dimension seven. The dispersion relation of massless modes in vacuum is unchanged, but under certain conditions in this theory, particles can travel at superluminal velocities.
NASA Astrophysics Data System (ADS)
Yang, Xu; Zhang, Yong; Yang, Chenghua; Xu, Lu; Wang, Qiang; Zhao, Yuan
2016-06-01
Conventional three dimensional (3D) ghost imaging measures range of target based on pulse fight time measurement method. Due to the limit of data acquisition system sampling rate, range resolution of the conventional 3D ghost imaging is usually low. In order to take off the effect of sampling rate to range resolution of 3D ghost imaging, a heterodyne 3D ghost imaging (HGI) system is presented in this study. The source of HGI is a continuous wave laser instead of pulse laser. Temporal correlation and spatial correlation of light are both utilized to obtain the range image of target. Through theory analysis and numerical simulations, it is demonstrated that HGI can obtain high range resolution image with low sampling rate.
NASA Astrophysics Data System (ADS)
Choubey, Sanjay K.; Mariadasse, Richard; Rajendran, Santhosh; Jeyaraman, Jeyakanthan
2016-12-01
Overexpression of HDAC1, a member of Class I histone deacetylase is reported to be implicated in breast cancer. Epigenetic alteration in carcinogenesis has been the thrust of research for few decades. Increased deacetylation leads to accelerated cell proliferation, cell migration, angiogenesis and invasion. HDAC1 is pronounced as the potential drug target towards the treatment of breast cancer. In this study, the biochemical potential of 6-aminonicotinamide derivatives was rationalized. Five point pharmacophore model with one hydrogen-bond acceptor (A3), two hydrogen-bond donors (D5, D6), one ring (R12) and one hydrophobic group (H8) was developed using 6-aminonicotinamide derivatives. The pharmacophore hypothesis yielded a 3D-QSAR model with correlation-coefficient (r2 = 0.977, q2 = 0.801) and it was externally validated with (r2pred = 0.929, r2cv = 0.850 and r2m = 0.856) which reveals the statistical significance of the model having high predictive power. The model was then employed as 3D search query for virtual screening against compound libraries (Zinc, Maybridge, Enamine, Asinex, Toslab, LifeChem and Specs) in order to identify novel scaffolds which can be experimentally validated to design future drug molecule. Density Functional Theory (DFT) at B3LYP/6-31G* level was employed to explore the electronic features of the ligands involved in charge transfer reaction during receptor ligand interaction. Binding free energy (ΔGbind) calculation was done using MM/GBSA which defines the affinity of ligands towards the receptor.
Large-N reduction in QCD-like theories with massive adjoint fermions
Azeyanagi, Tatsuo; Hanada, Masanori; Unsal, Mithat; Yacoby, Ran; /Weizmann Inst.
2010-08-26
Large-N QCD with heavy adjoint fermions emulates pure Yang-Mills theory at long distances. We study this theory on a four- and three-torus, and analytically argue the existence of a large-small volume equivalence. For any finite mass, center symmetry unbroken phase exists at sufficiently small volume and this phase can be used to study the large-volume limit through the Eguchi-Kawai equivalence. A finite temperature version of volume independence implies that thermodynamics on R3 x S1 can be studied via a unitary matrix quantum mechanics on S1, by varying the temperature. To confirm this non-perturbatively, we numerically study both zero- and one-dimensional theories by using Monte-Carlo simulation. Order of finite-N corrections turns out to be 1/N. We introduce various twisted versions of the reduced QCD which systematically suppress finite-N corrections. Using a twisted model, we observe the confinement/deconfinement transition on a 1{sup 3} x 2-lattice. The result agrees with large volume simulations of Yang-Mills theory. We also comment that the twisted model can serve as a non-perturbative formulation of the non-commutative Yang-Mills theory.
Meng, Da; Zheng, Bin; Lin, Guang; Sushko, Maria L.
2014-08-29
We have developed efficient numerical algorithms for the solution of 3D steady-state Poisson-Nernst-Planck equations (PNP) with excess chemical potentials described by the classical density functional theory (cDFT). The coupled PNP equations are discretized by finite difference scheme and solved iteratively by Gummel method with relaxation. The Nernst-Planck equations are transformed into Laplace equations through the Slotboom transformation. Algebraic multigrid method is then applied to efficiently solve the Poisson equation and the transformed Nernst-Planck equations. A novel strategy for calculating excess chemical potentials through fast Fourier transforms is proposed which reduces computational complexity from O(N2) to O(NlogN) where N is the number of grid points. Integrals involving Dirac delta function are evaluated directly by coordinate transformation which yields more accurate result compared to applying numerical quadrature to an approximated delta function. Numerical results for ion and electron transport in solid electrolyte for Li ion batteries are shown to be in good agreement with the experimental data and the results from previous studies.
NASA Astrophysics Data System (ADS)
Meulien Ohlmann, Odile
2013-02-01
Today the industry offers a chain of 3D products. Learning to "read" and to "create in 3D" becomes an issue of education of primary importance. 25 years professional experience in France, the United States and Germany, Odile Meulien set up a personal method of initiation to 3D creation that entails the spatial/temporal experience of the holographic visual. She will present some different tools and techniques used for this learning, their advantages and disadvantages, programs and issues of educational policies, constraints and expectations related to the development of new techniques for 3D imaging. Although the creation of display holograms is very much reduced compared to the creation of the 90ies, the holographic concept is spreading in all scientific, social, and artistic activities of our present time. She will also raise many questions: What means 3D? Is it communication? Is it perception? How the seeing and none seeing is interferes? What else has to be taken in consideration to communicate in 3D? How to handle the non visible relations of moving objects with subjects? Does this transform our model of exchange with others? What kind of interaction this has with our everyday life? Then come more practical questions: How to learn creating 3D visualization, to learn 3D grammar, 3D language, 3D thinking? What for? At what level? In which matter? for whom?
Geometry and dynamics of a coupled 4 D-2 D quantum field theory
NASA Astrophysics Data System (ADS)
Bolognesi, Stefano; Chatterjee, Chandrasekhar; Evslin, Jarah; Konishi, Kenichi; Ohashi, Keisuke; Seveso, Luigi
2016-01-01
Geometric and dynamical aspects of a coupled 4 D-2 D interacting quantum field theory — the gauged nonAbelian vortex — are investigated. The fluctuations of the internal 2 D nonAbelian vortex zeromodes excite the massless 4 D Yang-Mills modes and in general give rise to divergent energies. This means that the well-known 2 D C{P}^{N-1} zeromodes associated with a nonAbelian vortex become nonnormalizable.
Landau singularities and symbology: one- and two-loop MHV amplitudes in SYM theory
NASA Astrophysics Data System (ADS)
Dennen, Tristan; Spradlin, Marcus; Volovich, Anastasia
2016-03-01
We apply the Landau equations, whose solutions parameterize the locus of possible branch points, to the one- and two-loop Feynman integrals relevant to MHV amplitudes in planar {N}=4 super-Yang-Mills theory. We then identify which of the Landau singularities appear in the symbols of the amplitudes, and which do not. We observe that all of the symbol entries in the two-loop MHV amplitudes are already present as Landau singularities of one-loop pentagon integrals.
Anti-de Sitter-space/conformal-field-theory correspondence and large-N volume independence
Poppitz, Erich; Uensal, Mithat
2010-09-15
We study the Eguchi-Kawai reduction in the strong-coupling domain of gauge theories via the gravity dual of N=4 super-Yang-Mills on R{sup 3}xS{sup 1}. We show that D-branes geometrize volume independence in the center-symmetric vacuum and give supergravity predictions for the range of validity of reduced large-N models at strong coupling.
NASA Astrophysics Data System (ADS)
Geistlinger, Helmut; Ataei-Dadavi, Iman; Mohammadian, Sadjad; Vogel, Hans-Jörg
2015-11-01
We study the impact of pore structure and surface roughness on capillary trapping of nonwetting gas phase during imbibition with water for capillary numbers between 10-7 and 5 × 10-5, within glass beads, natural sands, glass beads monolayers, and 2-D micromodels. The materials exhibit different roughness of the pore-solid interface. We found that glass beads and natural sands, which exhibit nearly the same grain size distribution, pore size distribution, and connectivity, showed a significant difference of the trapped gas phase of about 15%. This difference can be explained by the microstructure of the pore-solid interface. Based on the visualization of the trapping dynamics within glass beads monolayers and 2-D micromodels, we could show that bypass trapping controls the trapping process in glass beads monolayers, while snap-off trapping controls the trapping process in 2-D micromodels. We conclude that these different trapping processes are the reason for the different trapping efficiency, when comparing glass beads packs with natural sand packs. Moreover, for small capillary numbers of 10-6, we found that the cluster size distribution of trapped gas clusters of all 2-D and 3-D porous media can be described by a universal power law behavior predicted from percolation theory. This cannot be expected a priori for 2-D porous media, because bicontinuity of the two bulk phases is violated. Obviously, bicontinuity holds for the thin-film water phase and the bulk gas phase. The snap-off trapping process leads to ordinary bond percolation in front of the advancing bulk water phase and is the reason for the observed universal power law behavior in 2-D micromodels with rough surfaces.
ERIC Educational Resources Information Center
Hastings, S. K.
2002-01-01
Discusses 3 D imaging as it relates to digital representations in virtual library collections. Highlights include X-ray computed tomography (X-ray CT); the National Science Foundation (NSF) Digital Library Initiatives; output peripherals; image retrieval systems, including metadata; and applications of 3 D imaging for libraries and museums. (LRW)
Solitons and black holes in non-Abelian Einstein-Born-Infeld theory
NASA Astrophysics Data System (ADS)
Dyadichev, V. V.; Gal'tsov, D. V.
2000-08-01
Recently it was shown that the Born-Infeld modification of the quadratic Yang-Mills action gives rise to classical particle-like solutions in the flat space which have a striking similarity with the Bartnik-McKinnon solutions obtained within the gravity coupled Yang-Mills theory. We show that both families of solutions are continuously related within the framework of the Einstein-Born-Infeld theory via interpolating sequences of parameters. We also investigate an internal structure of the associated black holes and find that the Born-Infeld non-linearity changes drastically the black hole interior typical for the usual quadratic Yang-Mills theory. In the latter case a generic solution exhibits violent metric oscillations near the singularity. In the Born-Infeld case the generic interior solution is smooth, the metric tends to the standard Schwarzschild type singularity, and we did not observe internal horizons. Smoothing of the `violent' EYM singularity may be interpreted as a result of non-gravitational quantum effects.
Non-linear gauge transformations in D = 10 SYM theory and the BCJ duality
NASA Astrophysics Data System (ADS)
Lee, Seungjin; Mafra, Carlos R.; Schlotterer, Oliver
2016-03-01
Recent progress on scattering amplitudes in super Yang-Mills and super-string theory benefitted from the use of multiparticle superfields. They universally capture tree-level subdiagrams, and their generating series solve the non-linear equations of ten-dimensional super Yang-Mills. We provide simplified recursions for multiparticle superfields and relate them to earlier representations through non-linear gauge transformations of their generating series. Moreover, we discuss the gauge transformations which enforce their Lie symmetries as suggested by the Bern-Carrasco-Johansson duality between color and kine-matics. Another gauge transformation due to Harnad and Shnider is shown to streamline the theta-expansion of multiparticle superfields, bypassing the need to use their recursion relations beyond the lowest components. The findings of this work tremendously simplify the component extraction from kinematic factors in pure spinor superspace.
Crandall, K.R.
1987-08-01
TRACE 3-D is an interactive beam-dynamics program that calculates the envelopes of a bunched beam, including linear space-charge forces, through a user-defined transport system. TRACE 3-D provides an immediate graphics display of the envelopes and the phase-space ellipses and allows nine types of beam-matching options. This report describes the beam-dynamics calculations and gives detailed instruction for using the code. Several examples are described in detail.
Saririan, K.
1997-05-01
In this thesis, the author presents some works in the direction of studying quantum effects in locally supersymmetric effective field theories that appear in the low energy limit of superstring theory. After reviewing the Kaehler covariant formulation of supergravity, he shows the calculation of the divergent one-loop contribution to the effective boson Lagrangian for supergravity, including the Yang-Mills sector and the helicity-odd operators that arise from integration over fermion fields. The only restriction is on the Yang-Mills kinetic energy normalization function, which is taken diagonal in gauge indices, as in models obtained from superstrings. He then presents the full result for the divergent one-loop contribution to the effective boson Lagrangian for supergravity coupled to chiral and Yang-Mills supermultiplets. He also considers the specific case of dilaton couplings in effective supergravity Lagrangians from superstrings, for which the one-loop result is considerably simplified. He studies gaugino condensation in the presence of an intermediate mass scale in the hidden sector. S-duality is imposed as an approximate symmetry of the effective supergravity theory. Furthermore, the author includes in the Kaehler potential the renormalization of the gauge coupling and the one-loop threshold corrections at the intermediate scale. It is shown that confinement is indeed achieved. Furthermore, a new running behavior of the dilaton arises which he attributes to S-duality. He also discusses the effects of the intermediate scale, and possible phenomenological implications of this model.
NASA Astrophysics Data System (ADS)
Oldham, Mark
2015-01-01
Radiochromic materials exhibit a colour change when exposed to ionising radiation. Radiochromic film has been used for clinical dosimetry for many years and increasingly so recently, as films of higher sensitivities have become available. The two principle advantages of radiochromic dosimetry include greater tissue equivalence (radiologically) and the lack of requirement for development of the colour change. In a radiochromic material, the colour change arises direct from ionising interactions affecting dye molecules, without requiring any latent chemical, optical or thermal development, with important implications for increased accuracy and convenience. It is only relatively recently however, that 3D radiochromic dosimetry has become possible. In this article we review recent developments and the current state-of-the-art of 3D radiochromic dosimetry, and the potential for a more comprehensive solution for the verification of complex radiation therapy treatments, and 3D dose measurement in general.
Taming supersymmetric defects in 3d–3d correspondence
NASA Astrophysics Data System (ADS)
Gang, Dongmin; Kim, Nakwoo; Romo, Mauricio; Yamazaki, Masahito
2016-07-01
We study knots in 3d Chern–Simons theory with complex gauge group {SL}(N,{{C}}), in the context of its relation with 3d { N }=2 theory (the so-called 3d–3d correspondence). The defect has either co-dimension 2 or co-dimension 4 inside the 6d (2,0) theory, which is compactified on a 3-manifold \\hat{M}. We identify such defects in various corners of the 3d–3d correspondence, namely in 3d {SL}(N,{{C}}) CS theory, in 3d { N }=2 theory, in 5d { N }=2 super Yang–Mills theory, and in the M-theory holographic dual. We can make quantitative checks of the 3d–3d correspondence by computing partition functions at each of these theories. This Letter is a companion to a longer paper [1], which contains more details and more results.
NASA Astrophysics Data System (ADS)
Iliesiu, Luca; Kos, Filip; Poland, David; Pufu, Silviu S.; Simmons-Duffin, David; Yacoby, Ran
2016-03-01
We study the conformal bootstrap for a 4-point function of fermions < ψψψψ> in 3D. We first introduce an embedding formalism for 3D spinors and compute the conformal blocks appearing in fermion 4-point functions. Using these results, we find general bounds on the dimensions of operators appearing in the ψ × ψ OPE, and also on the central charge C T . We observe features in our bounds that coincide with scaling dimensions in the GrossNeveu models at large N . We also speculate that other features could coincide with a fermionic CFT containing no relevant scalar operators.
Large N phase transitions in massive N = 2 gauge theories
Russo, J. G.
2014-07-23
Using exact results obtained from localization on S{sup 4}, we explore the large N limit of N = 2 super Yang-Mills theories with massive matter multiplets. In this talk we discuss two cases: N = 2* theory, describing a massive hypermultiplet in the adjoint representation, and super QCD with massive quarks. When the radius of the four-sphere is sent to infinity these theories are described by solvable matrix models, which exhibit a number of interesting phenomena including quantum phase transitions at finite 't Hooft coupling.
SDiff gauge theory and the M2 condensate
NASA Astrophysics Data System (ADS)
Bandos, Igor A.; Townsend, Paul K.
2009-02-01
We develop a general formalism for the construction, in D-dimensional Minkowski space, of gauge theories for which the gauge group is the infinite-dimensional group SDiffn of volume-preserving diffeomorphisms of some closed n-dimensional manifold. We then focus on the D = 3 SDiff3 superconformal gauge theory describing a condensate of M2-branes; in particular, we derive its Script N = 8 superfield equations from a pure-spinor superspace action, and we describe its relationship to the D = 3 SDiff2 super-Yang-Mills theory describing a condensate of D2-branes.
Schmitt, Boris; Li, Tieyan; Kutty, Shelby; Khasheei, Alireza; Schmitt, Katharina R L; Anderson, Robert H; Lunkenheimer, Paul P; Berger, Felix; Kühne, Titus; Peters, Björn
2015-07-01
Beta-blockers contribute to treatment of heart failure. Their mechanism of action, however, is incompletely understood. Gradients in beta-blocker sensitivity of helically aligned cardiomyocytes compared with counteracting transversely intruding cardiomyocytes seem crucial. We hypothesize that selective blockade of transversely intruding cardiomyocytes by low-dose beta-blockade unloads ventricular performance. Cardiac magnetic resonance imaging (MRI) 3D tagging delivers parameters of myocardial performance. We studied 13 healthy volunteers by MRI 3D tagging during escalated intravenous administration of esmolol. The circumferential, longitudinal, and radial myocardial shortening was determined for each dose. The curves were analyzed for peak value, time-to-peak, upslope, and area-under-the-curve. At low doses, from 5 to 25 μg·kg(-1)·min(-1), peak contraction increased while time-to-peak decreased yielding a steeper upslope. Combining the values revealed a left shift of the curves at low doses compared with baseline without esmolol. At doses of 50 to 150 μg·kg(-1)·min(-1), a right shift with flattening occurred. In healthy volunteers we found more pronounced myocardial shortening at low compared with clinical dosage of beta-blockers. In patients with ventricular hypertrophy and higher prevalence of transversely intruding cardiomyocytes selective low-dose beta-blockade could be even more effective. MRI 3D tagging could help to determine optimal individual beta-blocker dosing avoiding undesirable side effects. PMID:25888512
New applications of on-shell methods in quantum field theory
NASA Astrophysics Data System (ADS)
Engelund, Oluf Tang
This thesis incorporates 4 years of work: it gives a small introduction to the field of scattering amplitudes and especially into the method of generalized unitarity then discuss 4 different projects all in the field of scattering amplitudes. First we will look at a duality between correlation functions in a special lightlike limit and Wilson loops in N = 4 Super-Yang-Mills. The duality, originally suggested by Alday, Eden, Korchemsky, Maldacena and Sokatchev, was part of a effort to put a firmer footing on the duality between scattering amplitudes and Wilson loops. The duality between correlation functions and Wilson loops does not have any regularization issues (like the other duality) as both have infrared divergences in the specific limits considered. We show how the duality works vertex-by-vertex using just Feynman rules. The method is sufficiently general to allow for extensions of the original duality including operators not taking part in the special light-like limit, other types of operators as well as other theories than N = 4 Super-Yang-Mills. After that we look at how to use generalized unitarity for correlation functions with some examples from N = 4 Super-Yang-Mills. For computations one needs quantities known as form factors which have both asymptotic states like scattering amplitudes and local operators like correlation functions. We compute several form factors using modern methods from scattering amplitudes. Thirdly, we study how to use generalized unitarity for two-dimensional integrable systems. Two-dimensional systems have their own unique set of challenges but generalized unitarity can be adapted to them and we show how one can carry out tests of integrability which would otherwise be difficult. Finally, we look at the 3-dimensional theory known as ABJ(M). Its tree-level amplitudes can be incorporated into a single formula very reminiscent of a result in N = 4 Super-Yang-Mills. Since the result from N = 4 Super-Yang-Mills follow directly from
NASA Astrophysics Data System (ADS)
Iizuka, Keigo
2008-02-01
In order to circumvent the fact that only one observer can view the image from a stereoscopic microscope, an attachment was devised for displaying the 3D microscopic image on a large LCD monitor for viewing by multiple observers in real time. The principle of operation, design, fabrication, and performance are presented, along with tolerance measurements relating to the properties of the cellophane half-wave plate used in the design.
Gravity as the square of gauge theory
Bern, Zvi; Dennen, Tristan; Huang Yutin; Kiermaier, Michael
2010-09-15
We explore consequences of the recently discovered duality between color and kinematics, which states that kinematic numerators in a diagrammatic expansion of gauge-theory amplitudes can be arranged to satisfy Jacobi-like identities in one-to-one correspondence to the associated color factors. Using on-shell recursion relations, we give a field-theory proof showing that the duality implies that diagrammatic numerators in gravity are just the product of two corresponding gauge-theory numerators, as previously conjectured. These squaring relations express gravity amplitudes in terms of gauge-theory ingredients, and are a recasting of the Kawai, Lewellen, and Tye relations. Assuming that numerators of loop amplitudes can be arranged to satisfy the duality, our tree-level proof immediately carries over to loop level via the unitarity method. We then present a Yang-Mills Lagrangian whose diagrams through five points manifestly satisfy the duality between color and kinematics. The existence of such Lagrangians suggests that the duality also extends to loop amplitudes, as confirmed at two and three loops in a concurrent paper. By ''squaring'' the novel Yang-Mills Lagrangian we immediately obtain its gravity counterpart. We outline the general structure of these Lagrangians for higher points. We also write down various new representations of gauge-theory and gravity amplitudes that follow from the duality between color and kinematics.
NASA Astrophysics Data System (ADS)
Engheta, Nader; Alu, Andrea
2006-03-01
In recent years metamaterials have offered new possibilities for overcoming some of the intrinsic limitations in wave propagation. Their realization at microwave frequencies has followed two different paths; one consisting of embedding resonant inclusions in a host dielectric, and the other following a transmission-line approach, i.e., building 1-D, 2-D, or 3-D cascades of circuit elements, respectively, as linear, planar or bulk right- or left-handed metamaterials. The latter is known to provide larger bandwidth and better robustness to ohmic losses. Extending these concepts to optical frequencies is a challenging task, due to changes in material response to electromagnetic waves at these frequencies. However, recently we have studied theoretically how it may be possible to have circuit nano-elements at these frequencies by properly exploiting plasmonic resonances. Here we present our theoretical work on translating the circuit concepts of right- and left-handed metamaterials into optical frequencies by applying the analogy between nanoparticles and nanocircuit elements in transmission lines. We discuss how it is possible to synthesize optical negative-refraction metamaterials by properly cascading plasmonic and non-plasmonic elements in 1-D, 2-D and 3-D geometries.
Gauge Theories of Vector Particles
DOE R&D Accomplishments Database
Glashow, S. L.; Gell-Mann, M.
1961-04-24
The possibility of generalizing the Yang-Mills trick is examined. Thus we seek theories of vector bosons invariant under continuous groups of coordinate-dependent linear transformations. All such theories may be expressed as superpositions of certain "simple" theories; we show that each "simple theory is associated with a simple Lie algebra. We may introduce mass terms for the vector bosons at the price of destroying the gauge-invariance for coordinate-dependent gauge functions. The theories corresponding to three particular simple Lie algebras - those which admit precisely two commuting quantum numbers - are examined in some detail as examples. One of them might play a role in the physics of the strong interactions if there is an underlying super-symmetry, transcending charge independence, that is badly broken. The intermediate vector boson theory of weak interactions is discussed also. The so-called "schizon" model cannot be made to conform to the requirements of partial gauge-invariance.
Role of division algebra in seven-dimensional gauge theory
NASA Astrophysics Data System (ADS)
Kalauni, Pushpa; Barata, J. C. A.
2015-03-01
The algebra of octonions 𝕆 forms the largest normed division algebra over the real numbers ℝ, complex numbers ℂ and quaternions ℍ. The usual three-dimensional vector product is given by quaternions, while octonions produce seven-dimensional vector product. Thus, octonionic algebra is closely related to the seven-dimensional algebra, therefore one can extend generalization of rotations in three dimensions to seven dimensions using octonions. An explicit algebraic description of octonions has been given to describe rotational transformation in seven-dimensional space. We have also constructed a gauge theory based on non-associative algebra to discuss Yang-Mills theory and field equation in seven-dimensional space.
The non-Abelian gauge theory of matrix big bangs
NASA Astrophysics Data System (ADS)
O'Loughlin, Martin; Seri, Lorenzo
2010-07-01
We study at the classical and quantum mechanical level the time-dependent Yang-Mills theory that one obtains via the generalisation of discrete light-cone quantization to singular homogeneous plane waves. The non-Abelian nature of this theory is known to be important for physics near the singularity, at least as far as the number of degrees of freedom is concerned. We will show that the quartic interaction is always subleading as one approaches the singularity and that close enough to t = 0 the evolution is driven by the diverging tachyonic mass term. The evolution towards asymptotically flat space-time also reveals some surprising features.
NASA Astrophysics Data System (ADS)
Kostrzewski, Andrew A.; Aye, Tin M.; Kim, Dai Hyun; Esterkin, Vladimir; Savant, Gajendra D.
1998-09-01
Physical Optics Corporation has developed an advanced 3-D virtual reality system for use with simulation tools for training technical and military personnel. This system avoids such drawbacks of other virtual reality (VR) systems as eye fatigue, headaches, and alignment for each viewer, all of which are due to the need to wear special VR goggles. The new system is based on direct viewing of an interactive environment. This innovative holographic multiplexed screen technology makes it unnecessary for the viewer to wear special goggles.
NASA Technical Reports Server (NTRS)
1992-01-01
Ames Research Center research into virtual reality led to the development of the Convolvotron, a high speed digital audio processing system that delivers three-dimensional sound over headphones. It consists of a two-card set designed for use with a personal computer. The Convolvotron's primary application is presentation of 3D audio signals over headphones. Four independent sound sources are filtered with large time-varying filters that compensate for motion. The perceived location of the sound remains constant. Possible applications are in air traffic control towers or airplane cockpits, hearing and perception research and virtual reality development.
NASA Astrophysics Data System (ADS)
Zhu, Chaoyuan; Kamisaka, Hideyuki; Nakamura, Hiroki
2002-02-01
The newly implemented trajectory surface hopping (TSH) method for the collinear system with use of the Zhu-Nakamura semiclassical theory of nonadiabatic transition [C. Zhu, K. Nobusada, and H. Nakamura, J. Chem. Phys. 115, 3031 (2001)] is extended to treat 3D nonadiabatic reactions. Since the avoided crossing seam becomes a two-dimensional surface in the 3D system, the nonadiabatic transition region and the possibility of classically forbidden hops are enlarged very much in comparison with those in the collinear case. As a result, the contribution of the classically forbidden hops is quite a bit enhanced in the 3D system. Conservation of total angular momentum J is taken into account by slightly rotating the direction of momentum during the hop in the classically forbidden case. The method is tested by applying to the charge transfer processes in the 3D DH2+ system for J=0. Numerical results clearly demonstrate that the new TSH method works very well at all energies and for all initial vibrational states considered compared to the old TSH method based on the Landau-Zener formula. The significant discrepancy between the two TSH methods survives even at high collision energy and high vibrational states in contrast to the collinear case, indicating the importance of the classically forbidden hops in 3D systems. The new TSH method is considered to be a very promising method to deal with high dimensional nonadiabatic dynamics. It should also be noted that the new TSH method does not require any knowledge of nonadiabatic coupling and is based only on adiabatic potentials.
Cevidanes, Lucia; Tucker, Scott; Styner, Martin; Kim, Hyungmin; Chapuis, Jonas; Reyes, Mauricio; Proffit, William; Turvey, Timothy; Jaskolka, Michael
2009-01-01
This paper discusses the development of methods for computer-aided jaw surgery. Computer-aided jaw surgery allows us to incorporate the high level of precision necessary for transferring virtual plans into the operating room. We also present a complete computer-aided surgery (CAS) system developed in close collaboration with surgeons. Surgery planning and simulation include construction of 3D surface models from Cone-beam CT (CBCT), dynamic cephalometry, semi-automatic mirroring, interactive cutting of bone and bony segment repositioning. A virtual setup can be used to manufacture positioning splints for intra-operative guidance. The system provides further intra-operative assistance with the help of a computer display showing jaw positions and 3D positioning guides updated in real-time during the surgical procedure. The CAS system aids in dealing with complex cases with benefits for the patient, with surgical practice, and for orthodontic finishing. Advanced software tools for diagnosis and treatment planning allow preparation of detailed operative plans, osteotomy repositioning, bone reconstructions, surgical resident training and assessing the difficulties of the surgical procedures prior to the surgery. CAS has the potential to make the elaboration of the surgical plan a more flexible process, increase the level of detail and accuracy of the plan, yield higher operative precision and control, and enhance documentation of cases. Supported by NIDCR DE017727, and DE018962 PMID:20816308
NASA Astrophysics Data System (ADS)
Correa, Diego H.; Silva, Guillermo A.
2008-07-01
We discuss how geometrical and topological aspects of certain 1/2-BPS type IIB geometries are captured by their dual operators in N = 4 Super Yang-Mills theory. The type IIB solutions are characterized by arbitrary droplet pictures in a plane and we consider, in particular, axially symmetric droplets. The 1-loop anomalous dimension of the dual gauge theory operators probed with single traces is described by some bosonic lattice Hamiltonians. These Hamiltonians are shown to encode the topology of the droplets. In appropriate BMN limits, the Hamiltonians spectrum reproduces the spectrum of near-BPS string excitations propagating along each of the individual edges of the droplet. We also study semiclassical regimes for the Hamiltonians. For droplets having disconnected constituents, the Hamiltonian admits different complimentary semiclassical descriptions, each one replicating the semiclassical description for closed strings extending in each of the constituents.
Correa, Diego H.; Silva, Guillermo A.
2008-07-28
We discuss how geometrical and topological aspects of certain (1/2)-BPS type IIB geometries are captured by their dual operators in N = 4 Super Yang-Mills theory. The type IIB solutions are characterized by arbitrary droplet pictures in a plane and we consider, in particular, axially symmetric droplets. The 1-loop anomalous dimension of the dual gauge theory operators probed with single traces is described by some bosonic lattice Hamiltonians. These Hamiltonians are shown to encode the topology of the droplets. In appropriate BMN limits, the Hamiltonians spectrum reproduces the spectrum of near-BPS string excitations propagating along each of the individual edges of the droplet. We also study semiclassical regimes for the Hamiltonians. For droplets having disconnected constituents, the Hamiltonian admits different complimentary semiclassical descriptions, each one replicating the semiclassical description for closed strings extending in each of the constituents.
NASA Astrophysics Data System (ADS)
Gil, José J.; San José, Ignacio
2010-11-01
From our previous definition of the indices of polarimetric purity for 3D light beams [J.J. Gil, J.M. Correas, P.A. Melero and C. Ferreira, Monogr. Semin. Mat. G. de Galdeano 31, 161 (2004)], an analysis of their geometric and physical interpretation is presented. It is found that, in agreement with previous results, the first parameter is a measure of the degree of polarization, whereas the second parameter (called the degree of directionality) is a measure of the mean angular aperture of the direction of propagation of the corresponding light beam. This pair of invariant, non-dimensional, indices of polarimetric purity contains complete information about the polarimetric purity of a light beam. The overall degree of polarimetric purity is obtained as a weighted quadratic average of the degree of polarization and the degree of directionality.
Caspi, S.; Helm, M.; Laslett, L.J.
1991-03-30
We have developed an harmonic representation for the three dimensional field components within the windings of accelerator magnets. The form by which the field is presented is suitable for interfacing with other codes that make use of the 3D field components (particle tracking and stability). The field components can be calculated with high precision and reduced cup time at any location (r,{theta},z) inside the magnet bore. The same conductor geometry which is used to simulate line currents is also used in CAD with modifications more readily available. It is our hope that the format used here for magnetic fields can be used not only as a means of delivering fields but also as a way by which beam dynamics can suggest correction to the conductor geometry. 5 refs., 70 figs.
NASA Technical Reports Server (NTRS)
2004-01-01
The Mars Exploration Rover Spirit took this 3-D navigation camera mosaic of the crater called 'Bonneville' after driving approximately 13 meters (42.7 feet) to get a better vantage point. Spirit's current position is close enough to the edge to see the interior of the crater, but high enough and far enough back to get a view of all of the walls. Because scientists and rover controllers are so pleased with this location, they will stay here for at least two more martian days, or sols, to take high resolution panoramic camera images of 'Bonneville' in its entirety. Just above the far crater rim, on the left side, is the rover's heatshield, which is visible as a tiny reflective speck.
ERIC Educational Resources Information Center
Rias, Riaza Mohd; Zaman, Halimah Badioze
2011-01-01
Higher learning based instruction may be primarily concerned in most cases with the content of their academic lessons, and not very much with their instructional delivery. However, the effective application of learning theories and technology in higher education has an impact on student performance. With the rapid progress in the computer and…
NASA Astrophysics Data System (ADS)
Capdeville, Y.; Gung, Y.; Romanowicz, B.
2002-12-01
The spectral element method (SEM) has recently been adapted successfully for global spherical earth wave propagation applications. Its advantage is that it provides a way to compute exact seismograms in a 3D earth, without restrictions on the size or wavelength of lateral heterogeneity at any depth, and can handle diffraction and other interactions with major structural boundaries. Its disadvantage is that it is computationally heavy. In order to partly address this drawback, a coupled SEM/normal mode method was developed (Capdeville et al., 2000). This enables us to more efficiently compute bodywave seismograms to realistically short periods (10s or less). In particular, the coupled SEM/normal mode method is a powerful tool to test the validity of some analytical approximations that are currently used in global waveform tomography, and that are considerably faster computationally. Here, we focus on several approximations based on normal mode perturbation theory: the classical "path-average approximation" (PAVA) introduced by Woodhouse and Dziewonski (1984) and well suited for fundamental mode surface waves (1D sensitivity kernels); the non-linear asymptotic coupling theory (NACT), which introduces coupling between mode branches and 2D kernels in the vertical plane containing the source and the receiver (Li and Tanimoto, 1993; Li and Romanowicz, 1995); an extension of NACT which includes out of plane focusing terms computed asymptotically (e.g. Romanowicz, 1987) and introduces 3D kernels; we also consider first order perturbation theory without asymptotic approximations, such as developed for example by Dahlen et al. (2000). We present the results of comparisons of realistic seismograms for different models of heterogeneity, varying the strength and sharpness of the heterogeneity and its location in depth in the mantle. We discuss the consequences of different levels of approximations on our ability to resolve 3D heterogeneity in the earth's mantle.
Noncommutative Geometry in M-Theory and Conformal Field Theory
Morariu, Bogdan
1999-05-01
In the first part of the thesis I will investigate in the Matrix theory framework, the subgroup of dualities of the Discrete Light Cone Quantization of M-theory compactified on tori, which corresponds to T-duality in the auxiliary Type II string theory. After a review of matrix theory compactification leading to noncommutative supersymmetric Yang-Mills gauge theory, I will present solutions for the fundamental and adjoint sections on a two-dimensional twisted quantum torus and generalize to three-dimensional twisted quantum tori. After showing how M-theory T-duality is realized in supersymmetric Yang-Mills gauge theories on dual noncommutative tori I will relate this to the mathematical concept of Morita equivalence of C*-algebras. As a further generalization, I consider arbitrary Ramond-Ramond backgrounds. I will also discuss the spectrum of the toroidally compactified Matrix theory corresponding to quantized electric fluxes on two and three tori. In the second part of the thesis I will present an application to conformal field theory involving quantum groups, another important example of a noncommutative space. First, I will give an introduction to Poisson-Lie groups and arrive at quantum groups using the Feynman path integral. I will quantize the symplectic leaves of the Poisson-Lie group SU(2)*. In this way we obtain the unitary representations of U{sub q}(SU(2)). I discuss the X-structure of SU(2)* and give a detailed description of its leaves using various parametrizations. Then, I will introduce a new reality structure on the Heisenberg double of Fun{sub q} (SL(N,C)) for q phase, which can be interpreted as the quantum phase space of a particle on the q-deformed mass-hyperboloid. I also present evidence that the above real form describes zero modes of certain non-compact WZNW-models.
NASA Astrophysics Data System (ADS)
Sadri, Darius; Sheikh-Jabbari, Mohammad M.
2006-03-01
We consider Script N = 1, D = 4 superconformal U(N)p × q Yang-Mills theories dual to AdS5 × S5/Zp × Zq orbifolds. We construct the dilatation operator of this superconformal gauge theory at one-loop planar level. We demonstrate that a specific sector of this dilatation operator can be thought of as the transfer matrix for a two-dimensional statistical mechanical system, related to an integrable SU(3) ferromagnetic spin chain system, which in turn is equivalent to a 2+1-dimensional string theory where the spatial slices are discretized on a triangular lattice. This is an extension of the SO(6) spin chain picture of Script N = 4 super Yang-Mills theory. We comment on the integrability of this Script N = 1 gauge theory and hence the corresponding three-dimensional statistical mechanical system, its connection to three-dimensional lattice gauge theories, extensions to six-dimensional string theories, AdS/CFT type dualities and finally their construction via orbifolds and brane-box models. In the process we discover a new class of almost-BPS BMN type operators with large engineering dimensions but controllably small anomalous corrections.
Random center vortex lines in continuous 3D space-time
NASA Astrophysics Data System (ADS)
Höllwieser, Roman; Altarawneh, Derar; Engelhardt, Michael
2016-01-01
We present a model of center vortices, represented by closed random lines in continuous 2+1-dimensional space-time. These random lines are modeled as being piece-wise linear and an ensemble is generated by Monte Carlo methods. The physical space in which the vortex lines are defined is a cuboid with periodic boundary conditions. Besides moving, growing and shrinking of the vortex configuration, also reconnections are allowed. Our ensemble therefore contains not a fixed, but a variable number of closed vortex lines. This is expected to be important for realizing the deconfining phase transition. Using the model, we study both vortex percolation and the potential V(R) between quark and anti-quark as a function of distance R at different vortex densities, vortex segment lengths, reconnection conditions and at different temperatures. We have found three deconfinement phase transitions, as a function of density, as a function of vortex segment length, and as a function of temperature. The model reproduces the qualitative features of confinement physics seen in SU(2) Yang-Mills theory.
Compact 3D flash lidar video cameras and applications
NASA Astrophysics Data System (ADS)
Stettner, Roger
2010-04-01
The theory and operation of Advanced Scientific Concepts, Inc.'s (ASC) latest compact 3D Flash LIDAR Video Cameras (3D FLVCs) and a growing number of technical problems and solutions are discussed. The solutions range from space shuttle docking, planetary entry, decent and landing, surveillance, autonomous and manned ground vehicle navigation and 3D imaging through particle obscurants.
NASA Technical Reports Server (NTRS)
1997-01-01
Many prominent rocks near the Sagan Memorial Station are featured in this image, taken in stereo by the Imager for Mars Pathfinder (IMP) on Sol 3. 3D glasses are necessary to identify surface detail. Wedge is at lower left; Shark, Half-Dome, and Pumpkin are at center. Flat Top, about four inches high, is at lower right. The horizon in the distance is one to two kilometers away.
Mars Pathfinder is the second in NASA's Discovery program of low-cost spacecraft with highly focused science goals. The Jet Propulsion Laboratory, Pasadena, CA, developed and manages the Mars Pathfinder mission for NASA's Office of Space Science, Washington, D.C. JPL is an operating division of the California Institute of Technology (Caltech). The Imager for Mars Pathfinder (IMP) was developed by the University of Arizona Lunar and Planetary Laboratory under contract to JPL. Peter Smith is the Principal Investigator.
Click below to see the left and right views individually. [figure removed for brevity, see original site] Left [figure removed for brevity, see original site] Right
NASA Technical Reports Server (NTRS)
2004-01-01
This 3-D, microscopic imager mosaic of a target area on a rock called 'Diamond Jenness' was taken after NASA's Mars Exploration Rover Opportunity ground into the surface with its rock abrasion tool for a second time.
Opportunity has bored nearly a dozen holes into the inner walls of 'Endurance Crater.' On sols 177 and 178 (July 23 and July 24, 2004), the rover worked double-duty on Diamond Jenness. Surface debris and the bumpy shape of the rock resulted in a shallow and irregular hole, only about 2 millimeters (0.08 inch) deep. The final depth was not enough to remove all the bumps and leave a neat hole with a smooth floor. This extremely shallow depression was then examined by the rover's alpha particle X-ray spectrometer.
On Sol 178, Opportunity's 'robotic rodent' dined on Diamond Jenness once again, grinding almost an additional 5 millimeters (about 0.2 inch). The rover then applied its Moessbauer spectrometer to the deepened hole. This double dose of Diamond Jenness enabled the science team to examine the rock at varying layers. Results from those grindings are currently being analyzed.
The image mosaic is about 6 centimeters (2.4 inches) across.
ERIC Educational Resources Information Center
DuBois, Ann
2010-01-01
The blending of information from an academic class with projects from art class can do nothing but strengthen the learning power of the student. Creating three-dimensional color wheels provides the perfect opportunity to combine basic geometry knowledge with color theory. In this article, the author describes how her seventh-grade painting…
NASA Technical Reports Server (NTRS)
Volakis, John L.
1991-01-01
There are two tasks described in this report. First, an extension of a two dimensional formulation is presented for a three dimensional body of revolution. A Fourier series expansion of the vector electric and magnetic fields is employed to reduce the dimensionality of the system, and an exact boundary condition is employed to terminate the mesh. The mesh termination boundary is chosen such that it leads to convolutional boundary operators for low O(n) memory demand. Second, rigorous uniform geometrical theory of diffraction (UTD) diffraction coefficients are presented for a coated convex cylinder simulated with generalized impedance boundary conditions. Ray solutions are obtained which remain valid in the transition region and reduce uniformly those in the deep lit and shadow regions. A uniform asymptotic solution is also presented for observations in the close vicinity of the cylinder.
Almeida, P. G. C.; Benilov, M. S.
2013-10-15
The work is aimed at advancing the multiple steady-state solutions that have been found recently in the theory of direct current (DC) glow discharges. It is shown that an account of detailed plasma chemistry and non-locality of electron transport and kinetic coefficients results in an increase of the number of multiple solutions but does not change their pattern. Multiple solutions are shown to exist for discharges in argon and helium provided that discharge pressure is high enough. This result indicates that self-organization in DC glow microdischarges can be observed not only in xenon, which has been the case until recently, but also in other plasma-producing gases; a conclusion that has been confirmed by recent experiments. Existence of secondary bifurcations can explain why patterns of spots grouped in concentric rings, observed in the experiment, possess in many cases higher number of spots in outer rings than in inner ones.
Massive supersymmetric quantum gauge theory
NASA Astrophysics Data System (ADS)
Grigore, D. R.; Gut, M.; Scharf, G.
2005-08-01
We continue the study of the supersymmetric vector multiplet in a purely quantum framework. We obtain some new results which make the connection with the standard literature. First we construct the one-particle physical Hilbert space taking into account the (quantum) gauge structure of the model. Then we impose the condition of positivity for the scalar product only on the physical Hilbert space. Finally we obtain a full supersymmetric coupling which is gauge invariant in the supersymmetric sense in the first order of perturbation theory. By integrating out the Grassmann variables we get an interacting Lagrangian for a massive Yang-Mills theory related to ordinary gauge theory; however the number of ghost fields is doubled so we do not obtain the same ghost couplings as in the standard model Lagrangian.
Microscopic quantum superpotential in Script N = 1 gauge theories
NASA Astrophysics Data System (ADS)
Ferrari, Frank
2007-10-01
We consider the Script N = 1 super Yang-Mills theory with gauge group U(N), adjoint chiral multiplet X and tree-level superpotential Tr W(X). We compute the quantum effective superpotential Wmic as a function of arbitrary off-shell boundary conditions at infinity for the scalar field X. This effective superpotential has a remarkable property: its critical points are in one-to-one correspondence with the full set of quantum vacua of the theory, providing in particular a unified picture of solutions with different ranks for the low energy gauge group. In this sense, Wmic is a good microscopic effective quantum superpotential for the theory. This property is not shared by other quantum effective superpotentials commonly used in the literature, like in the strong coupling approach or the glueball superpotentials. The result of this paper is a first step in extending Nekrasov's microscopic derivation of the Seiberg-Witten solution of Script N = 2 super Yang-Mills theories to the realm of Script N = 1 gauge theories.
Hadronic density of states from string theory.
Pando Zayas, Leopoldo A; Vaman, Diana
2003-09-12
We present an exact calculation of the finite temperature partition function for the hadronic states corresponding to a Penrose-Güven limit of the Maldacena-Nùñez embedding of the N=1 super Yang-Mills (SYM) into string theory. It is established that the theory exhibits a Hagedorn density of states. We propose a semiclassical string approximation to the finite temperature partition function for confining gauge theories admitting a supergravity dual, by performing an expansion around classical solutions characterized by temporal windings. This semiclassical approximation reveals a hadronic energy density of states of a Hagedorn type, with the coefficient determined by the gauge theory string tension as expected for confining theories. We argue that our proposal captures primarily information about states of pure N=1 SYM theory, given that this semiclassical approximation does not entail a projection onto states of large U(1) charge. PMID:14525414
Evidence for large- N phase transitions in mathcal{N}={2^{*}} theory
NASA Astrophysics Data System (ADS)
Russo, Jorge G.; Zarembo, Konstantin
2013-04-01
We solve, using localization, for the large- N master field of {N}={2^{*}} superYang-Mills theory. From that we calculate expectation values of large Wilson loops and the free energy on the four-sphere. At weak coupling, these observables only receive nonperturbative contributions. The analytic solution holds for a finite range of the 't Hooft coupling and terminates at the point of a large- N phase transition. We find evidence that as the coupling is further increased the theory undergoes an infinite sequence of similar transitions that accumulate at infinity.
Supergrassmannian and large N limit of quantum field theory with bosons and fermions
Konechny, Anatoly; Turgut, O. Teoman
2002-03-01
We study a large N{sub c} limit of a two-dimensional Yang-Mills theory coupled to bosons and fermions in the fundamental representation. Extending an approach due to Rajeev we show that the limiting theory can be described as a classical Hamiltonian system whose phase space is an infinite-dimensional supergrassmannian. The linear approximation to the equations of motion and the constraint yields the 't Hooft equations for the mesonic spectrum. Two other approximation schemes to the exact equations are discussed.
Marrero-Ponce, Yovani; Santiago, Oscar Martínez; López, Yoan Martínez; Barigye, Stephen J; Torrens, Francisco
2012-11-01
In this report, we present a new mathematical approach for describing chemical structures of organic molecules at atomic-molecular level, proposing for the first time the use of the concept of the derivative ([Formula: see text]) of a molecular graph (MG) with respect to a given event (E), to obtain a new family of molecular descriptors (MDs). With this purpose, a new matrix representation of the MG, which generalizes graph's theory's traditional incidence matrix, is introduced. This matrix, denominated the generalized incidence matrix, Q, arises from the Boolean representation of molecular sub-graphs that participate in the formation of the graph molecular skeleton MG and could be complete (representing all possible connected sub-graphs) or constitute sub-graphs of determined orders or types as well as a combination of these. The Q matrix is a non-quadratic and unsymmetrical in nature, its columns (n) and rows (m) are conditions (letters) and collection of conditions (words) with which the event occurs. This non-quadratic and unsymmetrical matrix is transformed, by algebraic manipulation, to a quadratic and symmetric matrix known as relations frequency matrix, F, which characterizes the participation intensity of the conditions (letters) in the events (words). With F, we calculate the derivative over a pair of atomic nuclei. The local index for the atomic nuclei i, Δ(i), can therefore be obtained as a linear combination of all the pair derivatives of the atomic nuclei i with all the rest of the j's atomic nuclei. Here, we also define new strategies that generalize the present form of obtaining global or local (group or atom-type) invariants from atomic contributions (local vertex invariants, LOVIs). In respect to this, metric (norms), means and statistical invariants are introduced. These invariants are applied to a vector whose components are the values Δ(i) for the atomic nuclei of the molecule or its fragments. Moreover, with the purpose of differentiating
NASA Astrophysics Data System (ADS)
Mediavilla, Evencio; Arribas, Santiago; Roth, Martin; Cepa-Nogué, Jordi; Sánchez, Francisco
2011-09-01
Preface; Acknowledgements; 1. Introductory review and technical approaches Martin M. Roth; 2. Observational procedures and data reduction James E. H. Turner; 3. 3D Spectroscopy instrumentation M. A. Bershady; 4. Analysis of 3D data Pierre Ferruit; 5. Science motivation for IFS and galactic studies F. Eisenhauer; 6. Extragalactic studies and future IFS science Luis Colina; 7. Tutorials: how to handle 3D spectroscopy data Sebastian F. Sánchez, Begona García-Lorenzo and Arlette Pécontal-Rousset.
3D Elevation Program—Virtual USA in 3D
Lukas, Vicki; Stoker, J.M.
2016-01-01
The U.S. Geological Survey (USGS) 3D Elevation Program (3DEP) uses a laser system called ‘lidar’ (light detection and ranging) to create a virtual reality map of the Nation that is very accurate. 3D maps have many uses with new uses being discovered all the time.
MT3D was first developed by Chunmiao Zheng in 1990 at S.S. Papadopulos & Associates, Inc. with partial support from the U.S. Environmental Protection Agency (USEPA). Starting in 1990, MT3D was released as a pubic domain code from the USEPA. Commercial versions with enhanced capab...
NASA Technical Reports Server (NTRS)
1977-01-01
A market study of a proposed version of a 3-D eyetracker for initial use at NASA's Ames Research Center was made. The commercialization potential of a simplified, less expensive 3-D eyetracker was ascertained. Primary focus on present and potential users of eyetrackers, as well as present and potential manufacturers has provided an effective means of analyzing the prospects for commercialization.
Energy Science and Technology Software Center (ESTSC)
2013-10-01
Earth3D is a computer code designed to allow fast calculation of seismic rays and travel times through a 3D model of the Earth. LLNL is using this for earthquake location and global tomography efforts and such codes are of great interest to the Earth Science community.
[3-D ultrasound in gastroenterology].
Zoller, W G; Liess, H
1994-06-01
Three-dimensional (3D) sonography represents a development of noninvasive diagnostic imaging by real-time two-dimensional (2D) sonography. The use of transparent rotating scans, comparable to a block of glass, generates a 3D effect. The objective of the present study was to optimate 3D presentation of abdominal findings. Additional investigations were made with a new volumetric program to determine the volume of selected findings of the liver. The results were compared with the estimated volumes of 2D sonography and 2D computer tomography (CT). For the processing of 3D images, typical parameter constellations were found for the different findings, which facilitated processing of 3D images. In more than 75% of the cases examined we found an optimal 3D presentation of sonographic findings with respect to the evaluation criteria developed by us for the 3D imaging of processed data. Great differences were found for the estimated volumes of the findings of the liver concerning the three different techniques applied. 3D ultrasound represents a valuable method to judge morphological appearance in abdominal findings. The possibility of volumetric measurements enlarges its potential diagnostic significance. Further clinical investigations are necessary to find out if definite differentiation between benign and malign findings is possible. PMID:7919882
2013-10-30
This video provides an overview of the Sandia National Laboratories developed 3-D World Model Building capability that provides users with an immersive, texture rich 3-D model of their environment in minutes using a laptop and color and depth camera.
None
2014-02-26
This video provides an overview of the Sandia National Laboratories developed 3-D World Model Building capability that provides users with an immersive, texture rich 3-D model of their environment in minutes using a laptop and color and depth camera.
BCFW recursion relations and string theory
NASA Astrophysics Data System (ADS)
Cheung, Clifford; O'Connell, Donal; Wecht, Brian
2010-09-01
We demonstrate that all tree-level string theory amplitudes can be computed using the BCFW recursion relations. Our proof utilizes the pomeron vertex operator introduced by Brower, Polchinski, Strassler, and Tan. Surprisingly, we find that in a particular large complex momentum limit, the asymptotic expansion of massless string amplitudes is identical in form to that of the corresponding field theory amplitudes. This observation makes manifest the fact that field-theoretic Yang-Mills and graviton amplitudes obey KLT-like relations. Moreover, we conjecture that in this large momentum limit certain string theory and field theory amplitudes are identical, and provide evidence for this conjecture. Additionally, we find a new recursion relation which relates tachyon amplitudes to lower-point tachyon amplitudes.
Introduction to string and superstring theory II
Peskin, M.E.
1987-03-01
Conformal field theory is reviewed, then conformal invariance is used to rederive the basic results on the embedding dimensionality for bosonic and fermionic strings. The spectrum of the bosonic and the computation of scattering amplitudes are discussed. The formalism used is extended to clarify the origin of Yang-Mills gauge invariance in the open bosonic string theory. The question of the general-coordinate gauge invariance of string theory is addressed, presenting two disparate viewpoints on this question. A brief introduction is then given of the reduction from the idealized string theory in 10 extended dimensions to more realistic solutions in which all but 4 of these dimensions are compactified. The state of knowledge about the space-time supersymmetry of the superstring from the covariant viewpoint is outlined. An approach for identifying possible 6-dimensional spaces which might represent the form of the compact dimensions is discussed, and the orbifold scheme of compactification is presented. 77 refs., 18 figs. (LEW)
NASA Astrophysics Data System (ADS)
Walsh, J. R.
2004-02-01
The Euro3D RTN is an EU funded Research Training Network to foster the exploitation of 3D spectroscopy in Europe. 3D spectroscopy is a general term for spectroscopy of an area of the sky and derives its name from its two spatial + one spectral dimensions. There are an increasing number of instruments which use integral field devices to achieve spectroscopy of an area of the sky, either using lens arrays, optical fibres or image slicers, to pack spectra of multiple pixels on the sky (``spaxels'') onto a 2D detector. On account of the large volume of data and the special methods required to reduce and analyse 3D data, there are only a few centres of expertise and these are mostly involved with instrument developments. There is a perceived lack of expertise in 3D spectroscopy spread though the astronomical community and its use in the armoury of the observational astronomer is viewed as being highly specialised. For precisely this reason the Euro3D RTN was proposed to train young researchers in this area and develop user tools to widen the experience with this particular type of data in Europe. The Euro3D RTN is coordinated by Martin M. Roth (Astrophysikalisches Institut Potsdam) and has been running since July 2002. The first Euro3D science conference was held in Cambridge, UK from 22 to 23 May 2003. The main emphasis of the conference was, in keeping with the RTN, to expose the work of the young post-docs who are funded by the RTN. In addition the team members from the eleven European institutes involved in Euro3D also presented instrumental and observational developments. The conference was organized by Andy Bunker and held at the Institute of Astronomy. There were over thirty participants and 26 talks covered the whole range of application of 3D techniques. The science ranged from Galactic planetary nebulae and globular clusters to kinematics of nearby galaxies out to objects at high redshift. Several talks were devoted to reporting recent observations with newly
NASA Technical Reports Server (NTRS)
Walatka, Pamela P.; Buning, Pieter G.; Pierce, Larry; Elson, Patricia A.
1990-01-01
PLOT3D is a computer graphics program designed to visualize the grids and solutions of computational fluid dynamics. Seventy-four functions are available. Versions are available for many systems. PLOT3D can handle multiple grids with a million or more grid points, and can produce varieties of model renderings, such as wireframe or flat shaded. Output from PLOT3D can be used in animation programs. The first part of this manual is a tutorial that takes the reader, keystroke by keystroke, through a PLOT3D session. The second part of the manual contains reference chapters, including the helpfile, data file formats, advice on changing PLOT3D, and sample command files.
Dawood, A; Marti Marti, B; Sauret-Jackson, V; Darwood, A
2015-12-01
3D printing has been hailed as a disruptive technology which will change manufacturing. Used in aerospace, defence, art and design, 3D printing is becoming a subject of great interest in surgery. The technology has a particular resonance with dentistry, and with advances in 3D imaging and modelling technologies such as cone beam computed tomography and intraoral scanning, and with the relatively long history of the use of CAD CAM technologies in dentistry, it will become of increasing importance. Uses of 3D printing include the production of drill guides for dental implants, the production of physical models for prosthodontics, orthodontics and surgery, the manufacture of dental, craniomaxillofacial and orthopaedic implants, and the fabrication of copings and frameworks for implant and dental restorations. This paper reviews the types of 3D printing technologies available and their various applications in dentistry and in maxillofacial surgery. PMID:26657435
Cohomological gauge theory, quiver matrix models and Donaldson-Thomas theory
NASA Astrophysics Data System (ADS)
Cirafici, Michele; Sinkovics, Annamaria; Szabo, Richard J.
2009-03-01
We study the relation between Donaldson-Thomas theory of Calabi-Yau threefolds and a six-dimensional topological Yang-Mills theory. Our main example is the topological U(N) gauge theory on flat space in its Coulomb branch. To evaluate its partition function we use equivariant localization techniques on its noncommutative deformation. As a result the gauge theory localizes on noncommutative instantons which can be classified in terms of N-coloured three-dimensional Young diagrams. We give to these noncommutative instantons a geometrical description in terms of certain stable framed coherent sheaves on projective space by using a higher-dimensional generalization of the ADHM formalism. From this formalism we construct a topological matrix quantum mechanics which computes an index of BPS states and provides an alternative approach to the six-dimensional gauge theory.
PLOT3D/AMES, APOLLO UNIX VERSION USING GMR3D (WITH TURB3D)
NASA Technical Reports Server (NTRS)
Buning, P.
1994-01-01
PLOT3D is an interactive graphics program designed to help scientists visualize computational fluid dynamics (CFD) grids and solutions. Today, supercomputers and CFD algorithms can provide scientists with simulations of such highly complex phenomena that obtaining an understanding of the simulations has become a major problem. Tools which help the scientist visualize the simulations can be of tremendous aid. PLOT3D/AMES offers more functions and features, and has been adapted for more types of computers than any other CFD graphics program. Version 3.6b+ is supported for five computers and graphic libraries. Using PLOT3D, CFD physicists can view their computational models from any angle, observing the physics of problems and the quality of solutions. As an aid in designing aircraft, for example, PLOT3D's interactive computer graphics can show vortices, temperature, reverse flow, pressure, and dozens of other characteristics of air flow during flight. As critical areas become obvious, they can easily be studied more closely using a finer grid. PLOT3D is part of a computational fluid dynamics software cycle. First, a program such as 3DGRAPE (ARC-12620) helps the scientist generate computational grids to model an object and its surrounding space. Once the grids have been designed and parameters such as the angle of attack, Mach number, and Reynolds number have been specified, a "flow-solver" program such as INS3D (ARC-11794 or COS-10019) solves the system of equations governing fluid flow, usually on a supercomputer. Grids sometimes have as many as two million points, and the "flow-solver" produces a solution file which contains density, x- y- and z-momentum, and stagnation energy for each grid point. With such a solution file and a grid file containing up to 50 grids as input, PLOT3D can calculate and graphically display any one of 74 functions, including shock waves, surface pressure, velocity vectors, and particle traces. PLOT3D's 74 functions are organized into
PLOT3D/AMES, APOLLO UNIX VERSION USING GMR3D (WITHOUT TURB3D)
NASA Technical Reports Server (NTRS)
Buning, P.
1994-01-01
PLOT3D is an interactive graphics program designed to help scientists visualize computational fluid dynamics (CFD) grids and solutions. Today, supercomputers and CFD algorithms can provide scientists with simulations of such highly complex phenomena that obtaining an understanding of the simulations has become a major problem. Tools which help the scientist visualize the simulations can be of tremendous aid. PLOT3D/AMES offers more functions and features, and has been adapted for more types of computers than any other CFD graphics program. Version 3.6b+ is supported for five computers and graphic libraries. Using PLOT3D, CFD physicists can view their computational models from any angle, observing the physics of problems and the quality of solutions. As an aid in designing aircraft, for example, PLOT3D's interactive computer graphics can show vortices, temperature, reverse flow, pressure, and dozens of other characteristics of air flow during flight. As critical areas become obvious, they can easily be studied more closely using a finer grid. PLOT3D is part of a computational fluid dynamics software cycle. First, a program such as 3DGRAPE (ARC-12620) helps the scientist generate computational grids to model an object and its surrounding space. Once the grids have been designed and parameters such as the angle of attack, Mach number, and Reynolds number have been specified, a "flow-solver" program such as INS3D (ARC-11794 or COS-10019) solves the system of equations governing fluid flow, usually on a supercomputer. Grids sometimes have as many as two million points, and the "flow-solver" produces a solution file which contains density, x- y- and z-momentum, and stagnation energy for each grid point. With such a solution file and a grid file containing up to 50 grids as input, PLOT3D can calculate and graphically display any one of 74 functions, including shock waves, surface pressure, velocity vectors, and particle traces. PLOT3D's 74 functions are organized into
Stanton, M M; Samitier, J; Sánchez, S
2015-08-01
Three-dimensional (3D) bioprinting has recently emerged as an extension of 3D material printing, by using biocompatible or cellular components to build structures in an additive, layer-by-layer methodology for encapsulation and culture of cells. These 3D systems allow for cell culture in a suspension for formation of highly organized tissue or controlled spatial orientation of cell environments. The in vitro 3D cellular environments simulate the complexity of an in vivo environment and natural extracellular matrices (ECM). This paper will focus on bioprinting utilizing hydrogels as 3D scaffolds. Hydrogels are advantageous for cell culture as they are highly permeable to cell culture media, nutrients, and waste products generated during metabolic cell processes. They have the ability to be fabricated in customized shapes with various material properties with dimensions at the micron scale. 3D hydrogels are a reliable method for biocompatible 3D printing and have applications in tissue engineering, drug screening, and organ on a chip models. PMID:26066320
Unassisted 3D camera calibration
NASA Astrophysics Data System (ADS)
Atanassov, Kalin; Ramachandra, Vikas; Nash, James; Goma, Sergio R.
2012-03-01
With the rapid growth of 3D technology, 3D image capture has become a critical part of the 3D feature set on mobile phones. 3D image quality is affected by the scene geometry as well as on-the-device processing. An automatic 3D system usually assumes known camera poses accomplished by factory calibration using a special chart. In real life settings, pose parameters estimated by factory calibration can be negatively impacted by movements of the lens barrel due to shaking, focusing, or camera drop. If any of these factors displaces the optical axes of either or both cameras, vertical disparity might exceed the maximum tolerable margin and the 3D user may experience eye strain or headaches. To make 3D capture more practical, one needs to consider unassisted (on arbitrary scenes) calibration. In this paper, we propose an algorithm that relies on detection and matching of keypoints between left and right images. Frames containing erroneous matches, along with frames with insufficiently rich keypoint constellations, are detected and discarded. Roll, pitch yaw , and scale differences between left and right frames are then estimated. The algorithm performance is evaluated in terms of the remaining vertical disparity as compared to the maximum tolerable vertical disparity.
Arena3D: visualization of biological networks in 3D
Pavlopoulos, Georgios A; O'Donoghue, Seán I; Satagopam, Venkata P; Soldatos, Theodoros G; Pafilis, Evangelos; Schneider, Reinhard
2008-01-01
Background Complexity is a key problem when visualizing biological networks; as the number of entities increases, most graphical views become incomprehensible. Our goal is to enable many thousands of entities to be visualized meaningfully and with high performance. Results We present a new visualization tool, Arena3D, which introduces a new concept of staggered layers in 3D space. Related data – such as proteins, chemicals, or pathways – can be grouped onto separate layers and arranged via layout algorithms, such as Fruchterman-Reingold, distance geometry, and a novel hierarchical layout. Data on a layer can be clustered via k-means, affinity propagation, Markov clustering, neighbor joining, tree clustering, or UPGMA ('unweighted pair-group method with arithmetic mean'). A simple input format defines the name and URL for each node, and defines connections or similarity scores between pairs of nodes. The use of Arena3D is illustrated with datasets related to Huntington's disease. Conclusion Arena3D is a user friendly visualization tool that is able to visualize biological or any other network in 3D space. It is free for academic use and runs on any platform. It can be downloaded or lunched directly from . Java3D library and Java 1.5 need to be pre-installed for the software to run. PMID:19040715
NASA Astrophysics Data System (ADS)
Otis, Collin; Ferrero, Pietro; Candler, Graham; Givi, Peyman
2013-11-01
The scalar filtered mass density function (SFMDF) methodology is implemented into the computer code US3D. This is an unstructured Eulerian finite volume hydrodynamic solver and has proven very effective for simulation of compressible turbulent flows. The resulting SFMDF-US3D code is employed for large eddy simulation (LES) on unstructured meshes. Simulations are conducted of subsonic and supersonic flows under non-reacting and reacting conditions. The consistency and the accuracy of the simulated results are assessed along with appraisal of the overall performance of the methodology. The SFMDF-US3D is now capable of simulating high speed flows in complex configurations.
Chilcoat, S.R. Hildebrand, S.T.
1995-12-31
Travel time computation in inhomogeneous media is essential for pre-stack Kirchhoff imaging in areas such as the sub-salt province in the Gulf of Mexico. The 2D algorithm published by Vinje, et al, has been extended to 3D to compute wavefronts in complicated inhomogeneous media. The 3D wavefront construction algorithm provides many advantages over conventional ray tracing and other methods of computing travel times in 3D. The algorithm dynamically maintains a reasonably consistent ray density without making a priori guesses at the number of rays to shoot. The determination of caustics in 3D is a straight forward geometric procedure. The wavefront algorithm also enables the computation of multi-valued travel time surfaces.
Combinatorial 3D Mechanical Metamaterials
NASA Astrophysics Data System (ADS)
Coulais, Corentin; Teomy, Eial; de Reus, Koen; Shokef, Yair; van Hecke, Martin
2015-03-01
We present a class of elastic structures which exhibit 3D-folding motion. Our structures consist of cubic lattices of anisotropic unit cells that can be tiled in a complex combinatorial fashion. We design and 3d-print this complex ordered mechanism, in which we combine elastic hinges and defects to tailor the mechanics of the material. Finally, we use this large design space to encode smart functionalities such as surface patterning and multistability.
Crack interaction with 3-D dislocation loops
NASA Astrophysics Data System (ADS)
Gao, Huajian
CRACKS in a solid often interact with other crystal defects such as dislocation loops. The interaction effects are of 3-D character yet their analytical treatment has been mostly limited to the 2-D regime due to mathematical complications. This paper shows that distribution of the stress intensity factors along a crack front due to arbitrary dislocation loops may be expressed as simple line integrals along the loop contours. The method of analysis is based on the 3-D Bueckner-Rice weight function theory for elastic crack analysis. Our results have significantly simplified the calculations for 3-D dislocation loops produced in the plastic processes at the crack front due to highly concentrated crack tip stress fields. Examples for crack-tip 3-D loops and 2-D straight dislocations emerging from the crack tip are given to demonstrate applications of the derived formulae. The results are consistent with some previous analytical solutions existing in the literature. As further applications we also analyse straight dislocations that are parallel or perpendicular to the crack plane but are not parallel to the crack front.
NASA Astrophysics Data System (ADS)
Dima, M.; Farisato, G.; Bergomi, M.; Viotto, V.; Magrin, D.; Greggio, D.; Farinato, J.; Marafatto, L.; Ragazzoni, R.; Piazza, D.
2014-08-01
In the last few years 3D printing is getting more and more popular and used in many fields going from manufacturing to industrial design, architecture, medical support and aerospace. 3D printing is an evolution of bi-dimensional printing, which allows to obtain a solid object from a 3D model, realized with a 3D modelling software. The final product is obtained using an additive process, in which successive layers of material are laid down one over the other. A 3D printer allows to realize, in a simple way, very complex shapes, which would be quite difficult to be produced with dedicated conventional facilities. Thanks to the fact that the 3D printing is obtained superposing one layer to the others, it doesn't need any particular work flow and it is sufficient to simply draw the model and send it to print. Many different kinds of 3D printers exist based on the technology and material used for layer deposition. A common material used by the toner is ABS plastics, which is a light and rigid thermoplastic polymer, whose peculiar mechanical properties make it diffusely used in several fields, like pipes production and cars interiors manufacturing. I used this technology to create a 1:1 scale model of the telescope which is the hardware core of the space small mission CHEOPS (CHaracterising ExOPlanets Satellite) by ESA, which aims to characterize EXOplanets via transits observations. The telescope has a Ritchey-Chrétien configuration with a 30cm aperture and the launch is foreseen in 2017. In this paper, I present the different phases for the realization of such a model, focusing onto pros and cons of this kind of technology. For example, because of the finite printable volume (10×10×12 inches in the x, y and z directions respectively), it has been necessary to split the largest parts of the instrument in smaller components to be then reassembled and post-processed. A further issue is the resolution of the printed material, which is expressed in terms of layers
NASA Astrophysics Data System (ADS)
Je, U. K.; Lee, M. S.; Cho, H. S.; Hong, D. K.; Park, Y. O.; Park, C. K.; Cho, H. M.; Choi, S. I.; Woo, T. H.
2015-06-01
In practical applications of three-dimensional (3D) tomographic imaging, there are often challenges for image reconstruction from insufficient sampling data. In computed tomography (CT), for example, image reconstruction from sparse views and/or limited-angle (<360°) views would enable fast scanning with reduced imaging doses to the patient. In this study, we investigated and implemented a reconstruction algorithm based on the compressed-sensing (CS) theory, which exploits the sparseness of the gradient image with substantially high accuracy, for potential applications to low-dose, high-accurate dental cone-beam CT (CBCT). We performed systematic simulation works to investigate the image characteristics and also performed experimental works by applying the algorithm to a commercially-available dental CBCT system to demonstrate its effectiveness for image reconstruction in insufficient sampling problems. We successfully reconstructed CBCT images of superior accuracy from insufficient sampling data and evaluated the reconstruction quality quantitatively. Both simulation and experimental demonstrations of the CS-based reconstruction from insufficient data indicate that the CS-based algorithm can be applied directly to current dental CBCT systems for reducing the imaging doses and further improving the image quality.
Holography of 3D flat cosmological horizons.
Bagchi, Arjun; Detournay, Stéphane; Fareghbal, Reza; Simón, Joan
2013-04-01
We provide a first derivation of the Bekenstein-Hawking entropy of 3D flat cosmological horizons in terms of the counting of states in a dual field theory. These horizons appear in the flat limit of nonextremal rotating Banados-Teitleboim-Zanelli black holes and are remnants of the inner horizons. They also satisfy the first law of thermodynamics. We study flat holography as a limit of AdS(3)/CFT(2) to semiclassically compute the density of states in the dual theory, which is given by a contraction of a 2D conformal field theory, exactly reproducing the bulk entropy in the limit of large charges. We comment on how the dual theory reproduces the bulk first law and how cosmological bulk excitations are matched with boundary quantum numbers. PMID:25166977
YouDash3D: exploring stereoscopic 3D gaming for 3D movie theaters
NASA Astrophysics Data System (ADS)
Schild, Jonas; Seele, Sven; Masuch, Maic
2012-03-01
Along with the success of the digitally revived stereoscopic cinema, events beyond 3D movies become attractive for movie theater operators, i.e. interactive 3D games. In this paper, we present a case that explores possible challenges and solutions for interactive 3D games to be played by a movie theater audience. We analyze the setting and showcase current issues related to lighting and interaction. Our second focus is to provide gameplay mechanics that make special use of stereoscopy, especially depth-based game design. Based on these results, we present YouDash3D, a game prototype that explores public stereoscopic gameplay in a reduced kiosk setup. It features live 3D HD video stream of a professional stereo camera rig rendered in a real-time game scene. We use the effect to place the stereoscopic effigies of players into the digital game. The game showcases how stereoscopic vision can provide for a novel depth-based game mechanic. Projected trigger zones and distributed clusters of the audience video allow for easy adaptation to larger audiences and 3D movie theater gaming.
Phases of a two-dimensional large-N gauge theory on a torus
Mandal, Gautam; Morita, Takeshi
2011-10-15
We consider two-dimensional large N gauge theory with D adjoint scalars on a torus, which is obtained from a D+2-dimensional pure Yang-Mills theory on T{sup D+2} with D small radii. The two-dimensional model has various phases characterized by the holonomy of the gauge field around noncontractible cycles of the 2-torus. We determine the phase boundaries and derive the order of the phase transitions using a method developed in an earlier work (hep-th/0910.4526), which is nonperturbative in the 't Hooft coupling and uses a 1/D expansion. We embed our phase diagram in the more extensive phase structure of the D+2-dimensional Yang-Mills theory and match with the picture of a cascade of phase transitions found earlier in lattice calculations. We also propose a dual gravity system based on a Scherk-Schwarz compactification of a D2 brane wrapped on a 3-torus and find a phase structure which is similar to the phase diagram found in the gauge theory calculation.
Remote 3D Medical Consultation
NASA Astrophysics Data System (ADS)
Welch, Greg; Sonnenwald, Diane H.; Fuchs, Henry; Cairns, Bruce; Mayer-Patel, Ketan; Yang, Ruigang; State, Andrei; Towles, Herman; Ilie, Adrian; Krishnan, Srinivas; Söderholm, Hanna M.
Two-dimensional (2D) video-based telemedical consultation has been explored widely in the past 15-20 years. Two issues that seem to arise in most relevant case studies are the difficulty associated with obtaining the desired 2D camera views, and poor depth perception. To address these problems we are exploring the use of a small array of cameras to synthesize a spatially continuous range of dynamic three-dimensional (3D) views of a remote environment and events. The 3D views can be sent across wired or wireless networks to remote viewers with fixed displays or mobile devices such as a personal digital assistant (PDA). The viewpoints could be specified manually or automatically via user head or PDA tracking, giving the remote viewer virtual head- or hand-slaved (PDA-based) remote cameras for mono or stereo viewing. We call this idea remote 3D medical consultation (3DMC). In this article we motivate and explain the vision for 3D medical consultation; we describe the relevant computer vision/graphics, display, and networking research; we present a proof-of-concept prototype system; and we present some early experimental results supporting the general hypothesis that 3D remote medical consultation could offer benefits over conventional 2D televideo.
NASA Technical Reports Server (NTRS)
2002-01-01
In 1999, Genex submitted a proposal to Stennis Space Center for a volumetric 3-D display technique that would provide multiple users with a 360-degree perspective to simultaneously view and analyze 3-D data. The futuristic capabilities of the VolumeViewer(R) have offered tremendous benefits to commercial users in the fields of medicine and surgery, air traffic control, pilot training and education, computer-aided design/computer-aided manufacturing, and military/battlefield management. The technology has also helped NASA to better analyze and assess the various data collected by its satellite and spacecraft sensors. Genex capitalized on its success with Stennis by introducing two separate products to the commercial market that incorporate key elements of the 3-D display technology designed under an SBIR contract. The company Rainbow 3D(R) imaging camera is a novel, three-dimensional surface profile measurement system that can obtain a full-frame 3-D image in less than 1 second. The third product is the 360-degree OmniEye(R) video system. Ideal for intrusion detection, surveillance, and situation management, this unique camera system offers a continuous, panoramic view of a scene in real time.
Au, Anthony K; Huynh, Wilson; Horowitz, Lisa F; Folch, Albert
2016-03-14
The advent of soft lithography allowed for an unprecedented expansion in the field of microfluidics. However, the vast majority of PDMS microfluidic devices are still made with extensive manual labor, are tethered to bulky control systems, and have cumbersome user interfaces, which all render commercialization difficult. On the other hand, 3D printing has begun to embrace the range of sizes and materials that appeal to the developers of microfluidic devices. Prior to fabrication, a design is digitally built as a detailed 3D CAD file. The design can be assembled in modules by remotely collaborating teams, and its mechanical and fluidic behavior can be simulated using finite-element modeling. As structures are created by adding materials without the need for etching or dissolution, processing is environmentally friendly and economically efficient. We predict that in the next few years, 3D printing will replace most PDMS and plastic molding techniques in academia. PMID:26854878
3D Computations and Experiments
Couch, R; Faux, D; Goto, D; Nikkel, D
2004-04-05
This project consists of two activities. Task A, Simulations and Measurements, combines all the material model development and associated numerical work with the materials-oriented experimental activities. The goal of this effort is to provide an improved understanding of dynamic material properties and to provide accurate numerical representations of those properties for use in analysis codes. Task B, ALE3D Development, involves general development activities in the ALE3D code with the focus of improving simulation capabilities for problems of mutual interest to DoD and DOE. Emphasis is on problems involving multi-phase flow, blast loading of structures and system safety/vulnerability studies.
3D Computations and Experiments
Couch, R; Faux, D; Goto, D; Nikkel, D
2003-05-12
This project is in its first full year after the combining of two previously funded projects: ''3D Code Development'' and ''Dynamic Material Properties''. The motivation behind this move was to emphasize and strengthen the ties between the experimental work and the computational model development in the materials area. The next year's activities will indicate the merging of the two efforts. The current activity is structured in two tasks. Task A, ''Simulations and Measurements'', combines all the material model development and associated numerical work with the materials-oriented experimental activities. Task B, ''ALE3D Development'', is a continuation of the non-materials related activities from the previous project.
Schwarzschild Black Holes from Matrix Theory
Banks, T.; Fischler, W.; Klebanov, I.R.; Susskind, L.
1998-01-01
We consider matrix theory compactified on T{sup 3} and show that it correctly describes the properties of Schwarzschild black holes in 7+1 dimensions, including the mass-entropy relation, the Hawking temperature, and the physical size, up to numerical factors of order unity. The most economical description involves setting the cutoff N in the discretized light-cone quantization to be of order the black hole entropy. A crucial ingredient necessary for our work is the recently proposed equation of state for 3+1 dimensional supersymmetric Yang-Mills theory with 16supercharges. We give detailed arguments for the range of validity of this equation following the methods of Horowitz and Polchinski. {copyright} {ital 1998} {ital The American Physical Society}
Schwarzschild Black Holes from Matrix Theory
NASA Astrophysics Data System (ADS)
Banks, T.; Fischler, W.; Klebanov, I. R.; Susskind, L.
1998-01-01
We consider matrix theory compactified on T3 and show that it correctly describes the properties of Schwarzschild black holes in 7+1 dimensions, including the mass-entropy relation, the Hawking temperature, and the physical size, up to numerical factors of order unity. The most economical description involves setting the cutoff N in the discretized light-cone quantization to be of order the black hole entropy. A crucial ingredient necessary for our work is the recently proposed equation of state for 3+1 dimensional supersymmetric Yang-Mills theory with 16 supercharges. We give detailed arguments for the range of validity of this equation following the methods of Horowitz and Polchinski.
Energy Science and Technology Software Center (ESTSC)
2007-07-20
This software distribution contains MATLAB and C++ code to enable identity verification using 3D images that may or may not contain a texture component. The code is organized to support system performance testing and system capability demonstration through the proper configuration of the available user interface. Using specific algorithm parameters the face recognition system has been demonstrated to achieve a 96.6% verification rate (Pd) at 0.001 false alarm rate. The system computes robust facial featuresmore » of a 3D normalized face using Principal Component Analysis (PCA) and Fisher Linear Discriminant Analysis (FLDA). A 3D normalized face is obtained by alighning each face, represented by a set of XYZ coordinated, to a scaled reference face using the Iterative Closest Point (ICP) algorithm. The scaled reference face is then deformed to the input face using an iterative framework with parameters that control the deformed surface regulation an rate of deformation. A variety of options are available to control the information that is encoded by the PCA. Such options include the XYZ coordinates, the difference of each XYZ coordinates from the reference, the Z coordinate, the intensity/texture values, etc. In addition to PCA/FLDA feature projection this software supports feature matching to obtain similarity matrices for performance analysis. In addition, this software supports visualization of the STL, MRD, 2D normalized, and PCA synthetic representations in a 3D environment.« less
ERIC Educational Resources Information Center
Manos, Harry
2016-01-01
Visual aids are important to student learning, and they help make the teacher's job easier. Keeping with the "TPT" theme of "The Art, Craft, and Science of Physics Teaching," the purpose of this article is to show how teachers, lacking equipment and funds, can construct a durable 3-D model reference frame and a model gravity…
Russ, Trina; Koch, Mark; Koudelka, Melissa; Peters, Ralph; Little, Charles; Boehnen, Chris; Peters, Tanya
2007-07-20
This software distribution contains MATLAB and C++ code to enable identity verification using 3D images that may or may not contain a texture component. The code is organized to support system performance testing and system capability demonstration through the proper configuration of the available user interface. Using specific algorithm parameters the face recognition system has been demonstrated to achieve a 96.6% verification rate (Pd) at 0.001 false alarm rate. The system computes robust facial features of a 3D normalized face using Principal Component Analysis (PCA) and Fisher Linear Discriminant Analysis (FLDA). A 3D normalized face is obtained by alighning each face, represented by a set of XYZ coordinated, to a scaled reference face using the Iterative Closest Point (ICP) algorithm. The scaled reference face is then deformed to the input face using an iterative framework with parameters that control the deformed surface regulation an rate of deformation. A variety of options are available to control the information that is encoded by the PCA. Such options include the XYZ coordinates, the difference of each XYZ coordinates from the reference, the Z coordinate, the intensity/texture values, etc. In addition to PCA/FLDA feature projection this software supports feature matching to obtain similarity matrices for performance analysis. In addition, this software supports visualization of the STL, MRD, 2D normalized, and PCA synthetic representations in a 3D environment.
3D Printing: Exploring Capabilities
ERIC Educational Resources Information Center
Samuels, Kyle; Flowers, Jim
2015-01-01
As 3D printers become more affordable, schools are using them in increasing numbers. They fit well with the emphasis on product design in technology and engineering education, allowing students to create high-fidelity physical models to see and test different iterations in their product designs. They may also help students to "think in three…
Experimental Study of Electrothermal 3D Mixing using 3D microPIV
NASA Astrophysics Data System (ADS)
Kauffmann, Paul; Loire, Sophie; Meinhart, Carl; Mezic, Igor
2012-11-01
Mixing is a keystep which can greatly accelerate bio-reactions. For thirty years, dynamical system theory has predicted that chaotic mixing must involve at least 3 dimensions (either time dependent 2D flows or 3D flows). So far, 3D embedded chaotic mixing has been scarcely studied at microscale. In that regard, electrokinetics has emerged as an efficient embedded actuation to drive microflows. Physiological mediums can be driven by electrothermal flows generated by the interaction of an electric field with conductivity and permittivity gradients induced by Joule heating We present original electrothermal time dependant 3D (3D+1) mixing in microwells. The key point of our chaotic mixer is to generate overlapping asymmetric vortices, which switch periodically. When the two vortex configurations blink, flows stretch and fold, thereby generating chaotic advection. Each flow configuration is characterized by an original 3D PIV (3 Components / 3 Dimensions) based on the decomposition of the flows by Proper Orthogonal Decomposition. Velocity field distribution are then compared to COMSOL simulation and discussed. Mixing efficiency of low diffusive particles is studied using the mix-variance coefficient and shows a dramatic increase of mixing efficiency compared to steady flow.
TACO3D. 3-D Finite Element Heat Transfer Code
Mason, W.E.
1992-03-04
TACO3D is a three-dimensional, finite-element program for heat transfer analysis. An extension of the two-dimensional TACO program, it can perform linear and nonlinear analyses and can be used to solve either transient or steady-state problems. The program accepts time-dependent or temperature-dependent material properties, and materials may be isotropic or orthotropic. A variety of time-dependent and temperature-dependent boundary conditions and loadings are available including temperature, flux, convection, and radiation boundary conditions and internal heat generation. Additional specialized features treat enclosure radiation, bulk nodes, and master/slave internal surface conditions (e.g., contact resistance). Data input via a free-field format is provided. A user subprogram feature allows for any type of functional representation of any independent variable. A profile (bandwidth) minimization option is available. The code is limited to implicit time integration for transient solutions. TACO3D has no general mesh generation capability. Rows of evenly-spaced nodes and rows of sequential elements may be generated, but the program relies on separate mesh generators for complex zoning. TACO3D does not have the ability to calculate view factors internally. Graphical representation of data in the form of time history and spatial plots is provided through links to the POSTACO and GRAPE postprocessor codes.
Probing {N}=2 superconformal field theories with localization
NASA Astrophysics Data System (ADS)
Fiol, Bartomeu; Garolera, Blai; Torrentsa, Genís
2016-01-01
We use supersymmetric localization to study probes of four dimensional Lagrangian {N}=2 superconformal field theories. We first derive a unique equation for the eigenvalue density of these theories. We observe that these theories have a Wigner eigenvalue density precisely when they satisfy a necessary condition for having a holographic dual with a sensible higher-derivative expansion. We then compute in the saddle-point approximation the vacuum expectation value of 1/2-BPS circular Wilson loops, and the two-point functions of these Wilson loops with the Lagrangian density and with the stress-energy tensor. This last computation also provides the corresponding Bremsstrahlung functions and entanglement entropies. As expected, whenever a finite fraction of the matter is in the fundamental representation, the results are drastically different from those of {N}=4 supersymmetric Yang-Mills theory.
The 3D rocket combustor acoustics model
NASA Technical Reports Server (NTRS)
Priem, Richard J.; Breisacher, Kevin J.
1992-01-01
The theory and procedures for determining the characteristics of pressure oscillations in rocket engines with prescribed burning rate oscillations are presented. Analyses including radial and hub baffles and absorbers can be performed in one, two, and three dimensions. Pressure and velocity oscillations calculated using this procedure are presented for the SSME to show the influence of baffles and absorbers on the burning rate oscillations required to achieve neutral stability. Comparisons are made between the results obtained utilizing 1-D, 2-D, and 3-D assumptions with regards to capturing the physical phenomena of interest and computational requirements.
Optoplasmonics: hybridization in 3D
NASA Astrophysics Data System (ADS)
Rosa, L.; Gervinskas, G.; Žukauskas, A.; Malinauskas, M.; Brasselet, E.; Juodkazis, S.
2013-12-01
Femtosecond laser fabrication has been used to make hybrid refractive and di ractive micro-optical elements in photo-polymer SZ2080. For applications in micro- uidics, axicon lenses were fabricated (both single and arrays), for generation of light intensity patterns extending through the entire depth of a typically tens-of-micrometers deep channel. Further hybridisation of an axicon with a plasmonic slot is fabricated and demonstrated nu- merically. Spiralling chiral grooves were inscribed into a 100-nm-thick gold coating sputtered over polymerized micro-axicon lenses, using a focused ion beam. This demonstrates possibility of hybridisation between optical and plasmonic 3D micro-optical elements. Numerical modelling of optical performance by 3D-FDTD method is presented.
3-D Relativistic MHD Simulations
NASA Astrophysics Data System (ADS)
Nishikawa, K.-I.; Frank, J.; Koide, S.; Sakai, J.-I.; Christodoulou, D. M.; Sol, H.; Mutel, R. L.
1998-12-01
We present 3-D numerical simulations of moderately hot, supersonic jets propagating initially along or obliquely to the field lines of a denser magnetized background medium with Lorentz factors of W = 4.56 and evolving in a four-dimensional spacetime. The new results are understood as follows: Relativistic simulations have consistently shown that these jets are effectively heavy and so they do not suffer substantial momentum losses and are not decelerated as efficiently as their nonrelativistic counterparts. In addition, the ambient magnetic field, however strong, can be pushed aside with relative ease by the beam, provided that the degrees of freedom associated with all three spatial dimensions are followed self-consistently in the simulations. This effect is analogous to pushing Japanese ``noren'' or vertical Venetian blinds out of the way while the slats are allowed to bend in 3-D space rather than as a 2-D slab structure.
Forensic 3D Scene Reconstruction
LITTLE,CHARLES Q.; PETERS,RALPH R.; RIGDON,J. BRIAN; SMALL,DANIEL E.
1999-10-12
Traditionally law enforcement agencies have relied on basic measurement and imaging tools, such as tape measures and cameras, in recording a crime scene. A disadvantage of these methods is that they are slow and cumbersome. The development of a portable system that can rapidly record a crime scene with current camera imaging, 3D geometric surface maps, and contribute quantitative measurements such as accurate relative positioning of crime scene objects, would be an asset to law enforcement agents in collecting and recording significant forensic data. The purpose of this project is to develop a feasible prototype of a fast, accurate, 3D measurement and imaging system that would support law enforcement agents to quickly document and accurately record a crime scene.
Forensic 3D scene reconstruction
NASA Astrophysics Data System (ADS)
Little, Charles Q.; Small, Daniel E.; Peters, Ralph R.; Rigdon, J. B.
2000-05-01
Traditionally law enforcement agencies have relied on basic measurement and imaging tools, such as tape measures and cameras, in recording a crime scene. A disadvantage of these methods is that they are slow and cumbersome. The development of a portable system that can rapidly record a crime scene with current camera imaging, 3D geometric surface maps, and contribute quantitative measurements such as accurate relative positioning of crime scene objects, would be an asset to law enforcement agents in collecting and recording significant forensic data. The purpose of this project is to develop a fieldable prototype of a fast, accurate, 3D measurement and imaging system that would support law enforcement agents to quickly document and accurately record a crime scene.
NASA Astrophysics Data System (ADS)
Song, Yuanhe; Zhao, Hong; Chen, Wenyi; Tan, Yushan
1997-12-01
A new method of 360 degree turning 3D shape measurement in which light sectioning and phase shifting techniques are both used is presented in this paper. A sine light field is applied in the projected light stripe, meanwhile phase shifting technique is used to calculate phases of the light slit. Thereafter wrapped phase distribution of the slit is formed and the unwrapping process is made by means of the height information based on the light sectioning method. Therefore phase measuring results with better precision can be obtained. At last the target 3D shape data can be produced according to geometric relationships between phases and the object heights. The principles of this method are discussed in detail and experimental results are shown in this paper.
3D Printable Graphene Composite.
Wei, Xiaojun; Li, Dong; Jiang, Wei; Gu, Zheming; Wang, Xiaojuan; Zhang, Zengxing; Sun, Zhengzong
2015-01-01
In human being's history, both the Iron Age and Silicon Age thrived after a matured massive processing technology was developed. Graphene is the most recent superior material which could potentially initialize another new material Age. However, while being exploited to its full extent, conventional processing methods fail to provide a link to today's personalization tide. New technology should be ushered in. Three-dimensional (3D) printing fills the missing linkage between graphene materials and the digital mainstream. Their alliance could generate additional stream to push the graphene revolution into a new phase. Here we demonstrate for the first time, a graphene composite, with a graphene loading up to 5.6 wt%, can be 3D printable into computer-designed models. The composite's linear thermal coefficient is below 75 ppm·°C(-1) from room temperature to its glass transition temperature (Tg), which is crucial to build minute thermal stress during the printing process. PMID:26153673
NASA Technical Reports Server (NTRS)
Pizarro, Yaritzmar Rosario; Schuler, Jason M.; Lippitt, Thomas C.
2013-01-01
Dexterous robotic hands are changing the way robots and humans interact and use common tools. Unfortunately, the complexity of the joints and actuations drive up the manufacturing cost. Some cutting edge and commercially available rapid prototyping machines now have the ability to print multiple materials and even combine these materials in the same job. A 3D model of a robotic hand was designed using Creo Parametric 2.0. Combining "hard" and "soft" materials, the model was printed on the Object Connex350 3D printer with the purpose of resembling as much as possible the human appearance and mobility of a real hand while needing no assembly. After printing the prototype, strings where installed as actuators to test mobility. Based on printing materials, the manufacturing cost of the hand was $167, significantly lower than other robotic hands without the actuators since they have more complex assembly processes.
3D light scanning macrography.
Huber, D; Keller, M; Robert, D
2001-08-01
The technique of 3D light scanning macrography permits the non-invasive surface scanning of small specimens at magnifications up to 200x. Obviating both the problem of limited depth of field inherent to conventional close-up macrophotography and the metallic coating required by scanning electron microscopy, 3D light scanning macrography provides three-dimensional digital images of intact specimens without the loss of colour, texture and transparency information. This newly developed technique offers a versatile, portable and cost-efficient method for the non-invasive digital and photographic documentation of small objects. Computer controlled device operation and digital image acquisition facilitate fast and accurate quantitative morphometric investigations, and the technique offers a broad field of research and educational applications in biological, medical and materials sciences. PMID:11489078
Belenkov, E. A. Ali-Pasha, V. A.
2011-01-15
The structure of clusters of some new carbon 3D-graphite phases have been calculated using the molecular-mechanics methods. It is established that 3D-graphite polytypes {alpha}{sub 1,1}, {alpha}{sub 1,3}, {alpha}{sub 1,5}, {alpha}{sub 2,1}, {alpha}{sub 2,3}, {alpha}{sub 3,1}, {beta}{sub 1,2}, {beta}{sub 1,4}, {beta}{sub 1,6}, {beta}{sub 2,1}, and {beta}{sub 3,2} consist of sp{sup 2}-hybridized atoms, have hexagonal unit cells, and differ in regards to the structure of layers and order of their alternation. A possible way to experimentally synthesize new carbon phases is proposed: the polymerization and carbonization of hydrocarbon molecules.
NASA Astrophysics Data System (ADS)
Modesto, Leonardo; Piva, Marco; Rachwał, Lesław
2016-07-01
We explicitly compute the one-loop exact beta function for a nonlocal extension of the standard gauge theory, in particular, Yang-Mills and QED. The theory, made of a weakly nonlocal kinetic term and a local potential of the gauge field, is unitary (ghost-free) and perturbatively super-renormalizable. Moreover, in the action we can always choose the potential (consisting of one "killer operator") to make zero the beta function of the running gauge coupling constant. The outcome is a UV finite theory for any gauge interaction. Our calculations are done in D =4 , but the results can be generalized to even or odd spacetime dimensions. We compute the contribution to the beta function from two different killer operators by using two independent techniques, namely, the Feynman diagrams and the Barvinsky-Vilkovisky traces. By making the theories finite, we are able to solve also the Landau pole problems, in particular, in QED. Without any potential, the beta function of the one-loop super-renormalizable theory shows a universal Landau pole in the running coupling constant in the ultraviolet regime (UV), regardless of the specific higher-derivative structure. However, the dressed propagator shows neither the Landau pole in the UV nor the singularities in the infrared regime (IR).
[Real time 3D echocardiography].
Bauer, F; Shiota, T; Thomas, J D
2001-07-01
Three-dimensional representation of the heart is an old concern. Usually, 3D reconstruction of the cardiac mass is made by successive acquisition of 2D sections, the spatial localisation and orientation of which require complex guiding systems. More recently, the concept of volumetric acquisition has been introduced. A matricial emitter-receiver probe complex with parallel data processing provides instantaneous of a pyramidal 64 degrees x 64 degrees volume. The image is restituted in real time and is composed of 3 planes (planes B and C) which can be displaced in all spatial directions at any time during acquisition. The flexibility of this system of acquisition allows volume and mass measurement with greater accuracy and reproducibility, limiting inter-observer variability. Free navigation of the planes of investigation allows reconstruction for qualitative and quantitative analysis of valvular heart disease and other pathologies. Although real time 3D echocardiography is ready for clinical usage, some improvements are still necessary to improve its conviviality. Then real time 3D echocardiography could be the essential tool for understanding, diagnosis and management of patients. PMID:11494630
[Real time 3D echocardiography
NASA Technical Reports Server (NTRS)
Bauer, F.; Shiota, T.; Thomas, J. D.
2001-01-01
Three-dimensional representation of the heart is an old concern. Usually, 3D reconstruction of the cardiac mass is made by successive acquisition of 2D sections, the spatial localisation and orientation of which require complex guiding systems. More recently, the concept of volumetric acquisition has been introduced. A matricial emitter-receiver probe complex with parallel data processing provides instantaneous of a pyramidal 64 degrees x 64 degrees volume. The image is restituted in real time and is composed of 3 planes (planes B and C) which can be displaced in all spatial directions at any time during acquisition. The flexibility of this system of acquisition allows volume and mass measurement with greater accuracy and reproducibility, limiting inter-observer variability. Free navigation of the planes of investigation allows reconstruction for qualitative and quantitative analysis of valvular heart disease and other pathologies. Although real time 3D echocardiography is ready for clinical usage, some improvements are still necessary to improve its conviviality. Then real time 3D echocardiography could be the essential tool for understanding, diagnosis and management of patients.
GPU-Accelerated Denoising in 3D (GD3D)
Energy Science and Technology Software Center (ESTSC)
2013-10-01
The raw computational power GPU Accelerators enables fast denoising of 3D MR images using bilateral filtering, anisotropic diffusion, and non-local means. This software addresses two facets of this promising application: what tuning is necessary to achieve optimal performance on a modern GPU? And what parameters yield the best denoising results in practice? To answer the first question, the software performs an autotuning step to empirically determine optimal memory blocking on the GPU. To answer themore » second, it performs a sweep of algorithm parameters to determine the combination that best reduces the mean squared error relative to a noiseless reference image.« less
NASA Astrophysics Data System (ADS)
Kent, G. M.; Harding, A. J.; Babcock, J. M.; Orcutt, J. A.; Bazin, S.; Singh, S.; Detrick, R. S.; Canales, J. P.; Carbotte, S. M.; Diebold, J.
2002-12-01
Multichannel seismic (MCS) images of crustal magma chambers are ideal targets for advanced visualization techniques. In the mid-ocean ridge environment, reflections originating at the melt-lens are well separated from other reflection boundaries, such as the seafloor, layer 2A and Moho, which enables the effective use of transparency filters. 3-D visualization of seismic reflectivity falls into two broad categories: volume and surface rendering. Volumetric-based visualization is an extremely powerful approach for the rapid exploration of very dense 3-D datasets. These 3-D datasets are divided into volume elements or voxels, which are individually color coded depending on the assigned datum value; the user can define an opacity filter to reject plotting certain voxels. This transparency allows the user to peer into the data volume, enabling an easy identification of patterns or relationships that might have geologic merit. Multiple image volumes can be co-registered to look at correlations between two different data types (e.g., amplitude variation with offsets studies), in a manner analogous to draping attributes onto a surface. In contrast, surface visualization of seismic reflectivity usually involves producing "fence" diagrams of 2-D seismic profiles that are complemented with seafloor topography, along with point class data, draped lines and vectors (e.g. fault scarps, earthquake locations and plate-motions). The overlying seafloor can be made partially transparent or see-through, enabling 3-D correlations between seafloor structure and seismic reflectivity. Exploration of 3-D datasets requires additional thought when constructing and manipulating these complex objects. As numbers of visual objects grow in a particular scene, there is a tendency to mask overlapping objects; this clutter can be managed through the effective use of total or partial transparency (i.e., alpha-channel). In this way, the co-variation between different datasets can be investigated
3D reconstruction of tensors and vectors
Defrise, Michel; Gullberg, Grant T.
2005-02-17
Here we have developed formulations for the reconstruction of 3D tensor fields from planar (Radon) and line-integral (X-ray) projections of 3D vector and tensor fields. Much of the motivation for this work is the potential application of MRI to perform diffusion tensor tomography. The goal is to develop a theory for the reconstruction of both Radon planar and X-ray or line-integral projections because of the flexibility of MRI to obtain both of these type of projections in 3D. The development presented here for the linear tensor tomography problem provides insight into the structure of the nonlinear MRI diffusion tensor inverse problem. A particular application of tensor imaging in MRI is the potential application of cardiac diffusion tensor tomography for determining in vivo cardiac fiber structure. One difficulty in the cardiac application is the motion of the heart. This presents a need for developing future theory for tensor tomography in a motion field. This means developing a better understanding of the MRI signal for diffusion processes in a deforming media. The techniques developed may allow the application of MRI tensor tomography for the study of structure of fiber tracts in the brain, atherosclerotic plaque, and spine in addition to fiber structure in the heart. However, the relations presented are also applicable to other fields in medical imaging such as diffraction tomography using ultrasound. The mathematics presented can also be extended to exponential Radon transform of tensor fields and to other geometric acquisitions such as cone beam tomography of tensor fields.
Sasakian quiver gauge theories and instantons on the conifold
NASA Astrophysics Data System (ADS)
Geipel, Jakob C.; Lechtenfeld, Olaf; Popov, Alexander D.; Szabo, Richard J.
2016-06-01
We consider Spin (4)-equivariant dimensional reduction of Yang-Mills theory on manifolds of the form Md ×T 1 , 1, where Md is a smooth manifold and T 1 , 1 is a five-dimensional Sasaki-Einstein manifold Spin (4) / U (1). We obtain new quiver gauge theories on Md extending those induced via reduction over the leaf spaces CP1 × CP1 in T 1 , 1. We describe the Higgs branches of these quiver gauge theories as moduli spaces of Spin (4)-equivariant instantons on the conifold which is realized as the metric cone over T 1 , 1. We give an explicit construction of these moduli spaces as Kähler quotients.
Interactive 3D Mars Visualization
NASA Technical Reports Server (NTRS)
Powell, Mark W.
2012-01-01
The Interactive 3D Mars Visualization system provides high-performance, immersive visualization of satellite and surface vehicle imagery of Mars. The software can be used in mission operations to provide the most accurate position information for the Mars rovers to date. When integrated into the mission data pipeline, this system allows mission planners to view the location of the rover on Mars to 0.01-meter accuracy with respect to satellite imagery, with dynamic updates to incorporate the latest position information. Given this information so early in the planning process, rover drivers are able to plan more accurate drive activities for the rover than ever before, increasing the execution of science activities significantly. Scientifically, this 3D mapping information puts all of the science analyses to date into geologic context on a daily basis instead of weeks or months, as was the norm prior to this contribution. This allows the science planners to judge the efficacy of their previously executed science observations much more efficiently, and achieve greater science return as a result. The Interactive 3D Mars surface view is a Mars terrain browsing software interface that encompasses the entire region of exploration for a Mars surface exploration mission. The view is interactive, allowing the user to pan in any direction by clicking and dragging, or to zoom in or out by scrolling the mouse or touchpad. This set currently includes tools for selecting a point of interest, and a ruler tool for displaying the distance between and positions of two points of interest. The mapping information can be harvested and shared through ubiquitous online mapping tools like Google Mars, NASA WorldWind, and Worldwide Telescope.
NASA Technical Reports Server (NTRS)
2004-01-01
This is a 3-D anaglyph showing a microscopic image taken of an area measuring 3 centimeters (1.2 inches) across on the rock called Adirondack. The image was taken at Gusev Crater on the 33rd day of the Mars Exploration Rover Spirit's journey (Feb. 5, 2004), after the rover used its rock abrasion tool brush to clean the surface of the rock. Dust, which was pushed off to the side during cleaning, can still be seen to the left and in low areas of the rock.
NASA Astrophysics Data System (ADS)
Manos, Harry
2016-03-01
Visual aids are important to student learning, and they help make the teacher's job easier. Keeping with the TPT theme of "The Art, Craft, and Science of Physics Teaching," the purpose of this article is to show how teachers, lacking equipment and funds, can construct a durable 3-D model reference frame and a model gravity well tailored to specific class lessons. Most of the supplies are readily available in the home or at school: rubbing alcohol, a rag, two colors of spray paint, art brushes, and masking tape. The cost of these supplies, if you don't have them, is less than 20.
NASA Technical Reports Server (NTRS)
2004-01-01
This 3-D cylindrical-perspective mosaic taken by the navigation camera on the Mars Exploration Rover Spirit on sol 82 shows the view south of the large crater dubbed 'Bonneville.' The rover will travel toward the Columbia Hills, seen here at the upper left. The rock dubbed 'Mazatzal' and the hole the rover drilled in to it can be seen at the lower left. The rover's position is referred to as 'Site 22, Position 32.' This image was geometrically corrected to make the horizon appear flat.
NASA Technical Reports Server (NTRS)
2004-01-01
This 3-D image captured by the Mars Exploration Rover Opportunity's rear hazard-identification camera shows the now-empty lander that carried the rover 283 million miles to Meridiani Planum, Mars. Engineers received confirmation that Opportunity's six wheels successfully rolled off the lander and onto martian soil at 3:01 a.m. PST, January 31, 2004, on the seventh martian day, or sol, of the mission. The rover is approximately 1 meter (3 feet) in front of the lander, facing north.
Positional Awareness Map 3D (PAM3D)
NASA Technical Reports Server (NTRS)
Hoffman, Monica; Allen, Earl L.; Yount, John W.; Norcross, April Louise
2012-01-01
The Western Aeronautical Test Range of the National Aeronautics and Space Administration s Dryden Flight Research Center needed to address the aging software and hardware of its current situational awareness display application, the Global Real-Time Interactive Map (GRIM). GRIM was initially developed in the late 1980s and executes on older PC architectures using a Linux operating system that is no longer supported. Additionally, the software is difficult to maintain due to its complexity and loss of developer knowledge. It was decided that a replacement application must be developed or acquired in the near future. The replacement must provide the functionality of the original system, the ability to monitor test flight vehicles in real-time, and add improvements such as high resolution imagery and true 3-dimensional capability. This paper will discuss the process of determining the best approach to replace GRIM, and the functionality and capabilities of the first release of the Positional Awareness Map 3D.
3D Printable Graphene Composite
NASA Astrophysics Data System (ADS)
Wei, Xiaojun; Li, Dong; Jiang, Wei; Gu, Zheming; Wang, Xiaojuan; Zhang, Zengxing; Sun, Zhengzong
2015-07-01
In human being’s history, both the Iron Age and Silicon Age thrived after a matured massive processing technology was developed. Graphene is the most recent superior material which could potentially initialize another new material Age. However, while being exploited to its full extent, conventional processing methods fail to provide a link to today’s personalization tide. New technology should be ushered in. Three-dimensional (3D) printing fills the missing linkage between graphene materials and the digital mainstream. Their alliance could generate additional stream to push the graphene revolution into a new phase. Here we demonstrate for the first time, a graphene composite, with a graphene loading up to 5.6 wt%, can be 3D printable into computer-designed models. The composite’s linear thermal coefficient is below 75 ppm·°C-1 from room temperature to its glass transition temperature (Tg), which is crucial to build minute thermal stress during the printing process.
3D acoustic atmospheric tomography
NASA Astrophysics Data System (ADS)
Rogers, Kevin; Finn, Anthony
2014-10-01
This paper presents a method for tomographically reconstructing spatially varying 3D atmospheric temperature profiles and wind velocity fields based. Measurements of the acoustic signature measured onboard a small Unmanned Aerial Vehicle (UAV) are compared to ground-based observations of the same signals. The frequency-shifted signal variations are then used to estimate the acoustic propagation delay between the UAV and the ground microphones, which are also affected by atmospheric temperature and wind speed vectors along each sound ray path. The wind and temperature profiles are modelled as the weighted sum of Radial Basis Functions (RBFs), which also allow local meteorological measurements made at the UAV and ground receivers to supplement any acoustic observations. Tomography is used to provide a full 3D reconstruction/visualisation of the observed atmosphere. The technique offers observational mobility under direct user control and the capacity to monitor hazardous atmospheric environments, otherwise not justifiable on the basis of cost or risk. This paper summarises the tomographic technique and reports on the results of simulations and initial field trials. The technique has practical applications for atmospheric research, sound propagation studies, boundary layer meteorology, air pollution measurements, analysis of wind shear, and wind farm surveys.
Mannoor, Manu S.; Jiang, Ziwen; James, Teena; Kong, Yong Lin; Malatesta, Karen A.; Soboyejo, Winston O.; Verma, Naveen; Gracias, David H.; McAlpine, Michael C.
2013-01-01
The ability to three-dimensionally interweave biological tissue with functional electronics could enable the creation of bionic organs possessing enhanced functionalities over their human counterparts. Conventional electronic devices are inherently two-dimensional, preventing seamless multidimensional integration with synthetic biology, as the processes and materials are very different. Here, we present a novel strategy for overcoming these difficulties via additive manufacturing of biological cells with structural and nanoparticle derived electronic elements. As a proof of concept, we generated a bionic ear via 3D printing of a cell-seeded hydrogel matrix in the precise anatomic geometry of a human ear, along with an intertwined conducting polymer consisting of infused silver nanoparticles. This allowed for in vitro culturing of cartilage tissue around an inductive coil antenna in the ear, which subsequently enables readout of inductively-coupled signals from cochlea-shaped electrodes. The printed ear exhibits enhanced auditory sensing for radio frequency reception, and complementary left and right ears can listen to stereo audio music. Overall, our approach suggests a means to intricately merge biologic and nanoelectronic functionalities via 3D printing. PMID:23635097
3-D Relativistic MHD Simulations
NASA Astrophysics Data System (ADS)
Nishikaw, K.-I.; Frank, J.; Christodoulou, D. M.; Koide, S.; Sakai, J.-I.; Sol, H.; Mutel, R. L.
1998-12-01
We present 3-D numerical simulations of moderately hot, supersonic jets propagating initially along or obliquely to the field lines of a denser magnetized background medium with Lorentz factors of W=4.56 and evolving in a four-dimensional spacetime. The new results are understood as follows: Relativistic simulations have consistently shown that these jets are effectively heavy and so they do not suffer substantial momentum losses and are not decelerated as efficiently as their nonrelativistic counterparts. In addition, the ambient magnetic field, however strong, can be pushed aside with relative ease by the beam, provided that the degrees of freedom associated with all three spatial dimensions are followed self-consistently in the simulations. This effect is analogous to pushing Japanese ``noren'' or vertical Venetian blinds out of the way while the slats are allowed to bend in 3-D space rather than as a 2-D slab structure. We also simulate jets with the more realistic initial conditions for injecting jets for helical mangetic field, perturbed density, velocity, and internal energy, which are supposed to be caused in the process of jet generation. Three possible explanations for the observed variability are (i) tidal disruption of a star falling into the black hole, (ii) instabilities in the relativistic accretion disk, and (iii) jet-related PRocesses. New results will be reported at the meeting.
Mannoor, Manu S; Jiang, Ziwen; James, Teena; Kong, Yong Lin; Malatesta, Karen A; Soboyejo, Winston O; Verma, Naveen; Gracias, David H; McAlpine, Michael C
2013-06-12
The ability to three-dimensionally interweave biological tissue with functional electronics could enable the creation of bionic organs possessing enhanced functionalities over their human counterparts. Conventional electronic devices are inherently two-dimensional, preventing seamless multidimensional integration with synthetic biology, as the processes and materials are very different. Here, we present a novel strategy for overcoming these difficulties via additive manufacturing of biological cells with structural and nanoparticle derived electronic elements. As a proof of concept, we generated a bionic ear via 3D printing of a cell-seeded hydrogel matrix in the anatomic geometry of a human ear, along with an intertwined conducting polymer consisting of infused silver nanoparticles. This allowed for in vitro culturing of cartilage tissue around an inductive coil antenna in the ear, which subsequently enables readout of inductively-coupled signals from cochlea-shaped electrodes. The printed ear exhibits enhanced auditory sensing for radio frequency reception, and complementary left and right ears can listen to stereo audio music. Overall, our approach suggests a means to intricately merge biologic and nanoelectronic functionalities via 3D printing. PMID:23635097
3D Printable Graphene Composite
Wei, Xiaojun; Li, Dong; Jiang, Wei; Gu, Zheming; Wang, Xiaojuan; Zhang, Zengxing; Sun, Zhengzong
2015-01-01
In human being’s history, both the Iron Age and Silicon Age thrived after a matured massive processing technology was developed. Graphene is the most recent superior material which could potentially initialize another new material Age. However, while being exploited to its full extent, conventional processing methods fail to provide a link to today’s personalization tide. New technology should be ushered in. Three-dimensional (3D) printing fills the missing linkage between graphene materials and the digital mainstream. Their alliance could generate additional stream to push the graphene revolution into a new phase. Here we demonstrate for the first time, a graphene composite, with a graphene loading up to 5.6 wt%, can be 3D printable into computer-designed models. The composite’s linear thermal coefficient is below 75 ppm·°C−1 from room temperature to its glass transition temperature (Tg), which is crucial to build minute thermal stress during the printing process. PMID:26153673
3D medical thermography device
NASA Astrophysics Data System (ADS)
Moghadam, Peyman
2015-05-01
In this paper, a novel handheld 3D medical thermography system is introduced. The proposed system consists of a thermal-infrared camera, a color camera and a depth camera rigidly attached in close proximity and mounted on an ergonomic handle. As a practitioner holding the device smoothly moves it around the human body parts, the proposed system generates and builds up a precise 3D thermogram model by incorporating information from each new measurement in real-time. The data is acquired in motion, thus it provides multiple points of view. When processed, these multiple points of view are adaptively combined by taking into account the reliability of each individual measurement which can vary due to a variety of factors such as angle of incidence, distance between the device and the subject and environmental sensor data or other factors influencing a confidence of the thermal-infrared data when captured. Finally, several case studies are presented to support the usability and performance of the proposed system.