Non-perturbative effects and wall-crossing from topological strings

NASA Astrophysics Data System (ADS)

Collinucci, Andrés; Soler, Pablo; Uranga, Angel M.

2009-11-01

We argue that the Gopakumar-Vafa interpretation of the topological string partition function can be used to compute and resum certain non-perturbative brane instanton effects of type II CY compactifications. In particular the topological string A-model encodes the non-perturbative corrections to the hypermultiplet moduli space metric from general D1/D(-1)-brane instantons in 4d Script N = 2 IIB models. We also discuss the reduction to 4d Script N = 1 by fluxes and/or orientifolds and/or D-branes, and the prospects to resum brane instanton contributions to non-perturbative superpotentials. We argue that the connection between non-perturbative effects and the topological string underlies the continuity of non-perturbative effects across lines of BPS stability. We also confirm this statement in mirror B-model matrix model examples, relating matrix model instantons to non-perturbative D-brane instantons. The computation of non-perturbative effects from the topological string requires a 3d circle compactification and T-duality, relating effects from particles and instantons, reminiscent of that involved in the physical derivation of the Kontsevich-Soibelmann wall-crossing formula.

Ring-polymer instanton theory of electron transfer in the nonadiabatic limit

DOE Office of Scientific and Technical Information (OSTI.GOV)

Richardson, Jeremy O., E-mail: jeremy.richardson@fau.de

We take the golden-rule instanton method derived in the previous paper [J. O. Richardson, R. Bauer, and M. Thoss, J. Chem. Phys. 143, 134115 (2015)] and reformulate it using a ring-polymer instanton approach. This gives equations which can be used to compute the rates of electron-transfer reactions in the nonadiabatic (golden-rule) limit numerically within a semiclassical approximation. The multidimensional ring-polymer instanton trajectories are obtained efficiently by minimization of the action. In this form, comparison with Wolynes’ quantum instanton method [P. G. Wolynes, J. Chem. Phys. 87, 6559 (1987)] is possible and we show that our semiclassical approach is the steepest-descentmore » limit of this method. We discuss advantages and disadvantages of both methods and give examples of where the new approach is more accurate.« less

Nucleon QCD sum rules in the instanton medium

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ryskin, M. G.; Drukarev, E. G., E-mail: drukarev@pnpi.spb.ru; Sadovnikova, V. A.

2015-09-15

We try to find grounds for the standard nucleon QCD sum rules, based on a more detailed description of the QCD vacuum. We calculate the polarization operator of the nucleon current in the instanton medium. The medium (QCD vacuum) is assumed to be a composition of the small-size instantons and some long-wave gluon fluctuations. We solve the corresponding QCD sum rule equations and demonstrate that there is a solution with the value of the nucleon mass close to the physical one if the fraction of the small-size instantons contribution is w{sub s} ≈ 2/3.

Instanton dominance over $$a_s$$ at low momenta from lattice QCD simulations at $$N_f=0$$, $$N_f=2+1$$ and $$N_f=2+1+1$$

DOE Office of Scientific and Technical Information (OSTI.GOV)

Athenodorou, Andreas; Boucaud, Philippe; de Soto, Feliciano

We report on an instanton-based analysis of the gluon Green functions in the Landau gauge for low momenta; in particular we use lattice results for αs in the symmetric momentum subtraction scheme (MOM) for large-volume lattice simulations. We have exploited quenched gauge field configurations, Nf = 0, with both Wilson and tree-level Symanzik improved actions, and unquenched ones with Nf = 2 + 1 and Nf = 2 + 1 + 1 dynamical flavors (domain wall and twisted-mass fermions, respectively).We show that the dominance of instanton correlations on the low-momenta gluon Green functions can be applied to the determination ofmore » phenomenological parameters of the instanton liquid and, eventually, to a determination of the lattice spacing.We furthermore apply the Gradient Flow to remove short-distance fluctuations. The Gradient Flow gets rid of the QCD scale, ΛQCD, and reveals that the instanton prediction extents to large momenta. For those gauge field configurations free of quantum fluctuations, the direct study of topological charge density shows the appearance of large-scale lumps that can be identified as instantons, giving access to a direct study of the instanton density and size distribution that is compatible with those extracted from the analysis of the Green functions.« less

The curious incident of multi-instantons and the necessity of Lefschetz thimbles

DOE PAGES

Behtash, Alireza; Poppitz, Erich; Sulejmanpasic, Tin; ...

2015-11-25

Here, we smore » how that compatibility of supersymmetry with exact semi-classics demands that in calculating multi-instanton amplitudes, the “separation” quasi-zeromode must be complexified and the integration cycles must be found by using complex gradient flow (or Picard-Lefschetz equations.) As a non-trivial application, we study N = 2 extended supersymmetric quantum mechanics. Even though in this case supersymmetry is unbroken, the instanton-anti-instanton amplitude (naively calculated) seems to contribute to the ground state energy. We show, however, that the instanton-anti-instanton event consists of two parts: a fermion-correlated and a scalar-correlated event. Although both of these contributions are naively of the same sign and the latter is superficially higher order in the perturbative coupling, we show that the two contributions exactly cancel when they are evaluated on Lefschetz thimbles due to their relative Hidden Topological Angles (HTAs). This gives strong evidence that the semi-classical expansion using Lefschetz thimbles is not only a meaningful prescription for higher order semi-classics, but a necessary one. This deduction seems to be universal and applicable to both supersymmetric and non-supersymmetric theories. In conclusion we speculate that similar conspiracies are responsible for the non-formation of certain molecular contributions in theories where instantons have more than two fermionic zeromodes and do not contribute to the superpotential.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Arroja, Frederico; Chen, Che-Yu; Chen, Pisin

In this work, we investigate O (4)-symmetric instantons within the Eddington-inspired-Born-Infeld gravity theory (EiBI) . We discuss the regular Hawking-Moss instanton and find that the tunneling rate reduces to the General Relativity (GR) value, even though the action value is different by a constant. We give a thorough analysis of the singular Vilenkin instanton and the Hawking-Turok instanton with a quadratic scalar field potential in the EiBI theory. In both cases, we find that the singularity can be avoided in the sense that the physical metric, its scalar curvature and the scalar field are regular under some parameter restrictions, butmore » there is a curvature singularity of the auxiliary metric compatible with the connection. We find that the on-shell action is finite and the probability does not reduce to its GR value. We also find that the Vilenkin instanton in the EiBI theory would still cause the instability of the Minkowski space, similar to that in GR, and this is observationally inconsistent. This result suggests that the singularity of the auxiliary metric may be problematic at the quantum level and that these instantons should be excluded from the path integral.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Arroja, Frederico; Chen, Che -Yu; Chen, Pisin

In this study, we investigate O(4)-symmetric instantons within the Eddington-inspired-Born-Infeld gravity theory (EiBI) . We discuss the regular Hawking-Moss instanton and find that the tunneling rate reduces to the General Relativity (GR) value, even though the action value is different by a constant. We give a thorough analysis of the singular Vilenkin instanton and the Hawking-Turok instanton with a quadratic scalar field potential in the EiBI theory. In both cases, we find that the singularity can be avoided in the sense that the physical metric, its scalar curvature and the scalar field are regular under some parameter restrictions, but theremore » is a curvature singularity of the auxiliary metric compatible with the connection. We find that the on-shell action is finite and the probability does not reduce to its GR value. We also find that the Vilenkin instanton in the EiBI theory would still cause the instability of the Minkowski space, similar to that in GR, and this is observationally inconsistent. This result suggests that the singularity of the auxiliary metric may be problematic at the quantum level and that these instantons should be excluded from the path integral.« less

Seiberg-Witten/Whitham Equations and Instanton Corrections in {\\mathscr{N}}=2 Supersymmetric Yang-Mills Theory

NASA Astrophysics Data System (ADS)

Dai, Jia-Liang; Fan, En-Gui

2018-05-01

We obtain the instanton correction recursion relations for the low energy effective prepotential in pure {\\mathscr{N}}=2 SU(n) supersymmetric Yang-Mills gauge theory from Whitham hierarchy and Seiberg-Witten/Whitham equations. These formulae provide us a powerful tool to calculate arbitrary order instanton corrections coefficients from the perturbative contributions of the effective prepotential in Seiberg-Witten gauge theory. We apply this idea to evaluate one- and twoorder instanton corrections coefficients explicitly in SU(n) case in detail through the dynamical scale parameter expressed in terms of Riemann’s theta-function. Supported by the National Natural Science Foundation of China under Grant No. 11271079

Instantons on a non-commutative T4 from twisted (2,0) and little string theories

NASA Astrophysics Data System (ADS)

Cheung, Yeuk-Kwan E.; Ganor, Ori J.; Krogh, Morten; Mikhailov, Andrei Yu.

We show that the moduli space of the (2,0) and little-string theories compactified on T3 with R-symmetry twists is equal to the moduli space of U(1) instantons on a non-commutative T4. The moduli space of U( q) instantons on a non-commutative T4 is obtained from little-string theories of NS5-branes at Aq-1 singularities with twists. A large class of gauge theories with N=4 SUSY in 2+1D and N=2 SUSY in 3+1D are limiting cases of these theories. Hence, the moduli spaces of these gauge theories can be read off from the moduli spaces of instantons on non-commutative tori. We study the phase transitions in these theories and the action of T-duality. On the purely mathematical side, we give a prediction for the moduli space of two U(1) instantons on a non-commutative T4.

Hierarchies from D-brane instantons in globally defined calabi-yau orientifolds

DOE PAGES

Cvetič, Mirjam; Weigand, Timo

2008-06-01

We construct the first globally consistent semi-realistic Type I string vacua on an elliptically fibered manifold where the zero modes of the Euclidean D1-instanton sector allow for the generation of non-perturbative Majorana masses of an intermediate scale. In another class of global models, a D1-brane instanton can generate a Polonyi-type superpotential breaking supersymmetry at an exponentially suppressed scale.

Gravitational instantons from minimal surfaces

NASA Astrophysics Data System (ADS)

Aliev, A. N.; Hortaçsu, M.; Kalayci, J.; Nutku, Y.

1999-02-01

Physical properties of gravitational instantons which are derivable from minimal surfaces in three-dimensional Euclidean space are examined using the Newman-Penrose formalism for Euclidean signature. The gravitational instanton that corresponds to the helicoid minimal surface is investigated in detail. This is a metric of Bianchi type 0264-9381/16/2/024/img9, or E(2), which admits a hidden symmetry due to the existence of a quadratic Killing tensor. It leads to a complete separation of variables in the Hamilton-Jacobi equation for geodesics, as well as in Laplace's equation for a massless scalar field. The scalar Green function can be obtained in closed form, which enables us to calculate the vacuum fluctuations of a massless scalar field in the background of this instanton.

Confinement, holonomy, and correlated instanton-dyon ensemble: SU(2) Yang-Mills theory

NASA Astrophysics Data System (ADS)

Lopez-Ruiz, Miguel Angel; Jiang, Yin; Liao, Jinfeng

2018-03-01

The mechanism of confinement in Yang-Mills theories remains a challenge to our understanding of nonperturbative gauge dynamics. While it is widely perceived that confinement may arise from chromomagnetically charged gauge configurations with nontrivial topology, it is not clear what types of configurations could do that and how, in pure Yang-Mills and QCD-like (nonsupersymmetric) theories. Recently, a promising approach has emerged, based on statistical ensembles of dyons/anti-dyons that are constituents of instanton/anti-instanton solutions with nontrivial holonomy where the holonomy plays a vital role as an effective "Higgsing" mechanism. We report a thorough numerical investigation of the confinement dynamics in S U (2 ) Yang-Mills theory by constructing such a statistical ensemble of correlated instanton-dyons.

Baryon and lepton number violating effective operators in a non-universal extension of the standard model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fuentes-Martín, J.

2016-01-22

It is well known that non-abelian Yang-Mills theories present non-trivial minima of the action, the so-called instantons. In the context of electroweak theories these instanton solutions may induce violations of baryon and lepton number of the form ΔB = ΔL = n{sub f}, with n{sub f} being the number of families coupled to the gauge group. An interesting feature of these violations is that the flavor structure of the gauge couplings is inherited by the instanton transitions. This effect is generally neglected in the literature. We will show that the inclusion of flavor interactions in the instanton solutions may bemore » interesting in certain theoretical frameworks and will provide an approach to include these effects. In particular we will perform this implementation in the non-universal SU (2){sub l} ⊗SU (2){sub h} ⊗U (1){sub Y} model that singularizes the third family. Within this framework, we will use the instanton transitions to set a bound on the SU (2){sub h} gauge coupling.« less

Instanton rate constant calculations close to and above the crossover temperature.

PubMed

McConnell, Sean; Kästner, Johannes

2017-11-15

Canonical instanton theory is known to overestimate the rate constant close to a system-dependent crossover temperature and is inapplicable above that temperature. We compare the accuracy of the reaction rate constants calculated using recent semi-classical rate expressions to those from canonical instanton theory. We show that rate constants calculated purely from solving the stability matrix for the action in degrees of freedom orthogonal to the instanton path is not applicable at arbitrarily low temperatures and use two methods to overcome this. Furthermore, as a by-product of the developed methods, we derive a simple correction to canonical instanton theory that can alleviate this known overestimation of rate constants close to the crossover temperature. The combined methods accurately reproduce the rate constants of the canonical theory along the whole temperature range without the spurious overestimation near the crossover temperature. We calculate and compare rate constants on three different reactions: H in the Müller-Brown potential, methylhydroxycarbene → acetaldehyde and H 2  + OH → H + H 2 O. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

Worldsheet instantons and the amplitude for string pair production in an external field as a WKB exact functional integral

NASA Astrophysics Data System (ADS)

Gordon, James; Semenoff, Gordon W.

2018-05-01

We revisit the problem of charged string pair creation in a constant external electric field. The string states are massive and creation of pairs from the vacuum is a tunnelling process, analogous to the Schwinger process where charged particle-anti-particle pairs are created by an electric field. We find the instantons in the worldsheet sigma model which are responsible for the tunnelling events. We evaluate the sigma model partition function in the multi-instanton sector in the WKB approximation which keeps the classical action and integrates the quadratic fluctuations about the solution. We find that the summation of the result over all multi-instanton sectors reproduces the known amplitude. This suggests that corrections to the WKB limit must cancel. To show that they indeed cancel, we identify a fermionic symmetry of the sigma model which occurs in the instanton sectors and which is associated with collective coordinates. We demonstrate that the action is symmetric and that the interaction action is an exact form. These conditions are sufficient for localization of the worldsheet functional integral onto its WKB limit.

Tunnel determinants from spectral zeta functions. Instanton effects in quantum mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Izquierdo, A. Alonso; Guilarte, J. Mateos

2014-07-23

In this paper we develop an spectral zeta function regularization procedure on the determinants of instanton fluctuation operators that describe the semi-classical order of tunnel effects between degenerate vacua.

Recovering the negative mode for type B Coleman-de Luccia instantons

NASA Astrophysics Data System (ADS)

Yang, I.-Sheng

2013-04-01

The usual (type A) thin-wall Coleman—de Luccia instanton is made by a bigger-than-half sphere of the false vacuum and a smaller-than-half sphere of the true vacuum. It has the standard O(4) symmetric negative mode associated with changing the size of the true vacuum region. On the other hand, the type B instanton, made by two smaller-than-half spheres, was believed to have lost this negative mode. We argue that such a belief is misguided due to an overrestriction on the Euclidean path integral. We introduce the idea of a “purely geometric junction” to visualize why such a restriction could be removed, and then we explicitly construct this negative mode. We also show that type B and type A instantons have the same thermal interpretation for mediating tunnelings.

Instantons in Self-Organizing Logic Gates

NASA Astrophysics Data System (ADS)

Bearden, Sean R. B.; Manukian, Haik; Traversa, Fabio L.; Di Ventra, Massimiliano

2018-03-01

Self-organizing logic is a recently suggested framework that allows the solution of Boolean truth tables "in reverse"; i.e., it is able to satisfy the logical proposition of gates regardless to which terminal(s) the truth value is assigned ("terminal-agnostic logic"). It can be realized if time nonlocality (memory) is present. A practical realization of self-organizing logic gates (SOLGs) can be done by combining circuit elements with and without memory. By employing one such realization, we show, numerically, that SOLGs exploit elementary instantons to reach equilibrium points. Instantons are classical trajectories of the nonlinear equations of motion describing SOLGs and connect topologically distinct critical points in the phase space. By linear analysis at those points, we show that these instantons connect the initial critical point of the dynamics, with at least one unstable direction, directly to the final fixed point. We also show that the memory content of these gates affects only the relaxation time to reach the logically consistent solution. Finally, we demonstrate, by solving the corresponding stochastic differential equations, that, since instantons connect critical points, noise and perturbations may change the instanton trajectory in the phase space but not the initial and final critical points. Therefore, even for extremely large noise levels, the gates self-organize to the correct solution. Our work provides a physical understanding of, and can serve as an inspiration for, models of bidirectional logic gates that are emerging as important tools in physics-inspired, unconventional computing.

The instanton method and its numerical implementation in fluid mechanics

NASA Astrophysics Data System (ADS)

Grafke, Tobias; Grauer, Rainer; Schäfer, Tobias

2015-08-01

A precise characterization of structures occurring in turbulent fluid flows at high Reynolds numbers is one of the last open problems of classical physics. In this review we discuss recent developments related to the application of instanton methods to turbulence. Instantons are saddle point configurations of the underlying path integrals. They are equivalent to minimizers of the related Freidlin-Wentzell action and known to be able to characterize rare events in such systems. While there is an impressive body of work concerning their analytical description, this review focuses on the question on how to compute these minimizers numerically. In a short introduction we present the relevant mathematical and physical background before we discuss the stochastic Burgers equation in detail. We present algorithms to compute instantons numerically by an efficient solution of the corresponding Euler-Lagrange equations. A second focus is the discussion of a recently developed numerical filtering technique that allows to extract instantons from direct numerical simulations. In the following we present modifications of the algorithms to make them efficient when applied to two- or three-dimensional (2D or 3D) fluid dynamical problems. We illustrate these ideas using the 2D Burgers equation and the 3D Navier-Stokes equations.

New Kaluza-Klein instantons and the decay of AdS vacua

DOE PAGES

Ooguri, Hirosi; Spodyneiko, Lev

2017-07-19

We construct a generalization of Witten’s Kaluza-Klein instanton, where a higher-dimensional sphere (rather than a circle as in Witten’s instanton) collapses to zero size and the geometry terminates at a bubble of nothing, in a low energy effective theory of M theory. We then use the solution to exhibit the instability of nonsupersymmetric AdS 5 vacua in M theory compactified on positive Kähler-Einstein spaces, providing further evidence for the recent conjecture that any nonsupersymmetric anti–de Sitter vacuum supported by fluxes must be unstable.

Phantom of the Hartle–Hawking instanton: Connecting inflation with dark energy

DOE PAGES

Chen, Pisin; Qiu, Taotao; Yeom, Dong -han

2016-02-20

If the Hartle–Hawking wave function is the correct boundary condition of our universe, the history of our universe will be well approximated by an instanton. Although this instanton should be classicalized at infinity, as long as we are observing a process of each history, we may detect a non-classicalized part of field combinations. When we apply it to a dark energy model, this non-classicalized part of fields can be well embedded to a quintessence and a phantom model, i.e., a quintom model. Because of the property of complexified instantons, the phantomness will be naturally free from a big rip singularity.more » This phantomness does not cause perturbative instabilities, as it is an effect emergent from the entire wave function. Lastly, our work may thus provide a theoretical basis for the quintom models, whose equation of state can cross the cosmological constant boundary phenomenologically.« less

Effects of tunnelling and asymmetry for system-bath models of electron transfer

NASA Astrophysics Data System (ADS)

Mattiat, Johann; Richardson, Jeremy O.

2018-03-01

We apply the newly derived nonadiabatic golden-rule instanton theory to asymmetric models describing electron-transfer in solution. The models go beyond the usual spin-boson description and have anharmonic free-energy surfaces with different values for the reactant and product reorganization energies. The instanton method gives an excellent description of the behaviour of the rate constant with respect to asymmetry for the whole range studied. We derive a general formula for an asymmetric version of the Marcus theory based on the classical limit of the instanton and find that this gives significant corrections to the standard Marcus theory. A scheme is given to compute this rate based only on equilibrium simulations. We also compare the rate constants obtained by the instanton method with its classical limit to study the effect of tunnelling and other quantum nuclear effects. These quantum effects can increase the rate constant by orders of magnitude.

Phantom of the Hartle-Hawking instanton: connecting inflation with dark energy

NASA Astrophysics Data System (ADS)

Chen, Pisin; Qiu, Taotao; Yeom, Dong-han

2016-02-01

If the Hartle-Hawking wave function is the correct boundary condition of our universe, the history of our universe will be well approximated by an instanton. Although this instanton should be classicalized at infinity, as long as we are observing a process of each history, we may detect a non-classicalized part of field combinations. When we apply it to a dark energy model, this non-classicalized part of fields can be well embedded to a quintessence and a phantom model, i.e., a quintom model. Because of the property of complexified instantons, the phantomness will be naturally free from a big rip singularity. This phantomness does not cause perturbative instabilities, as it is an effect emergent from the entire wave function. Our work may thus provide a theoretical basis for the quintom models, whose equation of state can cross the cosmological constant boundary phenomenologically.

Finite-width Laplace sum rules for 0-+ pseudoscalar glueball in the instanton vacuum model

NASA Astrophysics Data System (ADS)

Wang, Feng; Chen, Junlong; Liu, Jueping

2015-10-01

The correlation function of the 0-+ pseudoscalar glueball current is calculated based on the semiclassical expansion for quantum chromodynamics (QCD) in the instanton liquid background. Besides taking the pure classical contribution from instantons and the perturbative one into account, we calculate the contribution arising from the interaction (or the interference) between instantons and the quantum gluon fields, which is infrared free and more important than the pure perturbative one. Instead of the usual zero-width approximation for the resonances, the Breit-Wigner form with a correct threshold behavior for the spectral function of the finite-width resonance is adopted. The properties of the 0-+ pseudoscalar glueball are investigated via a family of the QCD Laplacian sum rules. A consistency between the subtracted and unsubtracted sum rules is very well justified. The values of the mass, decay width, and coupling constants for the 0-+ resonance in which the glueball fraction is dominant are obtained.

Baryonic popcorn

NASA Astrophysics Data System (ADS)

Kaplunovsky, Vadim; Melnikov, Dmitry; Sonnenschein, Jacob

2012-11-01

In the large N c limit cold dense nuclear matter must be in a lattice phase. This applies also to holographic models of hadron physics. In a class of such models, like the generalized Sakai-Sugimoto model, baryons take the form of instantons of the effective flavor gauge theory that resides on probe flavor branes. In this paper we study the phase structure of baryonic crystals by analyzing discrete periodic configurations of such instantons. We find that instanton configurations exhibit a series of "popcorn" transitions upon increasing the density. Through these transitions normal (3D) lattices expand into the transverse dimension, eventually becoming a higher dimensional (4D) multi-layer lattice at large densities. We consider 3D lattices of zero size instantons as well as 1D periodic chains of finite size instantons, which serve as toy models of the full holographic systems. In particular, for the finite-size case we determine solutions of the corresponding ADHM equations for both a straight chain and for a 2D zigzag configuration where instantons pop up into the holographic dimension. At low density the system takes the form of an "abelian anti- ferromagnetic" straight periodic chain. Above a critical density there is a second order phase transition into a zigzag structure. An even higher density yields a rich phase space characterized by the formation of multi-layer zigzag structures. The finite size of the lattices in the transverse dimension is a signal of an emerging Fermi sea of quarks. We thus propose that the popcorn transitions indicate the onset of the "quarkyonic" phase of the cold dense nuclear matter.

LETTER TO THE EDITOR: Gravitational instantons

NASA Astrophysics Data System (ADS)

Nutku, Y.; Sheftel', M. B.; Malykh, A. A.

1997-03-01

New instanton solutions of the Einstein field equations are presented. These solutions are obtained from a reduction of the complex Monge - Ampère equation governing metrics with anti-self-dual curvature to an interesting two-dimensional real Monge - Ampère equation.

Compact singularity-free Kerr-Newman-de Sitter instantons

NASA Astrophysics Data System (ADS)

Chruściel, Piotr T.; Hörzinger, Michael

2017-04-01

Generalizing the results in Chruściel and Hörzinger [J. High Energy Phys. 16 (2016) 1, 10.1007/JHEP04(2016)012], we construct further families of compact Einstein-Maxwell instantons associated with the Kerr-Newman metrics with a positive cosmological constant.

Gravitational instantons admit hyper-Kähler structure

NASA Astrophysics Data System (ADS)

Aliev, A. N.; Nutku, Y.

1999-01-01

We construct the explicit form of three almost-complex structures that a Riemannian manifold with self-dual curvature admits and show that their Nijenhuis tensors vanish so that they are integrable. This proves that gravitational instantons with self-dual curvature admit hyper-Kähler structure. In order to arrive at the three vector-valued 1-forms defining almost-complex structure, we give a spinor description of real four-dimensional Riemannian manifolds with Euclidean signature in terms of two independent sets of two-component spinors. This is a version of the original Newman-Penrose formalism that is appropriate to the discussion of the mathematical, as well as physical properties of gravitational instantons. We shall build on the work of Goldblatt who first developed an NP formalism for gravitational instantons but we shall adopt it to differential forms in the NP basis to make the formalism much more compact. We shall show that the spin coefficients, connection 1-form, curvature 2-form, Ricci and Bianchi identities, as well as the Maxwell equations naturally split up into their self-dual and anti-self-dual parts corresponding to the two independent spin frames. We shall give the complex dyad as well as the spinor formulation of the almost-complex structures and show that they reappear under the guise of a triad basis for the Petrov classification of gravitational instantons. Completing the work of Salamon on hyper-Kähler structure, we show that the vanishing of the Nijenhuis tensor for all three almost-complex structures depends on the choice of a self-dual gauge for the connection which is guaranteed by virtue of the fact that the curvature 2-form is self-dual for gravitational instantons.

Dimension changing phase transitions in instanton crystals

NASA Astrophysics Data System (ADS)

Kaplunovsky, Vadim; Sonnenschein, Jacob

2014-04-01

We investigate lattices of instantons and the dimension-changing transitions between them. Our ultimate goal is the 3D → 4D transition, which is holographically dual to the phase transition between the baryonic and the quarkyonic phases of cold nuclear matter. However, in this paper (just as in [1]) we focus on lower dimensions — the 1D lattice of instantons in a harmonic potential V ∝ , and the zigzag-shaped lattice as a first stage of the 1D → 2D transition. We prove that in the low- and moderate-density regimes, interactions between the instantons are dominated by two-body forces. This drastically simplifies finding the ground state of the instantons' orientations, so we made a numeric scan of the whole orientation space instead of assuming any particular ansatz. We find that depending on the M 2 /M 3 /M 4 ratios, the ground state of instanton orientations can follow a wide variety of patterns. For the straight 1D lattices, we found orientations periodically running over elements of a , Klein, prismatic, or dihedral subgroup of the , as well as irrational but link-periodic patterns. For the zigzag-shaped lattices, we detected 4 distinct orientation phases — the anti-ferromagnet, another abelian phase, and two non-abelian phases. Allowing the zigzag amplitude to vary as a function of increasing compression force, we obtained the phase diagrams for the straight and zigzag-shaped lattices in the (force , M 3 /M 4), (chemical potential , M 3 /M 4), and (density , M 3 /M 4) planes. Some of the transitions between these phases are second-order while others are first-order. Our techniques can be applied to other types of non-abelian crystals.

Does standard Monte Carlo give justice to instantons?

NASA Astrophysics Data System (ADS)

Fucito, F.; Solomon, S.

1984-01-01

The results of the standard local Monte Carlo are changed by offering instantons as candidates in the Metropolis procedure. We also define an O(3) topological charge with no contribution from planar dislocations. The RG behavior is still not recovered. Bantrell Fellow in Theoretical Physics.

Gravitational Instantons and Minimal Surfaces

NASA Astrophysics Data System (ADS)

Nutku, Y.

1996-12-01

We show that for every minimal surface in E3 there is a gravitational instanton, an exact solution of the Einstein field equations with Euclidean signature and anti-self-dual curvature. The explicit metric establishing this correspondence is presented and a new class of exact solutions are obtained.

Instantons, quivers and noncommutative Donaldson-Thomas theory

NASA Astrophysics Data System (ADS)

Cirafici, Michele; Sinkovics, Annamaria; Szabo, Richard J.

2011-12-01

We construct noncommutative Donaldson-Thomas invariants associated with abelian orbifold singularities by analyzing the instanton contributions to a six-dimensional topological gauge theory. The noncommutative deformation of this gauge theory localizes on noncommutative instantons which can be classified in terms of three-dimensional Young diagrams with a colouring of boxes according to the orbifold group. We construct a moduli space for these gauge field configurations which allows us to compute its virtual numbers via the counting of representations of a quiver with relations. The quiver encodes the instanton dynamics of the noncommutative gauge theory, and is associated to the geometry of the singularity via the generalized McKay correspondence. The index of BPS states which compute the noncommutative Donaldson-Thomas invariants is realized via topological quantum mechanics based on the quiver data. We illustrate these constructions with several explicit examples, involving also higher rank Coulomb branch invariants and geometries with compact divisors, and connect our approach with other ones in the literature.

Scaling analysis and instantons for thermally assisted tunneling and quantum Monte Carlo simulations

NASA Astrophysics Data System (ADS)

Jiang, Zhang; Smelyanskiy, Vadim N.; Isakov, Sergei V.; Boixo, Sergio; Mazzola, Guglielmo; Troyer, Matthias; Neven, Hartmut

2017-01-01

We develop an instantonic calculus to derive an analytical expression for the thermally assisted tunneling decay rate of a metastable state in a fully connected quantum spin model. The tunneling decay problem can be mapped onto the Kramers escape problem of a classical random dynamical field. This dynamical field is simulated efficiently by path-integral quantum Monte Carlo (QMC). We show analytically that the exponential scaling with the number of spins of the thermally assisted quantum tunneling rate and the escape rate of the QMC process are identical. We relate this effect to the existence of a dominant instantonic tunneling path. The instanton trajectory is described by nonlinear dynamical mean-field theory equations for a single-site magnetization vector, which we solve exactly. Finally, we derive scaling relations for the "spiky" barrier shape when the spin tunneling and QMC rates scale polynomially with the number of spins N while a purely classical over-the-barrier activation rate scales exponentially with N .

A Symplectic Instanton Homology via Traceless Character Varieties

NASA Astrophysics Data System (ADS)

Horton, Henry T.

Since its inception, Floer homology has been an important tool in low-dimensional topology. Floer theoretic invariants of 3-manifolds tend to be either gauge theoretic or symplecto-geometric in nature, and there is a general philosophy that each gauge theoretic Floer homology should have a corresponding symplectic Floer homology and vice-versa. In this thesis, we construct a Lagrangian Floer invariant for any closed, oriented 3-manifold Y (called the symplectic instanton homology of Y and denoted SI(Y)) which is conjecturally equivalent to a Floer homology defined using a certain variant of Yang-Mills gauge theory. The crucial ingredient for defining SI( Y) is the use of traceless character varieties in the symplectic setting, which allow us to avoid the debilitating technical hurdles present when one attempts to define a symplectic version of instanton Floer homologies. Floer theories are also expected to roughly satisfy the axioms of a topological quantum field theory (TQFT), and furthermore Dehn surgeries on knots should induce exact triangles of Floer homologies. Following a strategy used by Ozsvath and Szabo in the context of Heegaard Floer homology, we prove that our theory is functorial with respect to connected 4-dimensional cobordisms, so that cobordisms induce homomorphisms between symplectic instanton homologies. By studying the effect of Dehn surgeries on traceless character varieties, we establish a surgery exact triangle using work of Seidel that relates the geometry of Lefschetz fibrations with exact triangles in Lagrangian Floer theory. We further prove that Dehn surgeries on a link L in a 3-manifold Y induce a spectral sequence of symplectic instanton homologies - the E2-page is isomorphic to a direct sum of symplectic instanton homologies of all possible combinations of 0- and 1-surgeries on the components of L, and the spectral sequence converges to SI(Y). For the branched double cover Sigma(L) of a link L in S3, we show there is a link surgery spectral sequence whose E 2-page is isomorphic to the reduced Khovanov homology of L and which converges to the symplectic instanton homology of Sigma( L).

Control and instanton trajectories for random transitions in turbulent flows

NASA Astrophysics Data System (ADS)

Bouchet, Freddy; Laurie, Jason; Zaboronski, Oleg

2011-12-01

Many turbulent systems exhibit random switches between qualitatively different attractors. The transition between these bistable states is often an extremely rare event, that can not be computed through DNS, due to complexity limitations. We present results for the calculation of instanton trajectories (a control problem) between non-equilibrium stationary states (attractors) in the 2D stochastic Navier-Stokes equations. By representing the transition probability between two states using a path integral formulation, we can compute the most probable trajectory (instanton) joining two non-equilibrium stationary states. Technically, this is equivalent to the minimization of an action, which can be related to a fluid mechanics control problem.

Three-dimensional gauge theories and gravitational instantons from string theory

NASA Astrophysics Data System (ADS)

Cherkis, Sergey Alexander

Various realizations of gauge theories in string theory allow an identification of their spaces of vacua with gravitational instantons. Also, they provide a correspondence of vacua of gauge theories with nonabelian monopole configurations and solutions of a system of integrable equations called Nahm equations. These identifications make it possible to apply powerful techniques of differential and algebraic geometry to solve the gauge theories in question. In other words, it becomes possible to find the exact metrics on their moduli spaces of vacua with all quantum corrections included. As another outcome we obtain for the first time the description of a series of all Dk-type gravitational instantons.

Imaginary potential of moving quarkonia in a D-instanton background

NASA Astrophysics Data System (ADS)

Zhang, Zi-qiang; Hou, De-fu; Chen, Gang

2017-11-01

The imaginary part of the inter-quark potential of moving heavy quarkonia is investigated in the context of dual super-gravity in an AdS background, deformed by a dilaton which induces the gauge field condensate in the dual gauge theory. A quark-anti-quark pair is analyzed, moving transverse and parallel to the plasma wind, in turn. It is shown that in both cases increased D-instanton density tends to increase the inter-distance and decrease the imaginary potential, opposite to the effect of the pair’s velocity. Moreover, it is found that the D-instanton density has stronger effects in the parallel case than the transverse.

Multiple D3-Instantons and Mock Modular Forms I

NASA Astrophysics Data System (ADS)

Alexandrov, Sergei; Banerjee, Sibasish; Manschot, Jan; Pioline, Boris

2017-07-01

We study D3-instanton corrections to the hypermultiplet moduli space in type IIB string theory compactified on a Calabi-Yau threefold. In a previous work, consistency of D3-instantons with S-duality was established at first order in the instanton expansion, using the modular properties of the M5-brane elliptic genus. We extend this analysis to the two-instanton level, where wall-crossing phenomena start playing a role. We focus on the contact potential, an analogue of the Kähler potential which must transform as a modular form under S-duality. We show that it can be expressed in terms of a suitable modification of the partition function of D4-D2-D0 BPS black holes, constructed out of the generating function of MSW invariants (the latter coincide with Donaldson-Thomas invariants in a particular chamber). Modular invariance of the contact potential then requires that, in the case where the D3-brane wraps a reducible divisor, the generating function of MSW invariants must transform as a vector-valued mock modular form, with a specific modular completion built from the MSW invariants of the constituents. Physically, this gives a powerful constraint on the degeneracies of BPS black holes. Mathematically, our result gives a universal prediction for the modular properties of Donaldson-Thomas invariants of pure two-dimensional sheaves.

FAST TRACK COMMUNICATION: Open string pair creation from worldsheet instantons

NASA Astrophysics Data System (ADS)

Schubert, Christian; Torrielli, Alessandro

2010-10-01

Worldline instantons provide a particularly elegant way to derive Schwinger's well-known formula for the pair creation rate due to a constant electric field in quantum electrodynamics. In this communication, we show how to extend this method to the corresponding problem of open string pair creation.

3d expansions of 5d instanton partition functions

NASA Astrophysics Data System (ADS)

Nieri, Fabrizio; Pan, Yiwen; Zabzine, Maxim

2018-04-01

We propose a set of novel expansions of Nekrasov's instanton partition functions. Focusing on 5d supersymmetric pure Yang-Mills theory with unitary gauge group on C_{q,{t}^{-1}}^2× S^1 , we show that the instanton partition function admits expansions in terms of partition functions of unitary gauge theories living on the 3d subspaces C_q× S^1 , C_{t^{-1}}× S^1 and their intersection along S^1 . These new expansions are natural from the BPS/CFT viewpoint, as they can be matched with W q,t correlators involving an arbitrary number of screening charges of two kinds. Our constructions generalize and interpolate existing results in the literature.

Instantons and entanglement entropy

NASA Astrophysics Data System (ADS)

Bhattacharyya, Arpan; Hung, Ling-Yan; Melby-Thompson, Charles M.

2017-10-01

We would like to put the area law — believed to be obeyed by entanglement entropies in the ground state of a local field theory — to scrutiny in the presence of nonperturbative effects. We study instanton corrections to entanglement entropy in various models whose instanton contributions are well understood, including U(1) gauge theory in 2+1 dimensions and false vacuum decay in ϕ 4 theory, and we demonstrate that the area law is indeed obeyed in these models. We also perform numerical computations for toy wavefunctions mimicking the theta vacuum of the (1+1)-dimensional Schwinger model. Our results indicate that such superpositions exhibit no more violation of the area law than the logarithmic behavior of a single Fermi surface.

Giant graviton interactions and M2-branes ending on multiple M5-branes

NASA Astrophysics Data System (ADS)

Hirano, Shinji; Sato, Yuki

2018-05-01

We study splitting and joining interactions of giant gravitons with angular momenta N 1/2 ≪ J ≪ N in the type IIB string theory on AdS 5 × S 5 by describing them as instantons in the tiny graviton matrix model introduced by Sheikh-Jabbari. At large J the instanton equation can be mapped to the four-dimensional Laplace equation and the Coulomb potential for m point charges in an n-sheeted Riemann space corresponds to the m-to- n interaction process of giant gravitons. These instantons provide the holographic dual of correlators of all semi-heavy operators and the instanton amplitudes exactly agree with the pp-wave limit of Schur polynomial correlators in N = 4 SYM computed by Corley, Jevicki and Ramgoolam. By making a slight change of variables the same instanton equation is mathematically transformed into the Basu-Harvey equation which describes the system of M2-branes ending on M5-branes. As it turns out, the solutions to the sourceless Laplace equation on an n-sheeted Riemann space correspond to n M5-branes connected by M2-branes and we find general solutions representing M2-branes ending on multiple M5-branes. Among other solutions, the n = 3 case describes an M2-branes junction ending on three M5-branes. The effective theory on the moduli space of our solutions might shed light on the low energy effective theory of multiple M5-branes.

Nonperturbative corrections to 4D string theory effective actions from SL(2,Z) duality and supersymmetry.

PubMed

Robles-Llana, Daniel; Rocek, Martin; Saueressig, Frank; Theis, Ulrich; Vandoren, Stefan

2007-05-25

We find the D(-1)- and D1-brane instanton contributions to the hypermultiplet moduli space of type IIB string compactifications on Calabi-Yau threefolds. These combine with known perturbative and world sheet instanton corrections into a single modular invariant function that determines the hypermultiplet low-energy effective action.

ABJM Wilson loops in arbitrary representations

NASA Astrophysics Data System (ADS)

Hatsuda, Yasuyuki; Honda, Masazumi; Moriyama, Sanefumi; Okuyama, Kazumi

2013-10-01

We study vacuum expectation values (VEVs) of circular half BPS Wilson loops in arbitrary representations in ABJM theory. We find that those in hook representations are reduced to elementary integrations thanks to the Fermi gas formalism, which are accessible from the numerical studies similar to the partition function in the previous studies. For non-hook representations, we show that the VEVs in the grand canonical formalism can be exactly expressed as determinants of those in the hook representations. Using these facts, we can study the instanton effects of the VEVs in various representations. Our results are consistent with the worldsheet instanton effects studied from the topological string and a prescription to include the membrane instanton effects by shifting the chemical potential, which has been successful for the partition function.

World sheet instantons via the Myers effect and Script N = 1* quiver superpotentials

NASA Astrophysics Data System (ADS)

Hollowood, Timothy J.; Kumar, S. Prem

2002-10-01

In this note we explore the stringy interpretation of non-perturbative effects in Script N = 1* deformations of the Ak-1 quiver models. For certain types of deformations we argue that the massive vacua are described by Nk fractional D3-branes at the orbifold polarizing into k concentric 5-brane spheres each carrying fractional brane charge. The polarization of the D3-branes induces a polarization of D-instantons into string world-sheets wrapped on the Myers spheres. We show that the superpotentials in these models are indeed generated by these world-sheet instantons. We point out that for certain parameter values the condensates yield the exact superpotential for a relevant deformation of the Klebanov-Witten conifold theory.

Spin coherent-state path integrals and the instanton calculus

NASA Astrophysics Data System (ADS)

Garg, Anupam; Kochetov, Evgueny; Park, Kee-Su; Stone, Michael

2003-01-01

We use an instanton approximation to the continuous-time spin coherent-state path integral to obtain the tunnel splitting of classically degenerate ground states. We show that provided the fluctuation determinant is carefully evaluated, the path integral expression is accurate to order O(1/j). We apply the method to the LMG model and to the molecular magnet Fe8 in a transverse field.

The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects

DOE PAGES

Argyres, Philip C.; Uensal, Mithat

2012-08-10

We study the dynamics of four dimensional gauge theories with adjoint fermions for all gauge groups, both in perturbation theory and non-perturbatively, by using circle compactification with periodic boundary conditions for the fermions. There are new gauge phenomena. We show that, to all orders in perturbation theory, many gauge groups are Higgsed by the gauge holonomy around the circle to a product of both abelian and nonabelian gauge group factors. Non-perturbatively there are monopole-instantons with fermion zero modes and two types of monopole-anti-monopole molecules, called bions. One type are magnetic bions which carry net magnetic charge and induce a massmore » gap for gauge fluctuations. Another type are neutral bions which are magnetically neutral, and their understanding requires a generalization of multi-instanton techniques in quantum mechanics — which we refer to as the Bogomolny-Zinn-Justin (BZJ) prescription — to compactified field theory. The BZJ prescription applied to bion-anti-bion topological molecules predicts a singularity on the positive real axis of the Borel plane (i.e., a divergence from summing large orders in peturbation theory) which is of order N times closer to the origin than the leading 4-d BPST instanton-anti-instanton singularity, where N is the rank of the gauge group. The position of the bion-anti-bion singularity is thus qualitatively similar to that of the 4-d IR renormalon singularity, and we conjecture that they are continuously related as the compactification radius is changed. By making use of transseries and Écalle’s resurgence theory we argue that a non-perturbative continuum definition of a class of field theories which admit semi-classical expansions may be possible.« less

Resurgence and dynamics of O(N) and Grassmannian sigma models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dunne, Gerald V.; Unsal, Mithat

Here, we study the non-perturbative dynamics of the two dimensional O( N) and Grassmannian sigma models by using compactification with twisted boundary conditions on R× S 1, semi-classical techniques and resurgence. While the O(N) model has no instantons for N > 3, it has (non-instanton) saddles on R 2, which we call 2d-saddles. On R× S 1, the resurgent relation between perturbation theory and non-perturbative physics is encoded in new saddles, which are associated with the affine root system of the o( N) algebra. These events may be viewed as fractionalizations of the 2d-saddles. The first beta function coefficient, givenmore » by the dual Coxeter number, can then be intepreted as the sum of the multiplicities (dual Kac labels) of these fractionalized objects. Surprisingly, the new saddles in O( N) models in compactified space are in one-to-one correspondence with monopole-instanton saddles in SO( N) gauge theory on R 3×S 1. The Grassmannian sigma models Gr( N, M) have 2d instantons, which fractionalize into N kink-instantons. The small circle dynamics of both sigma models can be described as a dilute gas of the one-events and two-events, bions. One-events are the leading source of a variety of non-perturbative effects, and produce the strong scale of the 2d theory in the compactified theory. We show that in both types of sigma models the neutral bion emulates the role of IR-renormalons. We also study the topological theta angle dependence in both the O(3) model and Gr( N, M), and describe the multi-branched structure of the observables in terms of the theta-angle dependence of the saddle amplitudes, providing a microscopic argument for Haldane’s conjecture.« less

Resurgence and dynamics of O(N) and Grassmannian sigma models

DOE PAGES

Dunne, Gerald V.; Unsal, Mithat

2015-09-29

Here, we study the non-perturbative dynamics of the two dimensional O( N) and Grassmannian sigma models by using compactification with twisted boundary conditions on R× S 1, semi-classical techniques and resurgence. While the O(N) model has no instantons for N > 3, it has (non-instanton) saddles on R 2, which we call 2d-saddles. On R× S 1, the resurgent relation between perturbation theory and non-perturbative physics is encoded in new saddles, which are associated with the affine root system of the o( N) algebra. These events may be viewed as fractionalizations of the 2d-saddles. The first beta function coefficient, givenmore » by the dual Coxeter number, can then be intepreted as the sum of the multiplicities (dual Kac labels) of these fractionalized objects. Surprisingly, the new saddles in O( N) models in compactified space are in one-to-one correspondence with monopole-instanton saddles in SO( N) gauge theory on R 3×S 1. The Grassmannian sigma models Gr( N, M) have 2d instantons, which fractionalize into N kink-instantons. The small circle dynamics of both sigma models can be described as a dilute gas of the one-events and two-events, bions. One-events are the leading source of a variety of non-perturbative effects, and produce the strong scale of the 2d theory in the compactified theory. We show that in both types of sigma models the neutral bion emulates the role of IR-renormalons. We also study the topological theta angle dependence in both the O(3) model and Gr( N, M), and describe the multi-branched structure of the observables in terms of the theta-angle dependence of the saddle amplitudes, providing a microscopic argument for Haldane’s conjecture.« less

Borel Summability of Perturbative Series in 4D N=2 and 5D N=1 Supersymmetric Theories.

PubMed

Honda, Masazumi

2016-05-27

We study weak coupling perturbative series in 4D N=2 and 5D N=1 supersymmetric gauge theories with Lagrangians. We prove that the perturbative series of these theories in the zero-instanton sector are Borel summable for various observables. Our result for the 4D N=2 case supports an expectation from a recent proposal on a semiclassical realization of infrared renormalons in QCD-like theories, where the semiclassical solution does not exist in N=2 theories and the perturbative series are unambiguous, namely, Borel summable. We also prove that the perturbative series in an arbitrary number of instanton sectors are Borel summable for a wide class of theories. It turns out that exact results can be obtained by summing over the Borel resummations with every instanton number.

Potential energy surface interpolation with neural networks for instanton rate calculations

NASA Astrophysics Data System (ADS)

Cooper, April M.; Hallmen, Philipp P.; Kästner, Johannes

2018-03-01

Artificial neural networks are used to fit a potential energy surface (PES). We demonstrate the benefits of using not only energies but also their first and second derivatives as training data for the neural network. This ensures smooth and accurate Hessian surfaces, which are required for rate constant calculations using instanton theory. Our aim was a local, accurate fit rather than a global PES because instanton theory requires information on the potential only in the close vicinity of the main tunneling path. Elongations along vibrational normal modes at the transition state are used as coordinates for the neural network. The method is applied to the hydrogen abstraction reaction from methanol, calculated on a coupled-cluster level of theory. The reaction is essential in astrochemistry to explain the deuteration of methanol in the interstellar medium.

Vector and Axial-Vector Current Correlators Within the Instanton Model of QCD Vacuum

NASA Astrophysics Data System (ADS)

Dorokhov, A. E.

2005-08-01

The pion electric polarizability, α {π ^ ± }E , the leading order hadronic contribution to the muon anomalous magnetic moment, aμ hvp(1) , and the ratio of the V - A and V + A correlators are found within the instanton model of QCD vacuum. The results are compared with phenomenological estimates of these quantities from the ALEPH and OPAL data on vector and axial-vector spectral densities.

Kinetic isotope effects and how to describe them

PubMed Central

Karandashev, Konstantin; Xu, Zhen-Hao; Meuwly, Markus; Vaníček, Jiří; Richardson, Jeremy O.

2017-01-01

We review several methods for computing kinetic isotope effects in chemical reactions including semiclassical and quantum instanton theory. These methods describe both the quantization of vibrational modes as well as tunneling and are applied to the ⋅H + H2 and ⋅H + CH4 reactions. The absolute rate constants computed with the semiclassical instanton method both using on-the-fly electronic structure calculations and fitted potential-energy surfaces are also compared directly with exact quantum dynamics results. The error inherent in the instanton approximation is found to be relatively small and similar in magnitude to that introduced by using fitted surfaces. The kinetic isotope effect computed by the quantum instanton is even more accurate, and although it is computationally more expensive, the efficiency can be improved by path-integral acceleration techniques. We also test a simple approach for designing potential-energy surfaces for the example of proton transfer in malonaldehyde. The tunneling splittings are computed, and although they are found to deviate from experimental results, the ratio of the splitting to that of an isotopically substituted form is in much better agreement. We discuss the strengths and limitations of the potential-energy surface and based on our findings suggest ways in which it can be improved. PMID:29282447

Perspective: Ring-polymer instanton theory

NASA Astrophysics Data System (ADS)

Richardson, Jeremy O.

2018-05-01

Since the earliest explorations of quantum mechanics, it has been a topic of great interest that quantum tunneling allows particles to penetrate classically insurmountable barriers. Instanton theory provides a simple description of these processes in terms of dominant tunneling pathways. Using a ring-polymer discretization, an efficient computational method is obtained for applying this theory to compute reaction rates and tunneling splittings in molecular systems. Unlike other quantum-dynamics approaches, the method scales well with the number of degrees of freedom, and for many polyatomic systems, the method may provide the most accurate predictions which can be practically computed. Instanton theory thus has the capability to produce useful data for many fields of low-temperature chemistry including spectroscopy, atmospheric and astrochemistry, as well as surface science. There is however still room for improvement in the efficiency of the numerical algorithms, and new theories are under development for describing tunneling in nonadiabatic transitions.

On the no-boundary proposal for ekpyrotic and cyclic cosmologies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Battarra, Lorenzo; Lehners, Jean-Luc, E-mail: lorenzo.battarra@aei.mpg.de, E-mail: jlehners@aei.mpg.de

2014-12-01

The no-boundary proposal provides a compelling theory for the initial conditions of our universe. We study the implications of such initial conditions for ekpyrotic and cyclic cosmologies. These cosmologies allow for the existence of a new type of ''ekpyrotic instanton'', which describes the creation of a universe in the ekpyrotic contraction phase. Remarkably, we find that the ekpyrotic attractor can explain how the universe became classical. In a cyclic context, in addition to the ekpyrotic instantons there exist de Sitter-like instantons describing the emergence of the universe in the dark energy phase. Our results show that typically the ekpyrotic instantonsmore » yield a higher probability. In fact, in a potential energy landscape allowing both inflationary and cyclic cosmologies, the no-boundary proposal implies that the probability for ekpyrotic and cyclic initial conditions is vastly higher than that for inflationary ones.« less

D-brane instantons and the effective field theory of flux compactifications

NASA Astrophysics Data System (ADS)

Uranga, Angel M.

2009-01-01

We provide a description of the effects of fluxes on euclidean D-brane instantons purely in terms of the 4d effective action. The effect corresponds to the dressing of the effective non-perturbative 4d effective vertex with 4d flux superpotential interactions, generated when the moduli fields made massive by the flux are integrated out. The description in terms of effective field theory allows a unified description of non-perturbative effects in all flux compactifications of a given underlying fluxless model, globally in the moduli space of the latter. It also allows us to describe explicitly the effects on D-brane instantons of fluxes with no microscopic description, like non-geometric fluxes. At the more formal level, the description has interesting connections with the bulk-boundary map of open-closed two-dimensional topological string theory, and with the Script N = 1 special geometry.

Yang-Mills instantons in Kähler spaces with one holomorphic isometry

NASA Astrophysics Data System (ADS)

Chimento, Samuele; Ortín, Tomás; Ruipérez, Alejandro

2018-03-01

We consider self-dual Yang-Mills instantons in 4-dimensional Kähler spaces with one holomorphic isometry and show that they satisfy a generalization of the Bogomol'nyi equation for magnetic monopoles on certain 3-dimensional metrics. We then search for solutions of this equation in 3-dimensional metrics foliated by 2-dimensional spheres, hyperboloids or planes in the case in which the gauge group coincides with the isometry group of the metric (SO(3), SO (1 , 2) and ISO(2), respectively). Using a generalized hedgehog ansatz the Bogomol'nyi equations reduce to a simple differential equation in the radial variable which admits a universal solution and, in some cases, a particular one, from which one finally recovers instanton solutions in the original Kähler space. We work out completely a few explicit examples for some Kähler spaces of interest.

Quadratic String Method for Locating Instantons in Tunneling Splitting Calculations.

PubMed

Cvitaš, Marko T

2018-03-13

The ring-polymer instanton (RPI) method is an efficient technique for calculating approximate tunneling splittings in high-dimensional molecular systems. In the RPI method, tunneling splitting is evaluated from the properties of the minimum action path (MAP) connecting the symmetric wells, whereby the extensive sampling of the full potential energy surface of the exact quantum-dynamics methods is avoided. Nevertheless, the search for the MAP is usually the most time-consuming step in the standard numerical procedures. Recently, nudged elastic band (NEB) and string methods, originaly developed for locating minimum energy paths (MEPs), were adapted for the purpose of MAP finding with great efficiency gains [ J. Chem. Theory Comput. 2016 , 12 , 787 ]. In this work, we develop a new quadratic string method for locating instantons. The Euclidean action is minimized by propagating the initial guess (a path connecting two wells) over the quadratic potential energy surface approximated by means of updated Hessians. This allows the algorithm to take many minimization steps between the potential/gradient calls with further reductions in the computational effort, exploiting the smoothness of potential energy surface. The approach is general, as it uses Cartesian coordinates, and widely applicable, with computational effort of finding the instanton usually lower than that of determining the MEP. It can be combined with expensive potential energy surfaces or on-the-fly electronic-structure methods to explore a wide variety of molecular systems.

Exact partition functions for the Ω-deformed {N}={2}^{ast } SU(2) gauge theory

NASA Astrophysics Data System (ADS)

Beccaria, Matteo; Macorini, Guido

2016-07-01

We study the low energy effective action of the Ω-deformed {N}={2}^{ast } SU(2) gauge theory. It depends on the deformation parameters ɛ 1, ɛ 2, the scalar field expectation value a, and the hypermultiplet mass m. We explore the plane (m/ɛ_1,ɛ_2/ɛ_1) looking for special features in the multi-instanton contributions to the prepotential, motivated by what happens in the Nekrasov-Shatashvili limit ɛ 2 → 0. We propose a simple condition on the structure of poles of the k-instanton prepotential and show that it is admissible at a finite set of points in the above plane. At these special points, the prepotential has poles at fixed positions independent on the instanton number. Besides and remarkably, both the instanton partition function and the full prepotential, including the perturbative contribution, may be given in closed form as functions of the scalar expectation value a and the modular parameter q appearing in special combinations of Eisenstein series and Dedekind η function. As a byproduct, the modular anomaly equation can be tested at all orders at these points. We discuss these special features from the point of view of the AGT correspondence and provide explicit toroidal 1-blocks in non-trivial closed form. The full list of solutions with 1, 2, 3, and 4 poles is determined and described in details.

Instanton and noninstanton tunneling in periodically perturbed barriers: semiclassical and quantum interpretations.

PubMed

Takahashi, Kin'ya; Ikeda, Kensuke S

2012-11-01

In multidimensional barrier tunneling, there exist two different types of tunneling mechanisms, instanton-type tunneling and noninstanton tunneling. In this paper we investigate transitions between the two tunneling mechanisms from the semiclassical and quantum viewpoints taking two simple models: a periodically perturbed Eckart barrier for the semiclassical analysis and a periodically perturbed rectangular barrier for the quantum analysis. As a result, similar transitions are observed with change of the perturbation frequency ω for both systems, and we obtain a comprehensive scenario from both semiclassical and quantum viewpoints for them. In the middle range of ω, in which the plateau spectrum is observed, noninstanton tunneling dominates the tunneling process, and the tunneling amplitude takes the maximum value. Noninstanton tunneling explained by stable-unstable manifold guided tunneling (SUMGT) from the semiclassical viewpoint is interpreted as multiphoton-assisted tunneling from the quantum viewpoint. However, in the limit ω→0, instanton-type tunneling takes the place of noninstanton tunneling, and the tunneling amplitude converges on a constant value depending on the perturbation strength. The spectrum localized around the input energy is observed, and there is a scaling law with respect to the width of the spectrum envelope, i.e., the width ∝ℏω. In the limit ω→∞, the tunneling amplitude converges on that of the unperturbed system, i.e., the instanton of the unperturbed system.

Euclidean mirrors: enhanced vacuum decay from reflected instantons

NASA Astrophysics Data System (ADS)

Akal, Ibrahim; Moortgat-Pick, Gudrid

2018-05-01

We study the tunnelling of virtual matter–antimatter pairs from the quantum vacuum in the presence of a spatially uniform, time-dependent electric background composed of a strong, slow field superimposed with a weak, rapid field. After analytic continuation to Euclidean spacetime, we obtain from the instanton equations two critical points. While one of them is the closing point of the instanton path, the other serves as an Euclidean mirror which reflects and squeezes the instanton. It is this reflection and shrinking which is responsible for an enormous enhancement of the vacuum pair production rate. We discuss how important features of two different mechanisms can be analysed and understood via such a rotation in the complex plane. (a) Consistent with previous studies, we first discuss the standard assisted mechanism with a static strong field and certain weak fields with a distinct pole structure in order to show that the reflection takes place exactly at the poles. We also discuss the effect of possible sub-cycle structures. We extend this reflection picture then to weak fields which have no poles present and illustrate the effective reflections with explicit examples. An additional field strength dependence for the rate occurs in such cases. We analytically compute the characteristic threshold for the assisted mechanism given by the critical combined Keldysh parameter. We discuss significant differences between these two types of fields. For various backgrounds, we present the contributing instantons and perform analytical computations for the corresponding rates treating both fields nonperturbatively. (b) In addition, we also study the case with a nonstatic strong field which gives rise to the assisted dynamical mechanism. For different strong field profiles we investigate the impact on the critical combined Keldysh parameter. As an explicit example, we analytically compute the rate by employing the exact reflection points. The validity of the predictions for both mechanisms is confirmed by numerical computations.

Instanton approach to large N Harish-Chandra-Itzykson-Zuber integrals.

PubMed

Bun, J; Bouchaud, J P; Majumdar, S N; Potters, M

2014-08-15

We reconsider the large N asymptotics of Harish-Chandra-Itzykson-Zuber integrals. We provide, using Dyson's Brownian motion and the method of instantons, an alternative, transparent derivation of the Matytsin formalism for the unitary case. Our method is easily generalized to the orthogonal and symplectic ensembles. We obtain an explicit solution of Matytsin's equations in the case of Wigner matrices, as well as a general expansion method in the dilute limit, when the spectrum of eigenvalues spreads over very wide regions.

Instanton tunneling for de Sitter space with real projective spatial sections

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ong, Yen Chin; Yeom, Dong-han, E-mail: ongyenchin@sjtu.edu.cn, E-mail: innocent.yeom@gmail.com

The physics of tunneling from one spacetime to another is often understood in terms of instantons. For some instantons, it was recently shown in the literature that there are two complementary ''interpretations'' for their analytic continuations. Dubbed ''something-to-something'' and ''nothing-to-something'' interpretations, respectively, the former involves situation in which the initial and final hypersurfaces are connected by a Euclidean manifold, whereas the initial and final hypersurfaces in the latter case are not connected in such a way. We consider a de Sitter space with real projective space RP{sup 3} spatial sections, as was originally understood by de Sitter himself. This originalmore » version of de Sitter space has several advantages over the usual de Sitter space with S{sup 3} spatial sections. In particular, the interpretation of the de Sitter entropy as entanglement entropy is much more natural. We discuss the subtleties involved in the tunneling of such a de Sitter space.« less

Finite-width Laplacian sum rules for 2++ tensor glueball in the instanton vacuum model

NASA Astrophysics Data System (ADS)

Chen, Junlong; Liu, Jueping

2017-01-01

The more carefully defined and more appropriate 2++ tensor glueball current is a S Uc(3 ) gauge-invariant, symmetric, traceless, and conserved Lorentz-irreducible tensor. After Lorentz decomposition, the invariant amplitude of the correlation function is abstracted and calculated based on the semiclassical expansion for quantum chromodynamics (QCD) in the instanton liquid background. In addition to taking the perturbative contribution into account, we calculate the contribution arising from the interaction (or the interference) between instantons and the quantum gluon fields, which is infrared free. Instead of the usual zero-width approximation for the resonances, the Breit-Wigner form with a correct threshold behavior for the spectral function of the finite-width three resonances is adopted. The properties of the 2++ tensor glueball are investigated via a family of the QCD Laplacian sum rules for the invariant amplitude. The values of the mass, decay width, and coupling constants for the 2++ resonance in which the glueball fraction is dominant are obtained.

Multiple D3-Instantons and Mock Modular Forms II

NASA Astrophysics Data System (ADS)

Alexandrov, Sergei; Banerjee, Sibasish; Manschot, Jan; Pioline, Boris

2018-03-01

We analyze the modular properties of D3-brane instanton corrections to the hypermultiplet moduli space in type IIB string theory compactified on a Calabi-Yau threefold. In Part I, we found a necessary condition for the existence of an isometric action of S-duality on this moduli space: the generating function of DT invariants in the large volume attractor chamber must be a vector-valued mock modular form with specified modular properties. In this work, we prove that this condition is also sufficient at two-instanton order. This is achieved by producing a holomorphic action of {SL(2,Z)} on the twistor space which preserves the holomorphic contact structure. The key step is to cancel the anomalous modular variation of the Darboux coordinates by a local holomorphic contact transformation, which is generated by a suitable indefinite theta series. For this purpose we introduce a new family of theta series of signature (2, n - 2), find their modular completion, and conjecture sufficient conditions for their convergence, which may be of independent mathematical interest.

S-duality in twistor space

NASA Astrophysics Data System (ADS)

Alexandrov, Sergei; Pioline, Boris

2012-08-01

In type IIB string compactifications on a Calabi-Yau threefold, the hypermultiplet moduli space {{M}_H} must carry an isometric action of the modular group SL(2 , {Z} ), inherited from the S-duality symmetry of type IIB string theory in ten dimensions. We investigate how this modular symmetry is realized at the level of the twistor space of {{M}_H} , and construct a general class of SL(2 , {Z} )-invariant quaternion-Kähler metrics with two commuting isometries, parametrized by a suitably covariant family of holomorphic transition functions. This family should include {{M}_H} corrected by D3-D1-D(-1)-instantons (with five-brane corrections ignored) and, after taking a suitable rigid limit, the Coulomb branch of five-dimensional {N} = {2} gauge theories compactified on a torus, including monopole string instantons. These results allow us to considerably simplify the derivation of the mirror map between type IIA and IIB fields in the sector where only D1-D(-1)-instantons are retained.

Intersecting surface defects and instanton partition functions

NASA Astrophysics Data System (ADS)

Pan, Yiwen; Peelaers, Wolfger

2017-07-01

We analyze intersecting surface defects inserted in interacting four-dimensional N=2 supersymmetric quantum field theories. We employ the realization of a class of such systems as the infrared fixed points of renormalization group flows from larger theories, triggered by perturbed Seiberg-Witten monopole-like configurations, to compute their partition functions. These results are cast into the form of a partition function of 4d/2d/0d coupled systems. Our computations provide concrete expressions for the instanton partition function in the presence of intersecting defects and we study the corresponding ADHM model.

Instantons and Massless Fermions in Two Dimensions

DOE R&D Accomplishments Database

Callan, C. G. Jr.; Dashen, R.; Gross, D. J.

1977-05-01

The role of instantons in the breakdown of chiral U(N) symmetry is studied in a two dimensional model. Chiral U(1) is always destroyed by the axial vector anomaly. For N = 2 chiral SU(N) is also spontaneously broken yielding massive fermions and three (decoupled) Goldstone bosons. For N greater than or equal to 3 the fermions remain massless. Realistic four dimensional theories are believed to behave in a similar way but the critical N above which the fermions cease to be massive is not known in four dimensions.

Explicit Computations of Instantons and Large Deviations in Beta-Plane Turbulence

NASA Astrophysics Data System (ADS)

Laurie, J.; Bouchet, F.; Zaboronski, O.

2012-12-01

We use a path integral formalism and instanton theory in order to make explicit analytical predictions about large deviations and rare events in beta-plane turbulence. The path integral formalism is a concise way to get large deviation results in dynamical systems forced by random noise. In the most simple cases, it leads to the same results as the Freidlin-Wentzell theory, but it has a wider range of applicability. This approach is however usually extremely limited, due to the complexity of the theoretical problems. As a consequence it provides explicit results in a fairly limited number of models, often extremely simple ones with only a few degrees of freedom. Few exception exist outside the realm of equilibrium statistical physics. We will show that the barotropic model of beta-plane turbulence is one of these non-equilibrium exceptions. We describe sets of explicit solutions to the instanton equation, and precise derivations of the action functional (or large deviation rate function). The reason why such exact computations are possible is related to the existence of hidden symmetries and conservation laws for the instanton dynamics. We outline several applications of this apporach. For instance, we compute explicitly the very low probability to observe flows with an energy much larger or smaller than the typical one. Moreover, we consider regimes for which the system has multiple attractors (corresponding to different numbers of alternating jets), and discuss the computation of transition probabilities between two such attractors. These extremely rare events are of the utmost importance as the dynamics undergo qualitative macroscopic changes during such transitions.

ADHM and the 4d quantum Hall effect

NASA Astrophysics Data System (ADS)

Barns-Graham, Alec; Dorey, Nick; Lohitsiri, Nakarin; Tong, David; Turner, Carl

2018-04-01

Yang-Mills instantons are solitonic particles in d = 4 + 1 dimensional gauge theories. We construct and analyse the quantum Hall states that arise when these particles are restricted to the lowest Landau level. We describe the ground state wavefunctions for both Abelian and non-Abelian quantum Hall states. Although our model is purely bosonic, we show that the excitations of this 4d quantum Hall state are governed by the Nekrasov partition function of a certain five dimensional supersymmetric gauge theory with Chern-Simons term. The partition function can also be interpreted as a variant of the Hilbert series of the instanton moduli space, counting holomorphic sections rather than holomorphic functions. It is known that the Hilbert series of the instanton moduli space can be rewritten using mirror symmetry of 3d gauge theories in terms of Coulomb branch variables. We generalise this approach to include the effect of a five dimensional Chern-Simons term. We demonstrate that the resulting Coulomb branch formula coincides with the corresponding Higgs branch Molien integral which, in turn, reproduces the standard formula for the Nekrasov partition function.

Note on gauge and gravitational anomalies of discrete Z N symmetries

NASA Astrophysics Data System (ADS)

Byakti, Pritibhajan; Ghosh, Diptimoy; Sharma, Tarun

2018-01-01

In this note, we discuss the consistency conditions which a discrete Z N symmetry should satisfy in order that it is not violated by gauge and gravitational instantons. As examples, we enlist all the Z N ℛ-symmetries as well as non-ℛ Z N symmetries (N=2,3,4) in the minimally supersymmetric standard model (MSSM) that are free from gauge and gravitational anomalies. We show that there exists non-anomalous discrete symmetries that forbid Baryon number violation up to dimension 6 level (in superspace). We also observe that there exists no non-anomalous Z 3 ℛ-symmetry in the MSSM. Furthermore, we point out that in a theory with one Majorana spin 3/2 gravitino, a large class of Z 4 ℛ-symmetries are violated in the presence of Eguchi-Hanson (EH) gravitational instanton. This is also in general true for higher Z N ℛ-symmetries. We also notice that in 4 dimensional N=1 supergravity, the global U(1) ℛ-symmetry is always violated by the EH instanton irrespective of the matter content of the theory.

Gravitational instantons, self-duality, and geometric flows

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bourliot, F.; Estes, J.; Petropoulos, P. M.

2010-05-15

We discuss four-dimensional 'spatially homogeneous' gravitational instantons. These are self-dual solutions of Euclidean vacuum Einstein equations. They are endowed with a product structure RxM{sub 3} leading to a foliation into three-dimensional subspaces evolving in Euclidean time. For a large class of homogeneous subspaces, the dynamics coincides with a geometric flow on the three-dimensional slice, driven by the Ricci tensor plus an so(3) gauge connection. The flowing metric is related to the vielbein of the subspace, while the gauge field is inherited from the anti-self-dual component of the four-dimensional Levi-Civita connection.

Intersecting surface defects and instanton partition functions

DOE PAGES

Pan, Yiwen; Peelaers, Wolfger

2017-07-14

We analyze intersecting surface defects inserted in interacting four-dimensional N = 2 supersymmetric quantum field theories. We employ the realization of a class of such systems as the infrared xed points of renormalization group flows from larger theories, triggered by perturbed Seiberg-Witten monopole-like con gurations, to compute their partition functions. These results are cast into the form of a partition function of 4d/2d/0d coupled systems. In conclusion, our computations provide concrete expressions for the instanton partition function in the presence of intersecting defects and we study the corresponding ADHM model.

Numeric Solutions of Dirac-Gursey Spinor Field Equation Under External Gaussian White Noise

NASA Astrophysics Data System (ADS)

Aydogmus, Fatma

2016-06-01

In this paper, we consider the Dirac-Gursey spinor field equation that has particle-like solutions derived classical field equations so-called instantons, formed by using Heisenberg ansatz, under the effect of an additional Gaussian white noise term. Our purpose is to understand how the behavior of spinor-type excited instantons in four dimensions can be affected by noise. Thus, we simulate the phase portraits and Poincaré sections of the obtained system numerically both with and without noise. Recurrence plots are also given for more detailed information regarding the system.

Baryon number violation and nonperturbative weak processes at Superconducting Super Collider energies

NASA Astrophysics Data System (ADS)

Shuryak, E. V.; Verbaarschot, J. J. M.

1992-04-01

Baryon number violation and multiple production of W and Higgs bosons are described semiclassically in terms of the instanton-anti-instanton valley. We find (i) two saddle points, one describing reflection from a barrier and the other describing tunneling through it. We find (ii) a critical energy Ec~35 TeV where the cross section is suppressed as exp(-const/g2w), but the formulas are no longer valid; (iii) however, depending on the (still uncertain) Higgs bosson action, the cross section at this point may be large enough to be observable.

Intersecting surface defects and instanton partition functions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pan, Yiwen; Peelaers, Wolfger

We analyze intersecting surface defects inserted in interacting four-dimensional N = 2 supersymmetric quantum field theories. We employ the realization of a class of such systems as the infrared xed points of renormalization group flows from larger theories, triggered by perturbed Seiberg-Witten monopole-like con gurations, to compute their partition functions. These results are cast into the form of a partition function of 4d/2d/0d coupled systems. In conclusion, our computations provide concrete expressions for the instanton partition function in the presence of intersecting defects and we study the corresponding ADHM model.

Quantum Chromodynamics and Color Confinement (confinement 2000) - Proceedings of the International Symposium

NASA Astrophysics Data System (ADS)

Suganuma, H.; Fukushima, M.; Toki, H.

The Table of Contents for the book is as follows: * Preface * Opening Address * Monopole Condensation and Quark Confinement * Dual QCD, Effective String Theory, and Regge Trajectories * Abelian Dominance and Monopole Condensation * Non-Abelian Stokes Theorem and Quark Confinement in QCD * Infrared Region of QCD and Confining Configurations * BRS Quartet Mechanism for Color Confinement * Color Confinement and Quartet Mechanism * Numerical Tests of the Kugo-Ojima Color Confinement Criterion * Monopoles and Confinement in Lattice QCD * SU(2) Lattice Gauge Theory at T > 0 in a Finite Box with Fixed Holonomy * Confining and Dirac Strings in Gluodynamics * Cooling, Monopoles, and Vortices in SU(2) Lattice Gauge Theory * Quark Confinement Physics from Lattice QCD * An (Almost) Perfect Lattice Action for SU(2) and SU(3) Gluodynamics * Vortices and Confinement in Lattice QCD * P-Vortices, Nexuses and Effects of Gribov Copies in the Center Gauges * Laplacian Center Vortices * Center Vortices at Strong Couplings and All Couplings * Simulations in SO(3) × Z(2) Lattice Gauge Theory * Exciting a Vortex - the Cost of Confinement * Instantons in QCD * Deformation of Instanton in External Color Fields * Field Strength Correlators in the Instanton Liquid * Instanton and Meron Physics in Lattice QCD * The Dual Ginzburg-Landau Theory for Confinement and the Role of Instantons * Lattice QCD for Quarks, Gluons and Hadrons * Hadronic Spectral Functions in QCD * Universality and Chaos in Quantum Field Theories * Lattice QCD Study of Three Quark Potential * Probing the QCD Vacuum with Flavour Singlet Objects : η' on the Lattice * Lattice Studies of Quarks and Gluons * Quarks and Hadrons in QCD * Supersymmetric Nonlinear Sigma Models * Chiral Transition and Baryon-number Susceptibility * Light Quark Masses in QCD * Chiral Symmetry of Baryons and Baryon Resonances * Confinement and Bound States in QCD * Parallel Session * Off-diagonal Gluon Mass Generation and Strong Randomness of Off-diagonal Gluon Phase in the Maximally Abelian Gauge * On the Colour Confinement and the Minimal Surface * Glueball Mass and String Tension of SU(2) Gluodynamics from Abelian Monopoles and Strings * Application of the Non-Perturbative Renormalization Group to the Nambu-Jona-Lasinio Model at Finite Temperature and Density * Confining Flux-Tube and Hadrons in QCD * Gauge Symmetry Breakdown due to Dynamical Higgs Scalar * Spatial Structure of Quark Cooper Pairs * New Approach to Axial Coupling Constants in the QCD Sum Rule and Instanton Effects * String Breaking on a Lattice * Bethe-Salpeter Approach for Mesons within the Dual Ginzburg-Landau Theory * Gauge Dependence and Matching Procedure of a Nonrelativistic QCD Boundstate Formalism * A Mathematical Approach to the SU(2)-Quark Confinement * Simulations of Odd Flavors QCD by Hybrid Monte Carlo * Non-Perturbative Renormalization Group Analysis of Dynamical Chiral Symmetry Breaking with Beyond Ladder Contributions * Charmonium Physics in Finite Temperature Lattice QCD * From Meson-Nucleon Scattering to Vector Mesons in Nuclear Matter * Symposium Program * List of Participants

Nekrasov and Argyres-Douglas theories in spherical Hecke algebra representation

NASA Astrophysics Data System (ADS)

Rim, Chaiho; Zhang, Hong

2017-06-01

AGT conjecture connects Nekrasov instanton partition function of 4D quiver gauge theory with 2D Liouville conformal blocks. We re-investigate this connection using the central extension of spherical Hecke algebra in q-coordinate representation, q being the instanton expansion parameter. Based on AFLT basis together with intertwiners we construct gauge conformal state and demonstrate its equivalence to the Liouville conformal state, with careful attention to the proper scaling behavior of the state. Using the colliding limit of regular states, we obtain the formal expression of irregular conformal states corresponding to Argyres-Douglas theory, which involves summation of functions over Young diagrams.

Instantons in Quantum Annealing: Thermally Assisted Tunneling Vs Quantum Monte Carlo Simulations

NASA Technical Reports Server (NTRS)

Jiang, Zhang; Smelyanskiy, Vadim N.; Boixo, Sergio; Isakov, Sergei V.; Neven, Hartmut; Mazzola, Guglielmo; Troyer, Matthias

2015-01-01

Recent numerical result (arXiv:1512.02206) from Google suggested that the D-Wave quantum annealer may have an asymptotic speed-up than simulated annealing, however, the asymptotic advantage disappears when it is compared to quantum Monte Carlo (a classical algorithm despite its name). We show analytically that the asymptotic scaling of quantum tunneling is exactly the same as the escape rate in quantum Monte Carlo for a class of problems. Thus, the Google result might be explained in our framework. We also found that the transition state in quantum Monte Carlo corresponds to the instanton solution in quantum tunneling problems, which is observed in numerical simulations.

A low-dimensional analogue of holographic baryons

NASA Astrophysics Data System (ADS)

Bolognesi, Stefano; Sutcliffe, Paul

2014-04-01

Baryons in holographic QCD correspond to topological solitons in the bulk. The most prominent example is the Sakai-Sugimoto model, where the bulk soliton in the five-dimensional spacetime of AdS-type can be approximated by the flat space self-dual Yang-Mills instanton with a small size. Recently, the validity of this approximation has been verified by comparison with the numerical field theory solution. However, multi-solitons and solitons with finite density are currently beyond numerical field theory computations. Various approximations have been applied to investigate these important issues and have led to proposals for finite density configurations that include dyonic salt and baryonic popcorn. Here we introduce and investigate a low-dimensional analogue of the Sakai-Sugimoto model, in which the bulk soliton can be approximated by a flat space sigma model instanton. The bulk theory is a baby Skyrme model in a three-dimensional spacetime with negative curvature. The advantage of the lower-dimensional theory is that numerical simulations of multi-solitons and finite density solutions can be performed and compared with flat space instanton approximations. In particular, analogues of dyonic salt and baryonic popcorn configurations are found and analysed.

Langevin Dynamics, Large Deviations and Instantons for the Quasi-Geostrophic Model and Two-Dimensional Euler Equations

NASA Astrophysics Data System (ADS)

Bouchet, Freddy; Laurie, Jason; Zaboronski, Oleg

2014-09-01

We investigate a class of simple models for Langevin dynamics of turbulent flows, including the one-layer quasi-geostrophic equation and the two-dimensional Euler equations. Starting from a path integral representation of the transition probability, we compute the most probable fluctuation paths from one attractor to any state within its basin of attraction. We prove that such fluctuation paths are the time reversed trajectories of the relaxation paths for a corresponding dual dynamics, which are also within the framework of quasi-geostrophic Langevin dynamics. Cases with or without detailed balance are studied. We discuss a specific example for which the stationary measure displays either a second order (continuous) or a first order (discontinuous) phase transition and a tricritical point. In situations where a first order phase transition is observed, the dynamics are bistable. Then, the transition paths between two coexisting attractors are instantons (fluctuation paths from an attractor to a saddle), which are related to the relaxation paths of the corresponding dual dynamics. For this example, we show how one can analytically determine the instantons and compute the transition probabilities for rare transitions between two attractors.

Vector and Axial-Vector Correlators in AN Instanton-Like Quark Model

NASA Astrophysics Data System (ADS)

Dorokhov, Alexander E.

The behavior of the vector Adler function at spacelike momenta is studied in the framework of a covariant chiral quark model with instanton-like quark-quark interaction. This function describes the transition between the high energy asymptotically free region of almost massless current quarks to the low energy hadronized regime with massive constituent quarks. The model reproduces the Adler function and V-A correlator extracted from the ALEPH and OPAL data on hadronic τ lepton decays, transformed into the Euclidean domain via dispersion relations. The leading order contribution from hadronic part of the photon vacuum polarization to the anomalous magnetic moment of the muon, aμ hvp(1), is estimated.

Super Yang-Mills theory with impurity walls and instanton moduli spaces

NASA Astrophysics Data System (ADS)

Cherkis, Sergey A.; O'Hara, Clare; Sämann, Christian

2011-06-01

We explore maximally supersymmetric Yang-Mills theory with walls of impurities respecting half of the supersymmetries. The walls carry fundamental or bifundamental matter multiplets. We employ three-dimensional N=2 superspace language to identify the Higgs branch of this theory. We find that the vacuum conditions determining the Higgs branch are exactly the bow equations yielding Yang-Mills instantons on a multi-Taub-NUT space. Under electric-magnetic duality, the super Yang-Mills theory describing the bulk is mapped to itself, while the fundamental- and bifundamental-carrying impurity walls are interchanged. We perform a one-loop computation on the Coulomb branch of the dual theory to find the asymptotic metric on the original Higgs branch.

Gravitational instantons as models for charged particle systems

NASA Astrophysics Data System (ADS)

Franchetti, Guido; Manton, Nicholas S.

2013-03-01

In this paper we propose ALF gravitational instantons of types A k and D k as models for charged particle systems. We calculate the charges of the two families. These are -( k + 1) for A k , which is proposed as a model for k + 1 electrons, and 2 - k for D k , which is proposed as a model for either a particle of charge +2 and k electrons or a proton and k - 1 electrons. Making use of preferred topological and metrical structures of the manifolds, namely metrically preferred representatives of middle dimension homology classes, we construct two different energy functionals which reproduce the Coulomb interaction energy for a system of charged particles.

Notes on wall crossing and instanton in compactified gauge theory with matter

NASA Astrophysics Data System (ADS)

Chen, Heng-Yu; Petunin, Kirill

2010-10-01

We study the quantum effects on the Coulomb branch of mathcal{N} = 2 SU(2) super-symmetric Yang-Mills with fundamental matters compactified on {mathbb{R}^3} × {S^1} , and extract the explicit perturbative and leading non-perturbative corrections to the moduli space metric predicted from the recent work of Gaiotto, Moore and Neitzke on wall-crossing [1]. We verify the predicted metric by computing the leading weak coupling instanton contribution to the four fermion correlation using standard field theory techniques, and demonstrate perfect agreement. We also demonstrate how previously known three dimensional quantities can be recovered in appropriate small radius limit, and provide a simple geometric picture from brane construction.

QCD topological susceptibility from the nonlocal chiral quark model

NASA Astrophysics Data System (ADS)

Nam, Seung-Il; Kao, Chung-Wen

2017-06-01

We investigate the quantum chromodynamics (QCD) topological susceptibility χ by using the semi-bosonized nonlocal chiral-quark model (SB-NLχQM) for the leading large- N c contributions. This model is based on the liquid-instanton QCD-vacuum configuration, in which SU(3) flavor symmetry is explicitly broken by the finite current-quark mass ( m u,d, m s) ≈ (5, 135) MeV. To compute χ, we derive the local topological charge-density operator Q t( x) from the effective action of SB-NLχQM. We verify that the derived expression for χ in our model satisfies the Witten- Veneziano (WV) and the Leutwyler-Smilga (LS) formulae, and the Crewther theorem in the chiral limit by construction. Once the average instanton size and the inter-instanton distance are fixed with ρ¯ = 1/3 fm and R¯ = 1 fm, respectively, all the other parameters are determined self-consistently within the model. We obtain χ = (167.67MeV)4, which is comparable with the empirical value χ = (175±5MeV)4 whereas it turns out that χ QL = (194.30MeV)4 in the quenched limit. Thus, we conclude that the value of χ will be reduced around 10 20% by the dynamical-quark contribution.

Origin of the U(1) field mass in superconductors

NASA Astrophysics Data System (ADS)

Koizumi, Hiroyasu

2017-05-01

Recently, a new theory for superconductivity has been put forward, in which the persistent current generation is attributed to the emergent singularities of the electronic wave function that are created by the spin-twisting itinerant circular motion of electrons. The persistent current generated by this mechanism behaves in every respect like supercurrent in superconductors, yielding the flux quantum h/2e and the Josephson frequency 2eV/h, where h is Planck’s constant, -e is the electron charge, and V is the voltage across the Josephson junction. The mass generation of the U(1) gauge field (or the Meissner effect) in the new theory is due to the emergence of topological objects, ‘instantons’ generated by the single-valued requirement of the wave function in the presence of the emergent singularities. The current standard theory of superconductivity is based on the BCS theory, and explains the emergence of superconductivity as due to the global U(1) gauge symmetry breaking realized by the Cooper pair formation. The U(1) field mass generation is believed to be due to this global U(1) gauge symmetry breaking. However, the feasibility of this mechanism has been questioned since no known interaction can prepare the global U(1) symmetry broken state from the normal state. We argue here that the U(1) mass generation in the BCS superconductor can be attributed to the one by the instanton mentioned above if the Rashba spin-orbit interaction is added. Then, the occurrence of persistent current generation becomes due to the instanton formation, and the role of the Cooper pair formation is to stabilize the instanton by providing an energy gap for perturbative excitations. Upon forming the Cooper pair, the instanton is stabilized and persistent current generation becomes possible. Thus, the superconducting transition temperature coincides with the Cooper pair formation temperature.

Heterotic supergravity with internal almost-Kähler spaces; instantons for SO(32), or E 8 × E 8, gauge groups; and deformed black holes with soliton, quasiperiodic and/or pattern-forming structures

NASA Astrophysics Data System (ADS)

Bubuianu, Laurenţiu; Irwin, Klee; Vacaru, Sergiu I.

2017-04-01

Heterotic supergravity with (1  +  3)-dimensional domain wall configurations and (warped) internal, six dimensional, almost-Kähler manifolds {{}6}\\text{X} are studied. Considering ten dimensional spacetimes with nonholonomic distributions and conventional double fibrations, 2  +  2  +  ...  =  2  +  2  +  3  +  3, and associated SU(3) structures on internal space, we generalize for real, internal, almost symplectic gravitational structures the constructions with gravitational and gauge instantons of tanh-kink type [1, 2]. They include the first {α\\prime} corrections to the heterotic supergravity action, parameterized in a form to imply nonholonomic deformations of the Yang-Mills sector and corresponding Bianchi identities. We show how it is possible to construct a variety of solutions depending on the type of nonholonomic distributions and deformations of ‘prime’ instanton configurations characterized by two real supercharges. This corresponds to N=1/2 supersymmetric, nonholonomic manifolds from the four dimensional point of view. Our method provides a unified description of embedding nonholonomically deformed tanh-kink-type instantons into half-BPS solutions of heterotic supergravity. This allows us to elaborate new geometric methods of constructing exact solutions of motion equations, with first order {α\\prime} corrections to the heterotic supergravity. Such a formalism is applied for general and/or warped almost-Kähler configurations, which allows us to generate nontrivial (1  +  3)-d domain walls and black hole deformations determined by quasiperiodic internal space structures. This formalism is utilized in our associated publication [3] in order to construct and study generic off-diagonal nonholonomic deformations of the Kerr metric, encoding contributions from heterotic supergravity.

COLOR SUPERCONDUCTIVITY, INSTANTONS AND PARITY (NON?)-CONSERVATION AT HIGH BARYON DENSITY-VOLUME 5.

DOE Office of Scientific and Technical Information (OSTI.GOV)

GYULASSY,M.

1997-11-11

This one day Riken BNL Research Center workshop was organized to follow-up on the rapidly developing theoretical work on color super-conductivity, instanton dynamics, and possible signatures of parity violation in strong interactions that was stimulated by the talk of Frank Wilczek during the Riken BNL September Symposium. The workshop was held on November 11, 1997 at the center with over 30 participants. The program consisted of four talks on theory in the morning followed by two talks in the afternoon by experimentalists and open discussion. Krishna Rajagopal (MIT) first reviewed the status of the chiral condensate calculations at high baryonmore » density within the instanton model and the percolation transition at moderate densities restoring chiral symmetry. Mark Alford (Princeton) then discussed the nature of the novel color super-conducting diquark condensates. The main result was that the largest gap on the order of 100 MeV was found for the 0{sup +} condensate, with only a tiny gap << MeV for the other possible 1{sup +}. Thomas Schaefer (INT) gave a complete overview of the instanton effects on correlators and showed independent calculations in collaboration with Shuryak (SUNY) and Velkovsky (BNL) confirming the updated results of the Wilczek group (Princeton, MIT). Yang Pang (Columbia) addressed the general question of how breaking of discrete symmetries by any condensate with suitable quantum numbers could be searched for experimentally especially at the AGS through longitudinal A polarization measurements. Nicholas Samios (BNL) reviewed the history of measurements on {Lambda} polarization and suggested specific kinematical variables for such analysis. Brian Cole (Columbia) showed recent E910 measurements of {Lambda} production at the AGS in nuclear collisions and focused on the systematic biases that must be considered when looking for small symmetry breaking effects. Lively discussions led by Robert Jaffe (MIT) focused especially on speculations on the still unknown signatures of 0{sup +} color super-conductivity which of course would not be observable via discrete symmetry breaking.« less

Chaos in a 4D dissipative nonlinear fermionic model

NASA Astrophysics Data System (ADS)

Aydogmus, Fatma

2015-12-01

Gursey Model is the only possible 4D conformally invariant pure fermionic model with a nonlinear self-coupled spinor term. It has been assumed to be similar to the Heisenberg's nonlinear generalization of Dirac's equation, as a possible basis for a unitary description of elementary particles. Gursey Model admits particle-like solutions for the derived classical field equations and these solutions are instantonic in character. In this paper, the dynamical nature of damped and forced Gursey Nonlinear Differential Equations System (GNDES) are studied in order to get more information on spinor type instantons. Bifurcation and chaos in the system are observed by constructing the bifurcation diagrams and Poincaré sections. Lyapunov exponent and power spectrum graphs of GNDES are also constructed to characterize the chaotic behavior.

Special Issue on "Instanton Counting: Moduli Spaces, Representation Theory, and Integrable Systems"

NASA Astrophysics Data System (ADS)

Bruzzo, Ugo; Sala, Francesco

2016-11-01

This special issue of the Journal of Geometry and Physics collects some papers that were presented during the workshop ;Instanton Counting: Moduli Spaces, Representation Theory, and Integrable Systems; that took place at the Lorentz Center in Leiden, The Netherlands, from 16 to 20 June 2014. The workshop was supported by the Lorentz Center, the ;Geometry and Quantum Theory; Cluster, Centre Européen pour les Mathématiques, la Physique et leurs Interactions (Lille, France), Laboratoire Angevin de Recherche en Mathématiques (Angers, France), SISSA (Trieste, Italy), and Foundation Compositio (Amsterdam, the Netherlands). We deeply thank all these institutions for making the workshop possible. We also thank the other organizers of the workshop, Professors Dimitri Markushevich, Vladimir Rubtsov and Sergey Shadrin, for their efforts and great collaboration.

R-charge conservation and more in factorizable and non-factorizable orbifolds

NASA Astrophysics Data System (ADS)

Bizet, Nana G. Cabo; Kobayashi, Tatsuo; Peña, Damián K. Mayorga; Parameswaran, Susha L.; Schmitz, Matthias; Zavala, Ivonne

2013-05-01

We consider the string theory origin of R-charge conservation laws in heterotic orbifold compactifications, deriving the corresponding string coupling selection rule for factorizable and non-factorizable orbifolds, with prime ordered and non-prime ordered point groups. R-charge conservation arises due to symmetries among the worldsheet instantons that can mediate the couplings. Among our results is a previously missed non-trivial contribution to the conserved R-charges from the γ-phases in non-prime orbifolds, which weakens the R-charge selection rule. Symmetries among the worldsheet instantons can also lead to additional selection rules for some couplings. We make a similar analysis for Rule 4 or the "torus lattice selection rule". Moreover, we identify a new string selection rule, that we call Rule 6 or the "coset vector selection rule".

Spheres, charges, instantons, and bootstrap: A five-dimensional odyssey

NASA Astrophysics Data System (ADS)

Chang, Chi-Ming; Fluder, Martin; Lin, Ying-Hsuan; Wang, Yifan

2018-03-01

We combine supersymmetric localization and the conformal bootstrap to study five-dimensional superconformal field theories. To begin, we classify the admissible counter-terms and derive a general relation between the five-sphere partition function and the conformal and flavor central charges. Along the way, we discover a new superconformal anomaly in five dimensions. We then propose a precise triple factorization formula for the five-sphere partition function, that incorporates instantons and is consistent with flavor symmetry enhancement. We numerically evaluate the central charges for the rank-one Seiberg and Morrison-Seiberg theories, and find strong evidence for their saturation of bootstrap bounds, thereby determining the spectra of long multiplets in these theories. Lastly, our results provide new evidence for the F-theorem and possibly a C-theorem in five-dimensional superconformal theories.

Solving the flatness problem with an anisotropic instanton in Hořava-Lifshitz gravity

NASA Astrophysics Data System (ADS)

Bramberger, Sebastian F.; Coates, Andrew; Magueijo, João; Mukohyama, Shinji; Namba, Ryo; Watanabe, Yota

2018-02-01

In Hořava-Lifshitz gravity a scaling isotropic in space but anisotropic in spacetime, often called "anisotropic scaling," with the dynamical critical exponent z =3 , lies at the base of its renormalizability. This scaling also leads to a novel mechanism of generating scale-invariant cosmological perturbations, solving the horizon problem without inflation. In this paper we propose a possible solution to the flatness problem, in which we assume that the initial condition of the Universe is set by a small instanton respecting the same scaling. We argue that the mechanism may be more general than the concrete model presented here. We rely simply on the deformed dispersion relations of the theory, and on equipartition of the various forms of energy at the starting point.

Five-dimensional gauge theory and compactification on a torus

NASA Astrophysics Data System (ADS)

Haghighat, Babak; Vandoren, Stefan

2011-09-01

We study five-dimensional minimally supersymmetric gauge theory compactified on a torus down to three dimensions, and its embedding into string/M-theory using geometric engineering. The moduli space on the Coulomb branch is hyperkähler equipped with a metric with modular transformation properties. We determine the one-loop corrections to the metric and show that they can be interpreted as worldsheet and D1-brane instantons in type IIB string theory. Furthermore, we analyze instanton corrections coming from the solitonic BPS magnetic string wrapped over the torus. In particular, we show how to compute the path-integral for the zero-modes from the partition function of the M5 brane, or, using a 2d/4d correspondence, from the partition function of N=4 SYM theory on a Hirzebruch surface.

BOOK REVIEW: Solitons, Instantons, and Twistors Solitons, Instantons, and Twistors

NASA Astrophysics Data System (ADS)

Witt, Donald M.

2011-04-01

Solitons and instantons play important roles both in pure and applied mathematics as well as in theoretical physics where they are related to the topological structure of the vacuum. Twistors are a useful tool for solving nonlinear differential equations and are useful for the study of the antiself-dual Yang-Mills equations and the Einstein equations. Many books and more advanced monographs have been written on these topics. However, this new book by Maciej Dunajski is a complete first introduction to all of the topics in the title. Moreover, it covers them in a very unique way, through integrable systems. The approach taken in this book is that of mathematical physics à la field theory. The book starts by giving an introduction to integrable systems of ordinary and partial differential equations and proceeds from there. Gauge theories are not covered until chapter 6 which means the reader learning the material for the first time can build up confidence with simpler models of solitons and instantons before encountering them in gauge theories. The book also has an extremely clear introduction to twistor theory useful to both mathematicians and physicists. In particular, the twistor theory presentation may be of interest to string theorists wanting understand twistors. There are many useful connections to research into general relativity. Chapter 9 on gravitational instantons is great treatment useful to anyone doing research in classical or quantum gravity. There is also a nice discussion of Kaluza-Klein monopoles. The three appendices A-C cover the necessary background material of basic differential geometry, complex manifolds, and partial differential equations needed to fully understand the subject. The reader who has some level of expertise in any of the topics covered can jump right into that material without necessarily reading all of the earlier chapters because of the extremely clear writing style of the author. This makes the book an excellent reference on instantons, solitons and twistors. However, I found it useful to read the whole book because the author has a beautiful perspective on and presentation of the material. Maciej Dunajski developed the book out of notes from a series of lecture courses he taught on these subjects over a five year period at Cambridge University. This fact makes the book an excellent choice for a textbook on the subject with each of the 10 chapters containing nice problems and exercises. Additionally, the wealth of information contained in the book makes it a great reference book for any theoretical physicist or mathematician to own. As an introduction to an exciting area of research, this book is excellent because it is not only accessible but self contained. A wonderful feature of the book is the clear and informative explanation of the topics and the wealth of examples. The presentation style of the book means that it is accessible to readers ranging from advanced undergraduates doing research to experts. It would be an excellent textbook for a course at the advanced undergraduate level or graduate level in either mathematics or physics. This book will become a standard on the subject. The typesetting of the book is very clean, with nicely sized fonts and clean uniform notation. It includes 35 illustrations which helpfully illustrated text. It is my pleasure to highly recommend it to anyone from an advanced undergraduate to a researcher in the fields covered.

RG flows and instantons

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gava, Edi

2012-09-24

In these two lectures I discuss RG flow solutions in (1,0) six dimensional supergravity involving SU(2) Yang-Mills instantons. in the conformally flat part of the 6D metric. The solutions interpolate between two (4,0) supersymmetric AdS{sub 3} Multiplication-Sign S{sup 3} backgrounds with different values of AdS{sub 3} and S{sup 3} radii and describe RG flows in the dual 2D SCFT. The flows described are of v.e.v. type, driven by a vacuum expectation value of a (not exactly) marginal operator of dimension 2 in the UV. We give an interpretation of the supergravity solution in terms of the D1/D5 system in typemore » I string theory on K3, whose effective field theory is expected to flow to a (4,0) SCFT in the infrared.« less

Mayer-cluster expansion of instanton partition functions and thermodynamic bethe ansatz

NASA Astrophysics Data System (ADS)

Meneghelli, Carlo; Yang, Gang

2014-05-01

In [19] Nekrasov and Shatashvili pointed out that the = 2 instanton partition function in a special limit of the Ω-deformation parameters is characterized by certain thermodynamic Bethe ansatz (TBA) like equations. In this work we present an explicit derivation of this fact as well as generalizations to quiver gauge theories. To do so we combine various techniques like the iterated Mayer expansion, the method of expansion by regions, and the path integral tricks for non-perturbative summation. The TBA equations derived entirely within gauge theory have been proposed to encode the spectrum of a large class of quantum integrable systems. We hope that the derivation presented in this paper elucidates further this completely new point of view on the origin, as well as on the structure, of TBA equations in integrable models.

6d, Coulomb branch anomaly matching

NASA Astrophysics Data System (ADS)

Intriligator, Kenneth

2014-10-01

6d QFTs are constrained by the analog of 't Hooft anomaly matching: all anomalies for global symmetries and metric backgrounds are constants of RG flows, and for all vacua in moduli spaces. We discuss an anomaly matching mechanism for 6d theories on their Coulomb branch. It is a global symmetry analog of Green-Schwarz-West-Sagnotti anomaly cancellation, and requires the apparent anomaly mismatch to be a perfect square, . Then Δ I 8 is cancelled by making X 4 an electric/magnetic source for the tensor multiplet, so background gauge field instantons yield charged strings. This requires the coefficients in X 4 to be integrally quantized. We illustrate this for theories. We also consider the SCFTs from N small E8 instantons, verifying that the recent result for its anomaly polynomial fits with the anomaly matching mechanism.

Infinitesimal moduli of G2 holonomy manifolds with instanton bundles

NASA Astrophysics Data System (ADS)

de la Ossa, Xenia; Larfors, Magdalena; Svanes, Eirik E.

2016-11-01

We describe the infinitesimal moduli space of pairs ( Y, V) where Y is a manifold with G 2 holonomy, and V is a vector bundle on Y with an instanton connection. These structures arise in connection to the moduli space of heterotic string compactifications on compact and non-compact seven dimensional spaces, e.g. domain walls. Employing the canonical G 2 cohomology developed by Reyes-Carrión and Fernández and Ugarte, we show that the moduli space decomposes into the sum of the bundle moduli {H}_{{overset{ěe }{d}}_A}^1(Y,End(V)) plus the moduli of the G 2 structure preserving the instanton condition. The latter piece is contained in {H}_{overset{ěe }{d}θ}^1(Y,TY) , and is given by the kernel of a map overset{ěe }{F} which generalises the concept of the Atiyah map for holomorphic bundles on complex manifolds to the case at hand. In fact, the map overset{ěe }{F} is given in terms of the curvature of the bundle and maps {H}_{overset{ěe }{d}θ}^1(Y,TY) into {H}_{{overset{ěe }{d}}_A}^2(Y,End(V)) , and moreover can be used to define a cohomology on an extension bundle of TY by End( V). We comment further on the resemblance with the holomorphic Atiyah algebroid and connect the story to physics, in particular to heterotic compactifications on ( Y, V) when α' = 0.

Fuzzy Euclidean wormholes in de Sitter space

NASA Astrophysics Data System (ADS)

Chen, Pisin; Hu, Yao-Chieh; Yeom, Dong-han

2017-07-01

We investigate Euclidean wormholes in Einstein gravity with a massless scalar field in de Sitter space. Euclidean wormholes are possible due to the analytic continuation of the time as well as complexification of fields, where we need to impose the classicality after the Wick-rotation to the Lorentzian signatures. For some parameters, wormholes are preferred than Hawking-Moss instantons, and hence wormholes can be more fundamental than Hawking-Moss type instantons. Euclidean wormholes can be interpreted in three ways: (1) classical big bounce, (2) either tunneling from a small to a large universe or a creation of a collapsing and an expanding universe from nothing, and (3) either a transition from a contracting to a bouncing phase or a creation of two expanding universes from nothing. These various interpretations shed some light on challenges of singularities. In addition, these will help to understand tensions between various kinds of quantum gravity theories.

Rigid Calabi-Yau threefolds, Picard Eisenstein series and instantons

NASA Astrophysics Data System (ADS)

Bao, L.; Kleinschmidt, A.; Nilsson, B. E. W.; Persson, D.; Pioline, B.

2013-12-01

Type IIA string theory compactified on a rigid Calabi-Yau threefold gives rise to a classical moduli space that carries an isometric action of U(2, 1). Various quantum corrections break this continuous isometry to a discrete subgroup. Focussing on the case where the intermediate Jacobian of the Calabi-Yau admits complex multiplication by the ring of quadratic imaginary integers d, we argue that the remaining quantum duality group is an arithmetic Picard modular group PU(2, 1; d). Based on this proposal we construct an Eisenstein series invariant under this duality group and study its non-Abelian Fourier expansion. This allows the prediction of non-perturbative effects, notably the contribution of D2- and NS5-brane instantons. The present work extends our previous analysis in 0909.4299 which was restricted to the special case of the Gaussian integers 1 = Bbb Z[i].

One-loop Pfaffians and large-field inflation in string theory

NASA Astrophysics Data System (ADS)

Ruehle, Fabian; Wieck, Clemens

2017-06-01

We study the consistency of large-field inflation in low-energy effective field theories of string theory. In particular, we focus on the stability of Kähler moduli in the particularly interesting case where the non-perturbative superpotential of the Kähler sector explicitly depends on the inflaton field. This situation arises generically due to one-loop corrections to the instanton action. The field dependence of the modulus potential feeds back into the inflationary dynamics, potentially impairing slow roll. We distinguish between world-sheet instantons from Euclidean D-branes, which typically yield polynomial one-loop Pfaffians, and gaugino condensates, which can yield exponential or periodic corrections. In all scenarios successful slow-roll inflation imposes bounds on the magnitude of the one-loop correction, corresponding to constraints on possible compactifications. While we put a certain emphasis on Type IIB constructions with mobile D7-branes, our results seem to apply more generally.

Fuzzy Euclidean wormholes in de Sitter space

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Pisin; Hu, Yao-Chieh; Yeom, Dong-han, E-mail: pisinchen@phys.ntu.edu.tw, E-mail: r04244003@ntu.edu.tw, E-mail: innocent.yeom@gmail.com

We investigate Euclidean wormholes in Einstein gravity with a massless scalar field in de Sitter space. Euclidean wormholes are possible due to the analytic continuation of the time as well as complexification of fields, where we need to impose the classicality after the Wick-rotation to the Lorentzian signatures. For some parameters, wormholes are preferred than Hawking-Moss instantons, and hence wormholes can be more fundamental than Hawking-Moss type instantons. Euclidean wormholes can be interpreted in three ways: (1) classical big bounce, (2) either tunneling from a small to a large universe or a creation of a collapsing and an expanding universemore » from nothing, and (3) either a transition from a contracting to a bouncing phase or a creation of two expanding universes from nothing. These various interpretations shed some light on challenges of singularities. In addition, these will help to understand tensions between various kinds of quantum gravity theories.« less

Coleman-de Luccia instanton in dRGT massive gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Ying-li; Saito, Ryo; Yeom, Dong-han

2014-02-01

We study the Coleman-de Luccia (CDL) instanton characterizing the tunneling from a false vacuum to the true vacuum in a semi-classical way in dRGT (deRham-Gabadadze-Tolley) massive gravity theory, and evaluate the dependence of the tunneling rate on the model parameters. It is found that provided with the same physical Hubble parameters for the true vacuum H{sub T} and the false vacuum H{sub F} as in General Relativity (GR), the thin-wall approximation method implies the same tunneling rate as GR. However, deviations of tunneling rate from GR arise when one goes beyond the thin-wall approximation and they change monotonically until themore » Hawking-Moss (HM) case. Moreover, under the thin-wall approximation, the HM process may dominate over the CDL one if the value for the graviton mass is larger than the inverse of the radius of the bubble.« less

Fuzzy Euclidean wormholes in de Sitter space

DOE PAGES

Chen, Pisin; Hu, Yao-Chieh; Yeom, Dong-han

2017-07-03

Here, we investigate Euclidean wormholes in Einstein gravity with a massless scalar field in de Sitter space. Euclidean wormholes are possible due to the analytic continuation of the time as well as complexification of fields, where we need to impose the classicality after the Wick-rotation to the Lorentzian signatures. Furthermore, we prefer wormholes for some parameters, rather than Hawking-Moss instantons, and hence wormholes can be more fundamental than Hawking-Moss type instantons. Euclidean wormholes can be interpreted in three ways: (1) classical big bounce, (2) either tunneling from a small to a large universe or a creation of a collapsing andmore » an expanding universe from nothing, and (3) either a transition from a contracting to a bouncing phase or a creation of two expanding universes from nothing. These various interpretations shed some light on challenges of singularities. In addition, these will help to understand tensions between various kinds of quantum gravity theories.« less

Spherical Hecke algebra in the Nekrasov-Shatashvili limit

NASA Astrophysics Data System (ADS)

Bourgine, Jean-Emile

2015-01-01

The Spherical Hecke central (SHc) algebra has been shown to act on the Nekrasov instanton partition functions of gauge theories. Its presence accounts for both integrability and AGT correspondence. On the other hand, a specific limit of the Omega background, introduced by Nekrasov and Shatashvili (NS), leads to the appearance of TBA and Bethe like equations. To unify these two points of view, we study the NS limit of the SHc algebra. We provide an expression of the instanton partition function in terms of Bethe roots, and define a set of operators that generates infinitesimal variations of the roots. These operators obey the commutation relations defining the SHc algebra at first order in the equivariant parameter ɛ 2. Furthermore, their action on the bifundamental contributions reproduces the Kanno-Matsuo-Zhang transformation. We also discuss the connections with the Mayer cluster expansion approach that leads to TBA-like equations.

Instanton operators and symmetry enhancement in 5d supersymmetric quiver gauge theories

NASA Astrophysics Data System (ADS)

Yonekura, Kazuya

2015-07-01

We consider general 5d SU( N ) quiver gauge theories whose nodes form an ADE Dynkin diagram of type G. Each node has SU( N i ) gauge group of general rank, Chern-Simons level κ i and additional w i fundamentals. When the total flavor number at each node is less than or equal to 2 N i - 2| κ i |, we give general rules under which the symmetries associated to instanton currents are enhanced to G × G or a subgroup of it in the UV 5d superconformal theory. When the total flavor number violates that condition at some of the nodes, further enhancement of flavor symmetries occurs. In particular we find a large class of gauge theories interpreted as S 1 compactification of 6d superconformal theories which are waiting for string/F-theory realization. We also consider hypermultiplets in (anti-)symmetric representation.

Fuzzy Euclidean wormholes in de Sitter space

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Pisin; Hu, Yao-Chieh; Yeom, Dong-han

Here, we investigate Euclidean wormholes in Einstein gravity with a massless scalar field in de Sitter space. Euclidean wormholes are possible due to the analytic continuation of the time as well as complexification of fields, where we need to impose the classicality after the Wick-rotation to the Lorentzian signatures. Furthermore, we prefer wormholes for some parameters, rather than Hawking-Moss instantons, and hence wormholes can be more fundamental than Hawking-Moss type instantons. Euclidean wormholes can be interpreted in three ways: (1) classical big bounce, (2) either tunneling from a small to a large universe or a creation of a collapsing andmore » an expanding universe from nothing, and (3) either a transition from a contracting to a bouncing phase or a creation of two expanding universes from nothing. These various interpretations shed some light on challenges of singularities. In addition, these will help to understand tensions between various kinds of quantum gravity theories.« less

Quantum instanton calculation of rate constant for CH4 + OH → CH3 + H2O reaction: Torsional anharmonicity and kinetic isotope effect

NASA Astrophysics Data System (ADS)

Wang, Wenji; Zhao, Yi

2012-12-01

Thermal rate constants for the title reaction are calculated by using the quantum instanton approximation within the full dimensional Cartesian coordinates. The results reveal that the quantum effect is remarkable for the reaction at both low and high temperatures, and the obtained rates are in good agreement with experimental measurements at high temperatures. Compared to the harmonic approximation, the torsional anharmonic effect of the internal rotation has a little influence on the rates at low temperatures, however, it enhances the rate by about 20% at 1000 K. In addition, the free energy barriers for the isotopic reactions and the temperature dependence of kinetic isotope effects are also investigated. Generally speaking, for the title reaction, the replacement of OH with OD will reduce the free energy barrier, while substituting D for H (connected to C) will increase the free energy barrier.

Testing B-violating signatures from exotic instantons in future colliders

NASA Astrophysics Data System (ADS)

Addazi, Andrea; Kang, Xian-Wei; Khlopov, Maxim Yu.

2017-09-01

We discuss possible implications of exotic stringy instantons for baryon-violating signatures in future colliders. In particular, we discuss high-energy quark collisions and transitions. In principle, the process can be probed by high-luminosity electron-positron colliders. However, we find that an extremely high luminosity is needed in order to provide a (somewhat) stringent bound compared to the current data on NN → ππ,KK. On the other hand, (exotic) instanton-induced six-quark interactions can be tested in near future high-energy colliders beyond LHC, at energies around 20-100 TeV. The Super proton-proton Collider (SppC) would be capable of such measurement given the proposed energy level of 50-90 TeV. Comparison with other channels is made. In particular, we show the compatibility of our model with neutron-antineutron and NN → ππ,KK bounds. A. A.’s work was Supported in part by the MIUR research grant “Theoretical Astroparticle Physics" PRIN 2012CPPYP7. XWK's work is partly Supported by the DFG and the NSFC through funds provided to the Sino-German CRC 110 “Symmetries and the Emergence of Structure in QCD” when he was in Jülich, and by MOST, Taiwan, (104-2112-M-001-022) from April 2017. The work by MK was performed within the framework of the Center FRPP Supported by MEPhI Academic Excellence Project (contract 02.03.21.0005, 27.08.2013), Supported by the Ministry of Education and Science of Russian Federation, project 3.472.2014/K and grant RFBR 14-22-03048

Ultralight axion in supersymmetry and strings and cosmology at small scales

NASA Astrophysics Data System (ADS)

Halverson, James; Long, Cody; Nath, Pran

2017-09-01

Dynamical mechanisms to generate an ultralight axion of mass ˜10-21- 10-22 eV in supergravity and strings are discussed. An ultralight particle of this mass provides a candidate for dark matter that may play a role for cosmology at scales of 10 kpc or less. An effective operator approach for the axion mass provides a general framework for models of ultralight axions, and in one case recovers the scale 10-21- 10-22 eV as the electroweak scale times the square of the hierarchy with an O (1 ) Wilson coefficient. We discuss several classes of models realizing this framework where an ultralight axion of the necessary size can be generated. In one class of supersymmetric models an ultralight axion is generated by instanton-like effects. In the second class higher-dimensional operators involving couplings of Higgs, standard model singlets, and axion fields naturally lead to an ultralight axion. Further, for the class of models considered the hierarchy between the ultralight scale and the weak scale is maintained. We also discuss the generation of an ultralight scale within string-based models. In the single-modulus Kachru-Kallosh-Linde-Trivedi moduli stabilization scheme an ultralight axion would require an ultralow weak scale. However, within the large volume scenario, the desired hierarchy between the axion scale and the weak scale is achieved. A general analysis of couplings of Higgs fields to instantons within the string framework is discussed and it is shown that the condition necessary for achieving such couplings is the existence of vector-like zero modes of the instanton. Some of the phenomenological aspects of these models are also discussed.

Black holes as bubble nucleation sites

NASA Astrophysics Data System (ADS)

Gregory, Ruth; Moss, Ian G.; Withers, Benjamin

2014-03-01

We consider the effect of inhomogeneities on the rate of false vacuum decay. Modelling the inhomogeneity by a black hole, we construct explicit Euclidean instantons which describe the nucleation of a bubble of true vacuum centred on the inhomogeneity. We find that inhomogeneity significantly enhances the nucleation rate over that of the Coleman-de Luccia instanton — the black hole acts as a nucleation site for the bubble. The effect is larger than previously believed due to the contributions to the action from conical singularities. For a sufficiently low initial mass, the original black hole is replaced by flat space during this process, as viewed by a single causal patch observer. Increasing the initial mass, we find a critical value above which a black hole remnant survives the process. This resulting black hole can have a higher mass than the original black hole, but always has a lower entropy. We compare the process to bubble-to-bubble transitions, where there is a semi-classical Lorentzian description in the WKB approximation.

The topological susceptibility from grand canonical simulations in the interacting instanton liquid model: Chiral phase transition and axion mass

NASA Astrophysics Data System (ADS)

Wantz, Olivier; Shellard, E. P. S.

2010-04-01

This is the last in a series of papers on the topological susceptibility in the interacting instanton liquid model (IILM). We will derive improved finite temperature interactions to study the thermodynamic limit of grand canonical Monte Carlo simulations in the quenched and unquenched case with light, physical quark masses. In particular, we will be interested in chiral symmetry breaking. The paper culminates by giving, for the first time, a well-motivated temperature-dependent axion mass. Especially, this work finally provides a computation of the axion mass in the low temperature regime, ma2fa2=1.46×10-3Λ41+0.50 T/Λ1+(3.53 . It connects smoothly to the high temperature dilute gas approximation; the latter is improved by including quark threshold effects. To compare with earlier studies, we also provide the usual power-law ma2=αΛ4fa2(T, where Λ=400 MeV, n=6.68 and α=1.68×10-7.

Hawking-Moss instanton in nonlinear massive gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Ying-li; Saito, Ryo; Sasaki, Misao, E-mail: yingli@yukawa.kyoto-u.ac.jp, E-mail: rsaito@yukawa.kyoto-u.ac.jp, E-mail: misao@yukawa.kyoto-u.ac.jp

2013-02-01

As a first step toward understanding a lanscape of vacua in a theory of non-linear massive gravity, we consider a landscape of a single scalar field and study tunneling between a pair of adjacent vacua. We study the Hawking-Moss (HM) instanton that sits at a local maximum of the potential, and evaluate the dependence of the tunneling rate on the parameters of the theory. It is found that provided with the same physical HM Hubble parameter H{sub HM}, depending on the values of parameters α{sub 3} and α{sub 4} in the action (2.2), the corresponding tunneling rate can be eithermore » enhanced or suppressed when compared to the one in the context of General Relativity (GR). Furthermore, we find the constraint on the ratio of the physical Hubble parameter to the fiducial one, which constrains the form of potential. This result is in sharp contrast to GR where there is no bound on the minimum value of the potential.« less

BPS/CFT Correspondence III: Gauge Origami Partition Function and qq-Characters

NASA Astrophysics Data System (ADS)

Nekrasov, Nikita

2018-03-01

We study generalized gauge theories engineered by taking the low energy limit of the Dp branes wrapping {X × {T}^{p-3}}, with X a possibly singular surface in a Calabi-Yau fourfold Z. For toric Z and X the partition function can be computed by localization, making it a statistical mechanical model, called the gauge origami. The random variables are the ensembles of Young diagrams. The building block of the gauge origami is associated with a tetrahedron, whose edges are colored by vector spaces. We show the properly normalized partition function is an entire function of the Coulomb moduli, for generic values of the {Ω} -background parameters. The orbifold version of the theory defines the qq-character operators, with and without the surface defects. The analytic properties are the consequence of a relative compactness of the moduli spaces M({ěc n}, k) of crossed and spiked instantons, demonstrated in "BPS/CFT correspondence II: instantons at crossroads, moduli and compactness theorem".

Topological string, supersymmetric gauge theory and bps counting

NASA Astrophysics Data System (ADS)

Pan, Guang

In this thesis we study the Donaldson-Thomas theory on the local curve geometry, which arises in the context of geometric engineering of supersymmetric gauge theory from type IIA string compactification. The topological A-model amplitude gives the F-term interaction of the compactified theory. In particular, it is related to the instanton partition function via Nekrasov conjecture. We will introduce ADHM sheaves on curve, as an alternative description of local Donaldson-Thomas theory. We derive the wallcrossing of ADHM invariants and their refinements. We show that it is equivalent to the semi-primitive wallcrossing from supergravity, and the Kontsevich-Soibelman wallcrossing formula. As an application, we discuss the connection between ADHM moduli space with Hitchin system. In particular we give a recursive formula for the Poincare polynomial of Hitchin system in terms of instanton partition function, from refined wallcrossing. We also introduce higher rank generalization of Donaldson-Thomas invariant in the context of ADHM sheaves. We study their wallcrossing and discuss their physical interpretation via string duality.

Using a Family of Dividing Surfaces Normal to the Minimum EnergyPath for Quantum Instanton Rate Constants

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Yimin; Miller, Wlliam H.

2006-02-22

One of the outstanding issues in the quantum instanton (QI) theory (or any transition state-type theory) for thermal rate constants of chemical reactions is the choice of an appropriate ''dividing surface'' (DS) that separates reactants and products. (In the general version of the QI theory, there are actually two dividing surfaces involved.) This paper shows one simple and general way for choosing DS's for use in QI Theory, namely using the family of (hyper) planes normal to the minimum energy path (MEP) on the potential energy surface at various distances s along it. Here the reaction coordinate is not onemore » of the dynamical coordinates of the system (which will in general be the Cartesian coordinates of the atoms), but rather simply a parameter which specifies the DS. It is also shown how this idea can be implemented for an N-atom system in 3d space in a way that preserves overall translational and rotational invariance. Numerical application to a simple system (the colliner H + H{sub 2} reaction) is presented to illustrate the procedure.« less

A theory of self-organized zonal flow with fine radial structure in tokamak

NASA Astrophysics Data System (ADS)

Zhang, Y. Z.; Liu, Z. Y.; Xie, T.; Mahajan, S. M.; Liu, J.

2017-12-01

The (low frequency) zonal flow-ion temperature gradient (ITG) wave system, constructed on Braginskii's fluid model in tokamak, is shown to be a reaction-diffusion-advection system; it is derived by making use of a multiple spatiotemporal scale technique and two-dimensional (2D) ballooning theory. For real regular group velocities of ITG waves, two distinct temporal processes, sharing a very similar meso-scale radial structure, are identified in the nonlinear self-organized stage. The stationary and quasi-stationary structures reflect a particular feature of the poloidal group velocity. The equation set posed to be an initial value problem is numerically solved for JET low mode parameters; the results are presented in several figures and two movies that show the spatiotemporal evolutions as well as the spectrum analysis—frequency-wave number spectrum, auto power spectrum, and Lissajous diagram. This approach reveals that the zonal flow in tokamak is a local traveling wave. For the quasi-stationary process, the cycle of ITG wave energy is composed of two consecutive phases in distinct spatiotemporal structures: a pair of Cavitons growing and breathing slowly without long range propagation, followed by a sudden decay into many Instantons that carry negative wave energy rapidly into infinity. A spotlight onto the motion of Instantons for a given radial position reproduces a Blob-Hole temporal structure; the occurrence as well as the rapid decay of Caviton into Instantons is triggered by zero-crossing of radial group velocity. A sample of the radial profile of zonal flow contributed from 31 nonlinearly coupled rational surfaces near plasma edge is found to be very similar to that observed in the JET Ohmic phase [J. C. Hillesheim et al., Phys. Rev. Lett. 116, 165002 (2016)]. The theory predicts an interior asymmetric dipole structure associated with the zonal flow that is driven by the gradients of ITG turbulence intensity.

M-theoretic derivations of 4d-2d dualities: from a geometric Langlands duality for surfaces, to the AGT correspondence, to integrable systems

NASA Astrophysics Data System (ADS)

Tan, Meng-Chwan

2013-07-01

In part I, we extend our analysis in [arXiv:0807.1107], and show that a mathematically conjectured geometric Langlands duality for complex surfaces in [1], and its generalizations — which relate some cohomology of the moduli space of certain ("ramified") G-instantons to the integrable representations of the Langlands dual of certain affine (sub) G-algebras, where G is any compact Lie group — can be derived, purely physically, from the principle that the spacetime BPS spectra of string-dual M-theory compactifications ought to be equivalent. In part II, to the setup in part I, we introduce Omega-deformation via fluxbranes and add half-BPS boundary defects via M9-branes, and show that the celebrated AGT correspondence in [2, 3], and its generalizations — which essentially relate, among other things, some equivariant cohomology of the moduli space of certain ("ramified") G-instantons to the integrable representations of the Langlands dual of certain affine -algebras — can likewise be derived from the principle that the spacetime BPS spectra of string-dual M-theory compactifications ought to be equivalent. In part III, we consider various limits of our setup in part II, and connect our story to chiral fermions and integrable systems. Among other things, we derive the NekrasovOkounkov conjecture in [4] — which relates the topological string limit of the dual Nekrasov partition function for pure G to the integrable representations of the Langlands dual of an affine G-algebra — and also demonstrate that the Nekrasov-Shatashvili limit of the "fullyramified" Nekrasov instanton partition function for pure G is a simultaneous eigenfunction of the quantum Toda Hamiltonians associated with the Langlands dual of an affine G-algebra. Via the case with matter, we also make contact with Hitchin systems and the "ramified" geometric Langlands correspondence for curves.

QCD axion star collapse with the chiral potential

DOE PAGES

Eby, Joshua; Leembruggen, Madelyn; Suranyi, Peter; ...

2017-06-05

In a previous study, we analyzed collapsing axion stars using the low-energy instanton potential, showing that the total energy is always bounded and that collapsing axion stars do not form black holes. In this paper, we provide a proof that the conclusions are unchanged when using instead the more general chiral potential for QCD axions.

Bukhvostov-Lipatov model and quantum-classical duality

NASA Astrophysics Data System (ADS)

Bazhanov, Vladimir V.; Lukyanov, Sergei L.; Runov, Boris A.

2018-02-01

The Bukhvostov-Lipatov model is an exactly soluble model of two interacting Dirac fermions in 1 + 1 dimensions. The model describes weakly interacting instantons and anti-instantons in the O (3) non-linear sigma model. In our previous work [arxiv:arXiv:1607.04839] we have proposed an exact formula for the vacuum energy of the Bukhvostov-Lipatov model in terms of special solutions of the classical sinh-Gordon equation, which can be viewed as an example of a remarkable duality between integrable quantum field theories and integrable classical field theories in two dimensions. Here we present a complete derivation of this duality based on the classical inverse scattering transform method, traditional Bethe ansatz techniques and analytic theory of ordinary differential equations. In particular, we show that the Bethe ansatz equations defining the vacuum state of the quantum theory also define connection coefficients of an auxiliary linear problem for the classical sinh-Gordon equation. Moreover, we also present details of the derivation of the non-linear integral equations determining the vacuum energy and other spectral characteristics of the model in the case when the vacuum state is filled by 2-string solutions of the Bethe ansatz equations.

Multi-instantons and exact results III: Unification of even and odd anharmonic oscillators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jentschura, Ulrich D.; Surzhykov, Andrey; GSI Helmholtzzentrum fuer Schwerionenforschung, 64291 Darmstadt

2010-05-15

This is the third article in a series of three papers on the resonance energy levels of anharmonic oscillators. Whereas the first two papers mainly dealt with double-well potentials and modifications thereof [see J. Zinn-Justin, U.D. Jentschura, Ann. Phys. (N.Y.) 313 (2004) 197 and 269], we here focus on simple even and odd anharmonic oscillators for arbitrary magnitude and complex phase of the coupling parameter. A unification is achieved by the use of PT-symmetry inspired dispersion relations and generalized quantization conditions that include instanton configurations. Higher-order formulas are provided for the oscillators of degrees 3 to 8, which lead tomore » subleading corrections to the leading factorial growth of the perturbative coefficients describing the resonance energies. Numerical results are provided, and higher-order terms are found to be numerically significant. The resonances are described by generalized expansions involving intertwined nonanalytic exponentials, logarithmic terms and power series. Finally, we summarize spectral properties and dispersion relations of anharmonic oscillators, and their interconnections. The purpose is to look at one of the classic problems of quantum theory from a new perspective, through which we gain systematic access to the phenomenologically significant higher-order terms.« less

Super-light baryo-photons, weak gravity conjecture and exotic instantons in neutron-antineutron transitions

NASA Astrophysics Data System (ADS)

Addazi, Andrea

2018-05-01

In companion papers (A. Addazi, Nuovo Cim. C, 38(1): 21 (2015); A. Addazi, Z. Berezhiani, and Y. Kamyshkov, arXiv:1607.00348), we have discussed current bounds on a new super-light baryo-photon, associated with a U(1) B-L gauge, from current neutron-antineutron data, which are competitive with Eötvös-type experiments. Here, we discuss the implications of possible baryo-photon detection in string theory and quantum gravity. The discovery of a very light gauge boson should imply violation of the weak gravity conjecture, carrying deep consequences for our understanding of holography, quantum gravity and black holes. We also show how the detection of a baryo-photon would exclude the generation of all B–L violating operators from exotic stringy instantons. We will argue against the common statement in the literature that neutron-antineutron data may indirectly test at least the 300–1000 TeV scale. Searches for baryo-photons can provide indirect information on the Planck (or string) scale (quantum black holes, holography and non-perturbative stringy effects). This strongly motivates new neutron-antineutron experiments with adjustable magnetic fields dedicated to the detection of super-light baryo-photons.

Instantons in string theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ahlén, Olof, E-mail: olof.ahlen@aei.mpg.de

2015-12-17

These proceedings from the second Caesar Lattes meeting in Rio de Janeiro 2015 are a brief introduction to how automorphic forms appear in the low energy effective action of maximally supersymmetric string theory. The explicit example of the R{sup 4}-interaction of type IIB string theory in ten dimensions is discussed. Its Fourier expansion is interpreted in terms of perturbative and non-perturbative contributions to the four graviton amplitude.

European Scientific Notes. Volume 37, Number 1.

DTIC Science & Technology

1983-01-31

instantoneous sea-state condition can be tions vary widely in their realism , with computed from a special data base coded some producing dynamic color pictures...between the variables of accuracy, approach channels, the alignment of practicality, realism , and expense. jetties, and the establishment of Because the...tidal current variables The system certainly seems to be valid, have been played into some of the and the smooth dynamics, realism , and simulator runs

On functional determinants of matrix differential operators with multiple zero modes

NASA Astrophysics Data System (ADS)

Falco, G. M.; Fedorenko, Andrei A.; Gruzberg, Ilya A.

2017-12-01

We generalize the method of computing functional determinants with a single excluded zero eigenvalue developed by McKane and Tarlie to differential operators with multiple zero eigenvalues. We derive general formulas for such functional determinants of r× r matrix second order differential operators O with 0 < n ≤slant 2r linearly independent zero modes. We separately discuss the cases of the homogeneous Dirichlet boundary conditions, when the number of zero modes cannot exceed r, and the case of twisted boundary conditions, including the periodic and anti-periodic ones, when the number of zero modes is bounded above by 2r. In all cases the determinants with excluded zero eigenvalues can be expressed only in terms of the n zero modes and other r-n or 2r-n (depending on the boundary conditions) solutions of the homogeneous equation O h=0 , in the spirit of Gel’fand-Yaglom approach. In instanton calculations, the contribution of the zero modes is taken into account by introducing the so-called collective coordinates. We show that there is a remarkable cancellation of a factor (involving scalar products of zero modes) between the Jacobian of the transformation to the collective coordinates and the functional fluctuation determinant with excluded zero eigenvalues. This cancellation drastically simplifies instanton calculations when one uses our formulas.

Comparison of classical reaction paths and tunneling paths studied with the semiclassical instanton theory.

PubMed

Meisner, Jan; Markmeyer, Max N; Bohner, Matthias U; Kästner, Johannes

2017-08-30

Atom tunneling in the hydrogen atom transfer reaction of the 2,4,6-tri-tert-butylphenyl radical to 3,5-di-tert-butylneophyl, which has a short but strongly curved reaction path, was investigated using instanton theory. We found the tunneling path to deviate qualitatively from the classical intrinsic reaction coordinate, the steepest-descent path in mass-weighted Cartesian coordinates. To perform that comparison, we implemented a new variant of the predictor-corrector algorithm for the calculation of the intrinsic reaction coordinate. We used the reaction force analysis method as a means to decompose the reaction barrier into structural and electronic components. Due to the narrow energy barrier, atom tunneling is important in the abovementioned reaction, even above room temperature. Our calculated rate constants between 350 K and 100 K agree well with experimental values. We found a H/D kinetic isotope effect of almost 10 6 at 100 K. Tunneling dominates the protium transfer below 400 K and the deuterium transfer below 300 K. We compared the lengths of the tunneling path and the classical path for the hydrogen atom transfer in the reaction HCl + Cl and quantified the corner cutting in this reaction. At low temperature, the tunneling path is about 40% shorter than the classical path.

Non-Abelian Berry phase, instantons, and N=(0,4) supersymmetry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Laia, Joao N.

2010-12-15

In supersymmetric quantum mechanics, the non-Abelian Berry phase is known to obey certain differential equations. Here we study N=(0,4) systems and show that the non-Abelian Berry connection over R{sup 4n} satisfies a generalization of the self-dual Yang-Mills equations. Upon dimensional reduction, these become the tt* equations. We further study the Berry connection in N=(4,4) theories and show that the curvature is covariantly constant.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ovchinnikov, Igor V.

Here, a scenario is proposed, according to which a generic self-organized critical (SOC) system can be looked upon as a Witten-type topological field theory (W-TFT) with spontaneously broken Becchi-Rouet-Stora-Tyutin (BRST) symmetry. One of the conditions for the SOC is the slow driving noise, which unambiguously suggests Stratonovich interpretation of the corresponding stochastic differential equation (SDE). This, in turn, necessitates the use of Parisi-Sourlas-Wu stochastic quantization procedure, which straightforwardly leads to a model with BRST-exact action, i.e., to a W-TFT. In the parameter space of the SDE, there must exist full-dimensional regions where the BRST symmetry is spontaneously broken by instantons,more » which in the context of SOC are essentially avalanches. In these regions, the avalanche-type SOC dynamics is liberated from overwise a rightful dynamics-less W-TFT, and a Goldstone mode of Fadeev-Popov ghosts exists. Goldstinos represent moduli of instantons (avalanches) and being gapless are responsible for the critical avalanche distribution in the low-energy, long-wavelength limit. The above arguments are robust against moderate variations of the SDE's parameters and the criticality is 'self-tuned'. The proposition of this paper suggests that the machinery of W-TFTs may find its applications in many different areas of modern science studying various physical realizations of SOC. It also suggests that there may in principle exist a connection between some SOC's and the concept of topological quantum computing.« less

Intersecting solitons, amoeba, and tropical geometry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fujimori, Toshiaki; Nitta, Muneto; Ohta, Kazutoshi

2008-11-15

We study the generic intersection (or web) of vortices with instantons inside, which is a 1/4 Bogomol'nyi-Prasad-Sommerfield state in the Higgs phase of five-dimensional N=1 supersymmetric U(N{sub C}) gauge theory on R{sub t}x(C*){sup 2}{approx_equal}R{sup 2,1}xT{sup 2} with N{sub F}=N{sub C} Higgs scalars in the fundamental representation. In the case of the Abelian-Higgs model (N{sub F}=N{sub C}=1), the intersecting vortex sheets can be beautifully understood in a mathematical framework of amoeba and tropical geometry, and we propose a dictionary relating solitons and gauge theory to amoeba and tropical geometry. A projective shape of vortex sheets is described by the amoeba. Vortexmore » charge density is uniformly distributed among vortex sheets, and negative contribution to instanton charge density is understood as the complex Monge-Ampere measure with respect to a plurisubharmonic function on (C*){sup 2}. The Wilson loops in T{sup 2} are related with derivatives of the Ronkin function. The general form of the Kaehler potential and the asymptotic metric of the moduli space of a vortex loop are obtained as a by-product. Our discussion works generally in non-Abelian gauge theories, which suggests a non-Abelian generalization of the amoeba and tropical geometry.« less

Methods of Contemporary Gauge Theory

NASA Astrophysics Data System (ADS)

Makeenko, Yuri

2002-08-01

Preface; Part I. Path Integrals: 1. Operator calculus; 2. Second quantization; 3. Quantum anomalies from path integral; 4. Instantons in quantum mechanics; Part II. Lattice Gauge Theories: 5. Observables in gauge theories; 6. Gauge fields on a lattice; 7. Lattice methods; 8. Fermions on a lattice; 9. Finite temperatures; Part III. 1/N Expansion: 10. O(N) vector models; 11. Multicolor QCD; 12. QCD in loop space; 13. Matrix models; Part IV. Reduced Models: 14. Eguchi-Kawai model; 15. Twisted reduced models; 16. Non-commutative gauge theories.

Methods of Contemporary Gauge Theory

NASA Astrophysics Data System (ADS)

Makeenko, Yuri

2005-11-01

Preface; Part I. Path Integrals: 1. Operator calculus; 2. Second quantization; 3. Quantum anomalies from path integral; 4. Instantons in quantum mechanics; Part II. Lattice Gauge Theories: 5. Observables in gauge theories; 6. Gauge fields on a lattice; 7. Lattice methods; 8. Fermions on a lattice; 9. Finite temperatures; Part III. 1/N Expansion: 10. O(N) vector models; 11. Multicolor QCD; 12. QCD in loop space; 13. Matrix models; Part IV. Reduced Models: 14. Eguchi-Kawai model; 15. Twisted reduced models; 16. Non-commutative gauge theories.

Localization of effective actions in open superstring field theory

NASA Astrophysics Data System (ADS)

Maccaferri, Carlo; Merlano, Alberto

2018-03-01

We consider the construction of the algebraic part of D-branes tree-level effective action from Berkovits open superstring field theory. Applying this construction to the quartic potential of massless fields carrying a specific worldsheet charge, we show that the full contribution to the potential localizes at the boundary of moduli space, reducing to elementary two-point functions. As examples of this general mechanism, we show how the Yang-Mills quartic potential and the instanton effective action of a Dp/D( p - 4) system are reproduced.

Phases and approximations of baryonic popcorn in a low-dimensional analogue of holographic QCD

NASA Astrophysics Data System (ADS)

Elliot-Ripley, Matthew

2015-07-01

The Sakai-Sugimoto model is the most pre-eminent model of holographic QCD, in which baryons correspond to topological solitons in a five-dimensional bulk spacetime. Recently it has been shown that a single soliton in this model can be well approximated by a flat-space self-dual Yang-Mills instanton with a small size, although studies of multi-solitons and solitons at finite density are currently beyond numerical computations. A lower-dimensional analogue of the model has also been studied in which the Sakai-Sugimoto soliton is replaced by a baby Skyrmion in three spacetime dimensions with a warped metric. The lower dimensionality of this model means that full numerical field calculations are possible, and static multi-solitons and solitons at finite density were both investigated, in particular the baryonic popcorn phase transitions at high densities. Here we present and investigate an alternative lower-dimensional analogue of the Sakai-Sugimoto model in which the Sakai-Sugimoto soliton is replaced by an O(3)-sigma model instanton in a warped three-dimensional spacetime stabilized by a massive vector meson. A more detailed range of baryonic popcorn phase transitions are found, and the low-dimensional model is used as a testing ground to check the validity of common approximations made in the full five-dimensional model, namely approximating fields using their flat-space equations of motion, and performing a leading order expansion in the metric.

F-theoretic vs microscopic description of a conformal mathcal{N} = 2 SYM theory

NASA Astrophysics Data System (ADS)

Billò, Marco; Gallot, Laurent; Lerda, Alberto; Pesando, Igor

2010-11-01

The F-theory background of four D7 branes in a type I' orientifold was conjectured to be described by the Seiberg-Witten curve for the superconformal SU(2) gauge theory with four flavors. This relation was explained by considering in this background a probe D3 brane, which supports this theory with SU(2) realized as Sp(1). Here we explicitly compute the non-perturbative corrections to the D7/D3 system in type I' due to D-instantons. This computation provides both the quartic effective action on the D7 branes and the quadratic effective action on the D3 brane; the latter agrees with the F-theoretic prediction. The action obtained in this way is related to the one derived from the usual instanton calculus à la Nekrasov (or from its AGT realization in terms of Liouville conformal blocks) by means of a non-perturbative redefinition of the coupling constant. We also point out an intriguing relation between the four-dimensional theory on the probe D3 brane with SO(8) flavor symmetry and the eight-dimensional dynamics on the D7 branes. On the latter, SO(8) represents a gauge group and the flavor masses correspond to the vacuum expectation values of an adjoint scalar field m: what we find is that the exact effective coupling in four dimensions is obtained from its perturbative part by taking into account in its mass dependence the full quantum dynamics of the field m in eight dimensions.

Scale-invariant instantons and the complete lifetime of the standard model

NASA Astrophysics Data System (ADS)

Andreassen, Anders; Frost, William; Schwartz, Matthew D.

2018-03-01

In a classically scale-invariant quantum field theory, tunneling rates are infrared divergent due to the existence of instantons of any size. While one expects such divergences to be resolved by quantum effects, it has been unclear how higher-loop corrections can resolve a problem appearing already at one loop. With a careful power counting, we uncover a series of loop contributions that dominate over the one-loop result and sum all the necessary terms. We also clarify previously incomplete treatments of related issues pertaining to global symmetries, gauge fixing, and finite mass effects. In addition, we produce exact closed-form solutions for the functional determinants over scalars, fermions, and vector bosons around the scale-invariant bounce, demonstrating manifest gauge invariance in the vector case. With these problems solved, we produce the first complete calculation of the lifetime of our Universe: 1 0139 years . With 95% confidence, we expect our Universe to last more than 1 058 years . The uncertainty is part experimental uncertainty on the top quark mass and on αs and part theory uncertainty from electroweak threshold corrections. Using our complete result, we provide phase diagrams in the mt/mh and the mt/αs planes, with uncertainty bands. To rule out absolute stability to 3 σ confidence, the uncertainty on the top quark pole mass would have to be pushed below 250 MeV or the uncertainty on αs(mZ) pushed below 0.00025.

All conjugate-maximal-helicity-violating amplitudes from topological open string theory in twistor space.

PubMed

Roiban, Radu; Volovich, Anastasia

2004-09-24

It has recently been proposed that the D-instanton expansion of the open topological B model on P(3|4) is equivalent to the perturbative expansion of the maximally supersymmetric Yang-Mills theory in four dimensions. In this letter we show how to construct the gauge theory results for all n-point conjugate-maximal-helicity-violating amplitudes by computing the integral over the moduli space of curves of degree n-3 in P(3|4), providing strong support to the string theory construction.

Matrix theory interpretation of discrete light cone quantization string worldsheets

PubMed

Grignani; Orland; Paniak; Semenoff

2000-10-16

We study the null compactification of type-IIA string perturbation theory at finite temperature. We prove a theorem about Riemann surfaces establishing that the moduli spaces of infinite-momentum-frame superstring worldsheets are identical to those of branched-cover instantons in the matrix-string model conjectured to describe M theory. This means that the identification of string degrees of freedom in the matrix model proposed by Dijkgraaf, Verlinde, and Verlinde is correct and that its natural generalization produces the moduli space of Riemann surfaces at all orders in the genus expansion.

Multi-cut solutions in Chern-Simons matrix models

NASA Astrophysics Data System (ADS)

Morita, Takeshi; Sugiyama, Kento

2018-04-01

We elaborate the Chern-Simons (CS) matrix models at large N. The saddle point equations of these matrix models have a curious structure which cannot be seen in the ordinary one matrix models. Thanks to this structure, an infinite number of multi-cut solutions exist in the CS matrix models. Particularly we exactly derive the two-cut solutions at finite 't Hooft coupling in the pure CS matrix model. In the ABJM matrix model, we argue that some of multi-cut solutions might be interpreted as a condensation of the D2-brane instantons.

Modularity, quaternion-Kähler spaces, and mirror symmetry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Alexandrov, Sergei; Banerjee, Sibasish

2013-10-15

We provide an explicit twistorial construction of quaternion-Kähler manifolds obtained by deformation of c-map spaces and carrying an isometric action of the modular group SL(2,Z). The deformation is not assumed to preserve any continuous isometry and therefore this construction presents a general framework for describing NS5-brane instanton effects in string compactifications with N= 2 supersymmetry. In this context the modular invariant parametrization of twistor lines found in this work yields the complete non-perturbative mirror map between type IIA and type IIB physical fields.

Wilson-loop instantons

NASA Technical Reports Server (NTRS)

Lee, Kimyeong; Holman, Richard; Kolb, Edward W.

1987-01-01

Wilson-loop symmetry breaking is considered on a space-time of the form M4 x K, where M4 is a four-dimensional space-time and K is an internal space with nontrivial and finite fundamental group. It is shown in a simple model that the different vacua obtained by breaking a non-Abelian gauge group by Wilson loops are separated in the space of gauge potentials by a finite energy barrier. An interpolating gauge configuration is then constructed between these vacua and shown to have minimum energy. Finally some implications of this construction are discussed.

Instantons on ALE spaces and orbifold partitions

NASA Astrophysics Data System (ADS)

Dijkgraaf, Robbert; Sułkowski, Piotr

2008-03-01

We consider Script N = 4 theories on ALE spaces of Ak-1 type. As is well known, their partition functions coincide with Ak-1 affine characters. We show that these partition functions are equal to the generating functions of some peculiar classes of partitions which we introduce under the name 'orbifold partitions'. These orbifold partitions turn out to be related to the generalized Frobenius partitions introduced by G. E. Andrews some years ago. We relate the orbifold partitions to the blended partitions and interpret explicitly in terms of a free fermion system.

Twistor approach to string compactifications: A review

NASA Astrophysics Data System (ADS)

Alexandrov, Sergei

2013-01-01

We review a progress in obtaining the complete non-perturbative effective action of type II string theory compactified on a Calabi-Yau manifold. This problem is equivalent to understanding quantum corrections to the metric on the hypermultiplet moduli space. We show how all these corrections, which include D-brane and NS5-brane instantons, are incorporated in the framework of the twistor approach, which provides a powerful mathematical description of hyperkähler and quaternion-Kähler manifolds. We also present new insights on S-duality, quantum mirror symmetry, connections to integrable models and topological strings.

Darboux coordinates and instanton corrections in projective superspace

NASA Astrophysics Data System (ADS)

Crichigno, P. Marcos; Jain, Dharmesh

2012-10-01

By demanding consistency of the Legendre transform construction of hyperkähler metrics in projective superspace, we derive the expression for the Darboux coordinates on the hyperkähler manifold. We apply these results to study the Coulomb branch moduli space of 4D, {N}=2 super-Yang-Mills theory (SYM) on {{{R}}^3}× {S^1} , recovering the results by GMN. We also apply this method to study the electric corrections to the moduli space of 5D, {N}=1 SYM on {{{R}}^3}× {T^2} and give the Darboux coordinates explicitly.

Reliable semiclassical computations in QCD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dine, Michael; Department of Physics, Stanford University Stanford, California 94305-4060; Festuccia, Guido

We revisit the question of whether or not one can perform reliable semiclassical QCD computations at zero temperature. We study correlation functions with no perturbative contributions, and organize the problem by means of the operator product expansion, establishing a precise criterion for the validity of a semiclassical calculation. For N{sub f}>N, a systematic computation is possible; for N{sub f}

Why there is something rather than nothing: cosmological constant from summing over everything in lorentzian quantum gravity.

PubMed

Barvinsky, A O

2007-08-17

The density matrix of the Universe for the microcanonical ensemble in quantum cosmology describes an equipartition in the physical phase space of the theory (sum over everything), but in terms of the observable spacetime geometry this ensemble is peaked about the set of recently obtained cosmological instantons limited to a bounded range of the cosmological constant. This suggests the mechanism of constraining the landscape of string vacua and a possible solution to the dark energy problem in the form of the quasiequilibrium decay of the microcanonical state of the Universe.

Beta functions in Chirally deformed supersymmetric sigma models in two dimensions

NASA Astrophysics Data System (ADS)

Vainshtein, Arkady

2016-10-01

We study two-dimensional sigma models where the chiral deformation diminished the original 𝒩 = (2, 2) supersymmetry to the chiral one, 𝒩 = (0, 2). Such heterotic models were discovered previously on the world sheet of non-Abelian stringy solitons supported by certain four-dimensional 𝒩 = 1 theories. We study geometric aspects and holomorphic properties of these models, and derive a number of exact expressions for the β functions in terms of the anomalous dimensions analogous to the NSVZ β function in four-dimensional Yang-Mills. Instanton calculus provides a straightforward method for the derivation.

Beta Functions in Chirally Deformed Supersymmetric Sigma Models in Two Dimensions

NASA Astrophysics Data System (ADS)

Vainshtein, Arkady

We study two-dimensional sigma models where the chiral deformation diminished the original 𝒩 =(2, 2) supersymmetry to the chiral one, 𝒩 =(0, 2). Such heterotic models were discovered previously on the world sheet of non-Abelian stringy solitons supported by certain four-dimensional 𝒩 = 1 theories. We study geometric aspects and holomorphic properties of these models, and derive a number of exact expressions for the β functions in terms of the anomalous dimensions analogous to the NSVZ β function in four-dimensional Yang-Mills. Instanton calculus provides a straightforward method for the derivation.

Sauter-Schwinger pair creation dynamically assisted by a plane wave

NASA Astrophysics Data System (ADS)

Torgrimsson, Greger; Schneider, Christian; Schützhold, Ralf

2018-05-01

We study electron-positron pair creation by a strong and constant electric field superimposed with a weaker transversal plane wave which is incident perpendicularly (or under some angle). Comparing the fully nonperturbative approach based on the world-line instanton method with a perturbative expansion into powers of the strength of the weaker plane wave, we find good agreement—provided that the latter is carried out to sufficiently high orders. As usual for the dynamically assisted Sauter-Schwinger effect, the additional plane wave induces an exponential enhancement of the pair-creation probability if the combined Keldysh parameter exceeds a certain threshold.

Exact partition functions for deformed N=2 theories with N_f=4 flavours

NASA Astrophysics Data System (ADS)

Beccaria, Matteo; Fachechi, Alberto; Macorini, Guido; Martina, Luigi

2016-12-01

We consider the Ω-deformed N=2 SU(2) gauge theory in four dimensions with N f = 4 massive fundamental hypermultiplets. The low energy effective action depends on the deformation parameters ɛ 1 , ɛ 2, the scalar field expectation value a, and the hypermultiplet masses m = ( m 1 , m 2 , m 3 , m 4). Motivated by recent findings in the N={2}^{*} theory, we explore the theories that are characterized by special fixed ratios ɛ 2 /ɛ 1 and m /ɛ 1 and propose a simple condition on the structure of the multi-instanton contributions to the prepotential determining the effective action. This condition determines a finite set Π N of special points such that the prepotential has N poles at fixed positions independent on the instanton number. In analogy with what happens in the N={2}^{*} gauge theory, the full prepotential of the Π N theories may be given in closed form as an explicit function of a and the modular parameter q appearing in special combinations of Eisenstein series and Jacobi theta functions with well defined modular properties. The resulting finite pole partition functions are related by AGT correspondence to special 4-point spherical conformal blocks of the Virasoro algebra. We examine in full details special cases where the closed expression of the block is known and confirms our Ansatz. We systematically study the special features of Zamolodchikov's recursion for the Π N conformal blocks. As a result, we provide a novel effective recursion relation that can be exactly solved and allows to prove the conjectured closed expressions analytically in the case of the Π1 and Π2 conformal blocks.

Discrete Torsion, (Anti) de Sitter D4-Brane and Tunneling

NASA Astrophysics Data System (ADS)

Singh, Abhishek K.; Pandey, P. K.; Singh, Sunita; Kar, Supriya

2014-06-01

We obtain quantum geometries on a vacuum created pair of a (DDbar)3-brane, at a Big Bang singularity, by a local two form on a D4-brane. In fact our analysis is provoked by an established phenomenon leading to a pair creation by a gauge field at a black hole horizon by Stephen Hawking in 1975. Importantly, the five dimensional microscopic black holes are described by an effective non-perturbative curvature underlying a discrete torsion in a second order formalism. In the case for a non-propagating torsion, the effective curvature reduces to Riemannian, which in a low energy limit may describe Einstein vacuum in the formalism. In particular, our analysis suggests that a non-trivial space begin with a hot de Sitter brane-Universe underlying a nucleation of a vacuum pair of (DDbar)-instanton at a Big Bang. A pair of instanton nucleats a D-particle which in turn combines with an anti D-particle to describe a D-string and so on. The nucleation of a pair of higher dimensional pair of brane/anti-brane from a lower dimensional pair may be viewed via an expansion of the brane-Universe upon time. It is in conformity with the conjecture of a branes within a brane presumably in presence of the non-zero modes of two form. Interestingly, we perform a thermal analysis underlying various emergent quantum de Sitter vacua on a D4-brane and argue for the plausible tunneling geometries underlying a thermal equilibrium. It is argued that a de Sitter Schwarzschild undergoes quantum tunneling to an AdS-brane Schwarzschild via Nariai and de Sitter topological black hole.

Tunneling splitting in double-proton transfer: direct diagonalization results for porphycene.

PubMed

Smedarchina, Zorka; Siebrand, Willem; Fernández-Ramos, Antonio

2014-11-07

Zero-point and excited level splittings due to double-proton tunneling are calculated for porphycene and the results are compared with experiment. The calculation makes use of a multidimensional imaginary-mode Hamiltonian, diagonalized directly by an effective reduction of its dimensionality. Porphycene has a complex potential energy surface with nine stationary configurations that allow a variety of tunneling paths, many of which include classically accessible regions. A symmetry-based approach is used to show that the zero-point level, although located above the cis minimum, corresponds to concerted tunneling along a direct trans - trans path; a corresponding cis - cis path is predicted at higher energy. This supports the conclusion of a previous paper [Z. Smedarchina, W. Siebrand, and A. Fernández-Ramos, J. Chem. Phys. 127, 174513 (2007)] based on the instanton approach to a model Hamiltonian of correlated double-proton transfer. A multidimensional tunneling Hamiltonian is then generated, based on a double-minimum potential along the coordinate of concerted proton motion, which is newly evaluated at the RI-CC2/cc-pVTZ level of theory. To make it suitable for diagonalization, its dimensionality is reduced by treating fast weakly coupled modes in the adiabatic approximation. This results in a coordinate-dependent mass of tunneling, which is included in a unique Hermitian form into the kinetic energy operator. The reduced Hamiltonian contains three symmetric and one antisymmetric mode coupled to the tunneling mode and is diagonalized by a modified Jacobi-Davidson algorithm implemented in the Jadamilu software for sparse matrices. The results are in satisfactory agreement with the observed splitting of the zero-point level and several vibrational fundamentals after a partial reassignment, imposed by recently derived selection rules. They also agree well with instanton calculations based on the same Hamiltonian.

Double proton transfer in the complex of acetic acid with methanol: Theory versus experiment

NASA Astrophysics Data System (ADS)

Fernández-Ramos, Antonio; Smedarchina, Zorka; Rodríguez-Otero, Jesús

2001-01-01

To test the approximate instanton approach to intermolecular proton-transfer dynamics, we report multidimensional ab initio bimolecular rate constants of HH, HD, and DD exchange in the complex of acetic acid with methanol in tetrahydrofuran-d8, and compare them with the NMR (nuclear magnetic resonance) experiments of Gerritzen and Limbach. The bimolecular rate constants are evaluated as products of the exchange rates and the equilibrium rate constants of complex formation in solution. The two molecules form hydrogen-bond bridges and the exchange occurs via concerted transfer of two protons. The dynamics of this transfer is evaluated in the complete space of 36 vibrational degrees of freedom. The geometries of the two isolated molecules, the complex, and the transition states corresponding to double proton transfer are fully optimized at QCISD (quadratic configuration interaction including single and double substitutions) level of theory, and the normal-mode frequencies are calculated at MP2 (Møller-Plesset perturbation theory of second order) level with the 6-31G (d,p) basis set. The presence of the solvent is taken into account via single-point calculations over the gas phase geometries with the PCM (polarized continuum model). The proton exchange rate constants, calculated with the instanton method, show the effect of the structure and strength of the hydrogen bonds, reflected in the coupling between the tunneling motion and the other vibrations of the complex. Comparison with experiment, which shows substantial kinetic isotopic effects (KIE), indicates that tunneling prevails over classic exchange for the whole temperature range of observation. The unusual behavior of the experimental KIE upon single and double deuterium substitution is well reproduced and is related to the synchronicity of two-atom tunneling.

New excitations in the Thirring model

NASA Astrophysics Data System (ADS)

Cortés, J. L.; Gamboa, J.; Schmidt, I.; Zanelli, J.

1998-12-01

The quantization of the massless Thirring model in the light-cone using functional methods is considered. The need to compactify the coordinate x- in the light-cone spacetime implies that the quantum effective action for left-handed fermions contains excitations similar to abelian instantons produced by composite of left-handed fermions. Right-handed fermions don't have a similar effective action. Thus, quantum mechanically, chiral symmetry must be broken as a result of the topological excitations. The conserved charge associated to the topological states is quantized. Different cases with only fermionic excitations or bosonic excitations or both can occur depending on the boundary conditions and the value of the coupling.

What if? Exploring the multiverse through Euclidean wormholes.

PubMed

Bouhmadi-López, Mariam; Krämer, Manuel; Morais, João; Robles-Pérez, Salvador

2017-01-01

We present Euclidean wormhole solutions describing possible bridges within the multiverse. The study is carried out in the framework of third quantisation. The matter content is modelled through a scalar field which supports the existence of a whole collection of universes. The instanton solutions describe Euclidean solutions that connect baby universes with asymptotically de Sitter universes. We compute the tunnelling probability of these processes. Considering the current bounds on the energy scale of inflation and assuming that all the baby universes are nucleated with the same probability, we draw some conclusions about which universes are more likely to tunnel and therefore undergo a standard inflationary era.

What if? Exploring the multiverse through Euclidean wormholes

NASA Astrophysics Data System (ADS)

Bouhmadi-López, Mariam; Krämer, Manuel; Morais, João; Robles-Pérez, Salvador

2017-10-01

We present Euclidean wormhole solutions describing possible bridges within the multiverse. The study is carried out in the framework of third quantisation. The matter content is modelled through a scalar field which supports the existence of a whole collection of universes. The instanton solutions describe Euclidean solutions that connect baby universes with asymptotically de Sitter universes. We compute the tunnelling probability of these processes. Considering the current bounds on the energy scale of inflation and assuming that all the baby universes are nucleated with the same probability, we draw some conclusions about which universes are more likely to tunnel and therefore undergo a standard inflationary era.

Quantum Field Theories Coupled to Supergravity: AdS/CFT and Local Couplings

NASA Astrophysics Data System (ADS)

Große, Johannes

2007-11-01

This article is based on my PhD thesis and covers the following topics: Holographic meson spectra in a dilaton flow background, the mixed Coulomb-Higgs branch in terms of instantons on D7 branes, and a dual description of heavy-light mesons. Moreover, in a second part the conformal anomaly of four dimensional supersymmetric quantum field theories coupled to classical N=1 supergravity is explored in a superfield formulation. The complete basis for the anomaly and consistency conditions, which arise from cohomological considerations, are given. Possible implications for an extension of Zamolodchikov's c-theorem to four dimensional supersymmetric quantum field theories are discussed.

Twisted sigma-model solitons on the quantum projective line

NASA Astrophysics Data System (ADS)

Landi, Giovanni

2018-04-01

On the configuration space of projections in a noncommutative algebra, and for an automorphism of the algebra, we use a twisted Hochschild cocycle for an action functional and a twisted cyclic cocycle for a topological term. The latter is Hochschild-cohomologous to the former and positivity in twisted Hochschild cohomology results into a lower bound for the action functional. While the equations for the critical points are rather involved, the use of the positivity and the bound by the topological term lead to self-duality equations (thus yielding twisted noncommutative sigma-model solitons, or instantons). We present explicit nontrivial solutions on the quantum projective line.

Instantons re-examined: dynamical tunneling and resonant tunneling.

PubMed

Le Deunff, Jérémy; Mouchet, Amaury

2010-04-01

Starting from trace formulas for the tunneling splittings (or decay rates) analytically continued in the complex time domain, we obtain explicit semiclassical expansions in terms of complex trajectories that are selected with appropriate complex-time paths. We show how this instantonlike approach, which takes advantage of an incomplete Wick rotation, accurately reproduces tunneling effects not only in the usual double-well potential but also in situations where a pure Wick rotation is insufficient, for instance dynamical tunneling or resonant tunneling. Even though only one-dimensional autonomous Hamiltonian systems are quantitatively studied, we discuss the relevance of our method for multidimensional and/or chaotic tunneling.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dine, Michael; Draper, Patrick; Stephenson-Haskins, Laurel

Here, we study the large N θ dependence and the η' potential in supersymmetric QCD with small soft SUSY-breaking terms. Known exact results in SUSY QCD are found to reflect a variety of expectations from large N perturbation theory, including the presence of branches and the behavior of theories with matter (both with N f << N and N f ~ N ). But, there are also striking departures from ordinary QCD and the conventional large N description: instanton effects, when under control, are not exponentially suppressed at large N , and branched structure in supersymmetric QCD is always associatedmore » with approximate discrete symmetries. We suggest that these differences motivate further study of large N QCD on the lattice.« less

Transmogrifying fuzzy vortices

NASA Astrophysics Data System (ADS)

Murugan, Jeff; Millner, Antony

2004-04-01

We show that the construction of vortex solitons of the noncommutative abelian-Higgs model can be extended to a critically coupled gauged linear sigma model with Fayet-Illiopolous D-terms. Like its commutative counterpart, this fuzzy linear sigma model has a rich spectrum of BPS solutions. We offer an explicit construction of the degree-k static semilocal vortex and study in some detail the infinite coupling limit in which it descends to a degree-k Bbb CBbb PkN instanton. This relation between the fuzzy vortex and noncommutative lump is used to suggest an interpretation of the noncommutative sigma model soliton as tilted D-strings stretched between an NS5-brane and a stack of D3-branes in type-IIB superstring theory.

An A{sub r} threesome: Matrix models, 2d conformal field theories, and 4dN=2 gauge theories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schiappa, Ricardo; Wyllard, Niclas

We explore the connections between three classes of theories: A{sub r} quiver matrix models, d=2 conformal A{sub r} Toda field theories, and d=4N=2 supersymmetric conformal A{sub r} quiver gauge theories. In particular, we analyze the quiver matrix models recently introduced by Dijkgraaf and Vafa (unpublished) and make detailed comparisons with the corresponding quantities in the Toda field theories and the N=2 quiver gauge theories. We also make a speculative proposal for how the matrix models should be modified in order for them to reproduce the instanton partition functions in quiver gauge theories in five dimensions.

Prediction of Rare Transitions in Planetary Atmosphere Dynamics Between Attractors with Different Number of Zonal Jets

NASA Astrophysics Data System (ADS)

Bouchet, F.; Laurie, J.; Zaboronski, O.

2012-12-01

We describe transitions between attractors with either one, two or more zonal jets in models of turbulent atmosphere dynamics. Those transitions are extremely rare, and occur over times scales of centuries or millennia. They are extremely hard to observe in direct numerical simulations, because they require on one hand an extremely good resolution in order to simulate accurately the turbulence and on the other hand simulations performed over an extremely long time. Those conditions are usually not met together in any realistic models. However many examples of transitions between turbulent attractors in geophysical flows are known to exist (paths of the Kuroshio, Earth's magnetic field reversal, atmospheric flows, and so on). Their study through numerical computations is inaccessible using conventional means. We present an alternative approach, based on instanton theory and large deviations. Instanton theory provides a way to compute (both numerically and theoretically) extremely rare transitions between turbulent attractors. This tool, developed in field theory, and justified in some cases through the large deviation theory in mathematics, can be applied to models of turbulent atmosphere dynamics. It provides both new theoretical insights and new type of numerical algorithms. Those algorithms can predict transition histories and transition rates using numerical simulations run over only hundreds of typical model dynamical time, which is several order of magnitude lower than the typical transition time. We illustrate the power of those tools in the framework of quasi-geostrophic models. We show regimes where two or more attractors coexist. Those attractors corresponds to turbulent flows dominated by either one or more zonal jets similar to midlatitude atmosphere jets. Among the trajectories connecting two non-equilibrium attractors, we determine the most probable ones. Moreover, we also determine the transition rates, which are several of magnitude larger than a typical time determined from the jet structure. We discuss the medium-term generalization of those results to models with more complexity, like primitive equations or GCMs.

Nonadiabatic Molecular Dynamics and Orthogonality Constrained Density Functional Theory

NASA Astrophysics Data System (ADS)

Shushkov, Philip Georgiev

The exact quantum dynamics of realistic, multidimensional systems remains a formidable computational challenge. In many chemical processes, however, quantum effects such as tunneling, zero-point energy quantization, and nonadiabatic transitions play an important role. Therefore, approximate approaches that improve on the classical mechanical framework are of special practical interest. We propose a novel ring polymer surface hopping method for the calculation of chemical rate constants. The method blends two approaches, namely ring polymer molecular dynamics that accounts for tunneling and zero-point energy quantization, and surface hopping that incorporates nonadiabatic transitions. We test the method against exact quantum mechanical calculations for a one-dimensional, two-state model system. The method reproduces quite accurately the tunneling contribution to the rate and the distribution of reactants between the electronic states for this model system. Semiclassical instanton theory, an approach related to ring polymer molecular dynamics, accounts for tunneling by the use of periodic classical trajectories on the inverted potential energy surface. We study a model of electron transfer in solution, a chemical process where nonadiabatic events are prominent. By representing the tunneling electron with a ring polymer, we derive Marcus theory of electron transfer from semiclassical instanton theory after a careful analysis of the tunneling mode. We demonstrate that semiclassical instanton theory can recover the limit of Fermi's Golden Rule rate in a low-temperature, deep-tunneling regime. Mixed quantum-classical dynamics treats a few important degrees of freedom quantum mechanically, while classical mechanics describes affordably the rest of the system. But the interface of quantum and classical description is a challenging theoretical problem, especially for low-energy chemical processes. We therefore focus on the semiclassical limit of the coupled nuclear-electronic dynamics. We show that the time-dependent Schrodinger equation for the electrons employed in the widely used fewest switches surface hopping method is applicable only in the limit of nearly identical classical trajectories on the different potential energy surfaces. We propose a short-time decoupling algorithm that restricts the use of the Schrodinger equation only to the interaction regions. We test the short-time approximation on three model systems against exact quantum-mechanical calculations. The approximation improves the performance of the surface hopping approach. Nonadiabatic molecular dynamics simulations require the efficient and accurate computation of ground and excited state potential energy surfaces. Unlike the ground state calculations where standard methods exist, the computation of excited state properties is a challenging task. We employ time-independent density functional theory, in which the excited state energy is represented as a functional of the total density. We suggest an adiabatic-like approximation that simplifies the excited state exchange-correlation functional. We also derive a set of minimal conditions to impose exactly the orthogonality of the excited state Kohn-Sham determinant to the ground state determinant. This leads to an efficient, variational algorithm for the self-consistent optimization of the excited state energy. Finally, we assess the quality of the excitation energies obtained by the new method on a set of 28 organic molecules. The new approach provides results of similar accuracy to time-dependent density functional theory.

Quasimodular instanton partition function and the elliptic solution of Korteweg-de Vries equations

NASA Astrophysics Data System (ADS)

He, Wei

2015-02-01

The Gauge/Bethe correspondence relates Omega-deformed N = 2 supersymmetric gauge theories to some quantum integrable models, in simple cases the integrable models can be treated as solvable quantum mechanics models. For SU(2) gauge theory with an adjoint matter, or with 4 fundamental matters, the potential of corresponding quantum model is the elliptic function. If the mass of matter takes special value then the potential is an elliptic solution of KdV hierarchy. We show that the deformed prepotential of gauge theory can be obtained from the average densities of conserved charges of the classical KdV solution, the UV gauge coupling dependence is assembled into the Eisenstein series. The gauge theory with adjoint mass is taken as the example.

Non-Relativistic Twistor Theory and Newton-Cartan Geometry

NASA Astrophysics Data System (ADS)

Dunajski, Maciej; Gundry, James

2016-03-01

We develop a non-relativistic twistor theory, in which Newton-Cartan structures of Newtonian gravity correspond to complex three-manifolds with a four-parameter family of rational curves with normal bundle O oplus O(2)}. We show that the Newton-Cartan space-times are unstable under the general Kodaira deformation of the twistor complex structure. The Newton-Cartan connections can nevertheless be reconstructed from Merkulov's generalisation of the Kodaira map augmented by a choice of a holomorphic line bundle over the twistor space trivial on twistor lines. The Coriolis force may be incorporated by holomorphic vector bundles, which in general are non-trivial on twistor lines. The resulting geometries agree with non-relativistic limits of anti-self-dual gravitational instantons.

Charge instabilities due to local charge conjugation symmetry in /2+1 dimensions

NASA Astrophysics Data System (ADS)

Bais, F. A.; Striet, J.

2003-08-01

Alice electrodynamics (AED) is a theory of electrodynamics in which charge conjugation is a local gauge symmetry. In this paper we investigate a charge instability in alice electrodynamics in 2+1 dimensions due to this local charge conjugation. The instability manifests itself through the creation of a pair of alice fluxes. The final state is one in which the charge is completely delocalized, i.e., it is carried as cheshire charge by the flux pair that gets infinitely separated. We determine the decay rate in terms of the parameters of the model. The relation of this phenomenon with other salient features of 2-dimensional compact QED, such as linear confinement due to instantons/monopoles, is discussed.

θ and the η ' in large N supersymmetric QCD

DOE PAGES

Dine, Michael; Draper, Patrick; Stephenson-Haskins, Laurel; ...

2017-05-22

Here, we study the large N θ dependence and the η' potential in supersymmetric QCD with small soft SUSY-breaking terms. Known exact results in SUSY QCD are found to reflect a variety of expectations from large N perturbation theory, including the presence of branches and the behavior of theories with matter (both with N f << N and N f ~ N ). But, there are also striking departures from ordinary QCD and the conventional large N description: instanton effects, when under control, are not exponentially suppressed at large N , and branched structure in supersymmetric QCD is always associatedmore » with approximate discrete symmetries. We suggest that these differences motivate further study of large N QCD on the lattice.« less

Betti numbers of holomorphic symplectic quotients via arithmetic Fourier transform.

PubMed

Hausel, Tamás

2006-04-18

A Fourier transform technique is introduced for counting the number of solutions of holomorphic moment map equations over a finite field. This technique in turn gives information on Betti numbers of holomorphic symplectic quotients. As a consequence, simple unified proofs are obtained for formulas of Poincaré polynomials of toric hyperkähler varieties (recovering results of Bielawski-Dancer and Hausel-Sturmfels), Poincaré polynomials of Hilbert schemes of points and twisted Atiyah-Drinfeld-Hitchin-Manin (ADHM) spaces of instantons on C2 (recovering results of Nakajima-Yoshioka), and Poincaré polynomials of all Nakajima quiver varieties. As an application, a proof of a conjecture of Kac on the number of absolutely indecomposable representations of a quiver is announced.

Moving branes in the presence of background tachyon fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rezaei, Z., E-mail: z.rezaei@aut.ac.ir; Kamani, D., E-mail: kamani@aut.ac.ir

2011-12-15

We compute the boundary state associated with a moving Dp-brane in the presence of the open string tachyon field as a background field. The effect of the tachyon condensation on the boundary state is discussed. It leads to a boundary state associated with a lower-dimensional moving D-brane or a stationary instantonic D-brane. The former originates from condensation along the spatial directions and the latter comes from the temporal direction of the D-brane worldvolume. Using the boundary state, we also study the interaction amplitude between two arbitrary Dp{sub 1}- and Dp{sub 2}-branes. The long-range behavior of the amplitude is investigated, demonstratingmore » an obvious deviation from the conventional form, due to the presence of the background tachyon field.« less

QCD In Extreme Conditions

NASA Astrophysics Data System (ADS)

Wilczek, Frank

Introduction Symmetry and the Phenomena of QCD Apparent and Actual Symmetries Asymptotic Freedom Confinement Chiral Symmetry Breaking Chiral Anomalies and Instantons High Temperature QCD: Asymptotic Properties Significance of High Temperature QCD Numerical Indications for Quasi-Free Behavior Ideas About Quark-Gluon Plasma Screening Versus Confinement Models of Chiral Symmetry Breaking More Refined Numerical Experiments High-Temperature QCD: Phase Transitions Yoga of Phase Transitions and Order Parameters Application to Glue Theories Application to Chiral Transitions Close Up on Two Flavors A Genuine Critical Point! (?) High-Density QCD: Methods Hopes, Doubts, and Fruition Another Renormalization Group Pairing Theory Taming the Magnetic Singularity High-Density QCD: Color-Flavor Locking and Quark-Hadron Continuity Gauge Symmetry (Non)Breaking Symmetry Accounting Elementary Excitations A Modified Photon Quark-Hadron Continuity Remembrance of Things Past More Quarks Fewer Quarks and Reality

The topological susceptibility in finite temperature QCD and axion cosmology

DOE PAGES

Petreczky, Peter; Schadler, Hans-Peter; Sharma, Sayantan

2016-10-06

We study the topological susceptibility in 2+1 flavor QCD above the chiral crossover transition temperature using Highly Improved Staggered Quark action and several lattice spacings corresponding to temporal extent of the lattice, N τ=6,8,10 and 12. We observe very distinct temperature dependences of the topological susceptibility in the ranges above and below 250MeV. While for temperatures above 250MeV, the dependence is found to be consistent with dilute instanton gas approximation, at lower temperatures the fall-off of topological susceptibility is milder. We discuss the consequence of our results for cosmology wherein we estimate the bounds on the axion decay constant andmore » the oscillation temperature if indeed the QCD axion is a possible dark matter candidate.« less

The topological susceptibility in finite temperature QCD and axion cosmology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Petreczky, Peter; Schadler, Hans-Peter; Sharma, Sayantan

We study the topological susceptibility in 2+1 flavor QCD above the chiral crossover transition temperature using Highly Improved Staggered Quark action and several lattice spacings corresponding to temporal extent of the lattice, N τ=6,8,10 and 12. We observe very distinct temperature dependences of the topological susceptibility in the ranges above and below 250MeV. While for temperatures above 250MeV, the dependence is found to be consistent with dilute instanton gas approximation, at lower temperatures the fall-off of topological susceptibility is milder. We discuss the consequence of our results for cosmology wherein we estimate the bounds on the axion decay constant andmore » the oscillation temperature if indeed the QCD axion is a possible dark matter candidate.« less

Statistical properties of Charney-Hasegawa-Mima zonal flows

DOE Office of Scientific and Technical Information (OSTI.GOV)

Anderson, Johan, E-mail: anderson.johan@gmail.com; Botha, G. J. J.

2015-05-15

A theoretical interpretation of numerically generated probability density functions (PDFs) of intermittent plasma transport events in unforced zonal flows is provided within the Charney-Hasegawa-Mima (CHM) model. The governing equation is solved numerically with various prescribed density gradients that are designed to produce different configurations of parallel and anti-parallel streams. Long-lasting vortices form whose flow is governed by the zonal streams. It is found that the numerically generated PDFs can be matched with analytical predictions of PDFs based on the instanton method by removing the autocorrelations from the time series. In many instances, the statistics generated by the CHM dynamics relaxesmore » to Gaussian distributions for both the electrostatic and vorticity perturbations, whereas in areas with strong nonlinear interactions it is found that the PDFs are exponentially distributed.« less

Torus Knot Polynomials and Susy Wilson Loops

NASA Astrophysics Data System (ADS)

Giasemidis, Georgios; Tierz, Miguel

2014-12-01

We give, using an explicit expression obtained in (Jones V, Ann Math 126:335, 1987), a basic hypergeometric representation of the HOMFLY polynomial of ( n, m) torus knots, and present a number of equivalent expressions, all related by Heine's transformations. Using this result, the symmetry and the leading polynomial at large N are explicit. We show the latter to be the Wilson loop of 2d Yang-Mills theory on the plane. In addition, after taking one winding to infinity, it becomes the Wilson loop in the zero instanton sector of the 2d Yang-Mills theory, which is known to give averages of Wilson loops in = 4 SYM theory. We also give, using matrix models, an interpretation of the HOMFLY polynomial and the corresponding Jones-Rosso representation in terms of q-harmonic oscillators.

Surface operators in 5d gauge theories and duality relations

NASA Astrophysics Data System (ADS)

Ashok, S. K.; Billò, M.; Dell'Aquila, E.; Frau, M.; Gupta, V.; John, R. R.; Lerda, A.

2018-05-01

We study half-BPS surface operators in 5d N = 1 gauge theories compactified on a circle. Using localization methods and the twisted chiral ring relations of coupled 3d/5d quiver gauge theories, we calculate the twisted chiral superpotential that governs the infrared properties of these surface operators. We make a detailed analysis of the localization integrand, and by comparing with the results from the twisted chiral ring equations, we obtain constraints on the 3d and 5d Chern-Simons levels so that the instanton partition function does not depend on the choice of integration contour. For these values of the Chern-Simons couplings, we comment on how the distinct quiver theories that realize the same surface operator are related to each other by Aharony-Seiberg dualities.

Retrofitting and the mu Problem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Green, Daniel; Weigand, Timo; /SLAC /Stanford U., Phys. Dept.

2010-08-26

One of the challenges of supersymmetry (SUSY) breaking and mediation is generating a {mu} term consistent with the requirements of electro-weak symmetry breaking. The most common approach to the problem is to generate the {mu} term through a SUSY breaking F-term. Often these models produce unacceptably large B{mu} terms as a result. We will present an alternate approach, where the {mu} term is generated directly by non-perturtative effects. The same non-perturbative effect will also retrofit the model of SUSY breaking in such a way that {mu} is at the same scale as masses of the Standard Model superpartners. Because themore » {mu} term is not directly generated by SUSY breaking effects, there is no associated B{mu} problem. These results are demonstrated in a toy model where a stringy instanton generates {mu}.« less

Hydrodynamics of the Polyakov line in SU(N c) Yang-Mills

DOE PAGES

Liu, Yizhuang; Warchoł, Piotr; Zahed, Ismail

2015-12-08

We discuss a hydrodynamical description of the eigenvalues of the Polyakov line at large but finite N c 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 N c, and are consistent with the string model results at N c = ∞. The stochastic relaxation of the eigenvalues of the Polyakov line out ofmore » equilibrium is captured by a hydrodynamical instanton. An estimate of the probability of formation of a Z(N c)bubble using a piece-wise sound wave is suggested.« less

Inflation from periodic extra dimensions

NASA Astrophysics Data System (ADS)

Higaki, Tetsutaro; Tatsuta, Yoshiyuki

2017-07-01

We discuss a realization of a small field inflation based on string inspired supergravities. In theories accompanying extra dimensions, compactification of them with small radii is required for realistic situations. Since the extra dimension can have a periodicity, there will appear (quasi-)periodic functions under transformations of moduli of the extra dimensions in low energy scales. Such a periodic property can lead to a UV completion of so-called multi-natural inflation model where inflaton potential consists of a sum of multiple sinusoidal functions with a decay constant smaller than the Planck scale. As an illustration, we construct a SUSY breaking model, and then show that such an inflaton potential can be generated by a sum of world sheet instantons in intersecting brane models on extra dimensions containing orbifold. We show also predictions of cosmic observables by numerical analyzes.

Neutron Electric Dipole Moment from Gauge-String Duality.

PubMed

Bartolini, Lorenzo; Bigazzi, Francesco; Bolognesi, Stefano; Cotrone, Aldo L; Manenti, Andrea

2017-03-03

We compute the electric dipole moment of nucleons in the large N_{c} QCD model by Witten, Sakai, and Sugimoto with N_{f}=2 degenerate massive flavors. Baryons in the model are instantonic solitons of an effective five-dimensional action describing the whole tower of mesonic fields. We find that the dipole electromagnetic form factor of the nucleons, induced by a finite topological θ angle, exhibits complete vector meson dominance. We are able to evaluate the contribution of each vector meson to the final result-a small number of modes are relevant to obtain an accurate estimate. Extrapolating the model parameters to real QCD data, the neutron electric dipole moment is evaluated to be d_{n}=1.8×10^{-16}θ e cm. The electric dipole moment of the proton is exactly the opposite.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Scargill, James H. C.

Theories with more than one vacuum allow quantum transitions between them, which may proceed via bubble nucleation; theories with more than two vacua posses additional decay modes in which the wall of a bubble may further decay. The instantons which mediate such a process have O(3) symmetry (in four dimensions, rather than the usual O(4) symmetry of homogeneous vacuum decay), and have been called ‘barnacles’; previously they have been studied in flat space, in the thin wall limit, and this paper extends the analysis to include gravity. It is found that there are regions of parameter space in which, givenmore » an initial bubble, barnacles are the favoured subsequent decay process, and that the inclusion of gravity can enlarge this region. The relation to other heterogeneous vacuum decay scenarios, as well as some of the phenomenological implications of barnacles are briefly discussed.« less

Topology (and axion's properties) from lattice QCD with a dynamical charm

NASA Astrophysics Data System (ADS)

Burger, Florian; Ilgenfritz, Ernst-Michael; Lombardo, Maria Paola; Müller-Preussker, Michael; Trunin, Anton

2017-11-01

We present results on QCD with four dynamical flavors in the temperature range 0.9 ≲ T /Tc ≲ 2. We have performed lattice simulations with Wilson fermions at maximal twist and measured the topological charge with gluonic and fermionic methods. The topological charge distribution is studied by means of its cumulants, which encode relevant properties of the QCD axion, a plausible Dark Matter candidate. The topological susceptibility measured with the fermionic method exhibits a power-law decay for T /Tc ≳ 2, with an exponent close to the one predicted by the Dilute Instanton Gas Approximation (DIGA). Close to Tc the temperature dependent effective exponent approaches the DIGA result from above, in agreement with recent analytic calculations. These results constrain the axion window, once an assumption on the fraction of axions contributing to Dark Matter is made.

Magnetically charged calorons with non-trivial holonomy

NASA Astrophysics Data System (ADS)

Kato, Takumi; Nakamula, Atsushi; Takesue, Koki

2018-06-01

Instantons in pure Yang-Mills theories on partially periodic space R^3× {S}^1 are usually called calorons. The background periodicity brings on characteristic features of calorons such as non-trivial holonomy, which plays an essential role for confinement/deconfinement transition in pure Yang-Mills gauge theory. For the case of gauge group SU(2), calorons can be interpreted as composite objects of two constituent "monopoles" with opposite magnetic charges. There are often the cases that the two monopole charges are unbalanced so that the calorons possess net magnetic charge in R3. In this paper, we consider several mechanism how such net magnetic charges appear for certain types of calorons through the ADHM/Nahm construction with explicit examples. In particular, we construct analytically the gauge configuration of the (2 , 1)-caloron with U(1)-symmetry, which has intrinsically magnetic charge.

Reflection states in Ding-Iohara-Miki algebra and brane-web for D-type quiver

NASA Astrophysics Data System (ADS)

Bourgine, J.-E.; Fukuda, M.; Matsuo, Y.; Zhu, R.-D.

2017-12-01

Reflection states are introduced in the vertical and horizontal modules of the Ding-Iohara-Miki (DIM) algebra (quantum toroidal gl_1 ). Webs of DIM representations are in correspondence with ( p, q)-web diagrams of type IIB string theory, under the identification of the algebraic intertwiner of Awata, Feigin and Shiraishi with the refined topological vertex. Extending the correspondence to the vertical reflection states, it is possible to engineer the N=1 quiver gauge theory of D-type (with unitary gauge groups). In this way, the Nekrasov instanton partition function is reproduced from the evaluation of expectation values of intertwiners. This computation leads to the identification of the vertical reflection state with the orientifold plane of string theory. We also provide a translation of this construction in the Iqbal-Kozcaz-Vafa refined topological vertex formalism.

Inflation from periodic extra dimensions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Higaki, Tetsutaro; Tatsuta, Yoshiyuki, E-mail: thigaki@rk.phys.keio.ac.jp, E-mail: y_tatsuta@akane.waseda.jp

We discuss a realization of a small field inflation based on string inspired supergravities. In theories accompanying extra dimensions, compactification of them with small radii is required for realistic situations. Since the extra dimension can have a periodicity, there will appear (quasi-)periodic functions under transformations of moduli of the extra dimensions in low energy scales. Such a periodic property can lead to a UV completion of so-called multi-natural inflation model where inflaton potential consists of a sum of multiple sinusoidal functions with a decay constant smaller than the Planck scale. As an illustration, we construct a SUSY breaking model, andmore » then show that such an inflaton potential can be generated by a sum of world sheet instantons in intersecting brane models on extra dimensions containing orbifold. We show also predictions of cosmic observables by numerical analyzes.« less

Magnetic disorder in superconductors: Enhancement by mesoscopic fluctuations

NASA Astrophysics Data System (ADS)

Burmistrov, I. S.; Skvortsov, M. A.

2018-01-01

We study the density of states (DOS) and the transition temperature Tc in a dirty superconducting film with rare classical magnetic impurities of an arbitrary strength described by the Poissonian statistics. We take into account that the potential disorder is a source of mesoscopic fluctuations of the local DOS, and, consequently, of the effective strength of magnetic impurities. We find that these mesoscopic fluctuations result in a nonzero DOS for all energies in the region of the phase diagram where without this effect the DOS is zero within the standard mean-field theory. This mechanism can be more efficient in filling the mean-field superconducting gap than rare fluctuations of the potential disorder (instantons). Depending on the magnetic impurity strength, the suppression of Tc by spin-flip scattering can be faster or slower than in the standard mean-field theory.

Phases of five-dimensional theories, monopole walls, and melting crystals

NASA Astrophysics Data System (ADS)

Cherkis, Sergey A.

2014-06-01

Moduli spaces of doubly periodic monopoles, also called monopole walls or monowalls, are hyperkähler; thus, when four-dimensional, they are self-dual gravitational instantons. We find all monowalls with lowest number of moduli. Their moduli spaces can be identified, on the one hand, with Coulomb branches of five-dimensional supersymmetric quantum field theories on 3 × T 2 and, on the other hand, with moduli spaces of local Calabi-Yau metrics on the canonical bundle of a del Pezzo surface. We explore the asymptotic metric of these moduli spaces and compare our results with Seiberg's low energy description of the five-dimensional quantum theories. We also give a natural description of the phase structure of general monowall moduli spaces in terms of triangulations of Newton polygons, secondary polyhedra, and associahedral projections of secondary fans.

Small instanton transitions for M5 fractions

NASA Astrophysics Data System (ADS)

Mekareeya, Noppadol; Ohmori, Kantaro; Shimizu, Hiroyuki; Tomasiello, Alessandro

2017-10-01

M5-branes on an ADE singularity are described by certain six-dimensional "conformal matter" superconformal field theories. Their Higgs moduli spaces contain information about various dynamical processes for the M5s; however, they are not directly accessible due to the lack of a Lagrangian formulation. Using anomaly matching, we compute their dimensions. The result implies that M5 fractions can recombine in several different ways, where the M5s are leaving behind frozen versions of the singularity. The anomaly polynomial gives hints about the nature of the freezing. We also check the Higgs dimension formula by comparing it with various existing conjectures for the CFTs one obtains by torus compactifications down to four and three dimensions. Aided by our results, we also extend those conjectures to compactifications of theories not previously considered. These involve class S theories with twisted punctures in four dimensions, and affine-Dynkin-shaped quivers in three dimensions.

Barnacles and gravity

DOE PAGES

Scargill, James H. C.

2017-09-18

Theories with more than one vacuum allow quantum transitions between them, which may proceed via bubble nucleation; theories with more than two vacua posses additional decay modes in which the wall of a bubble may further decay. The instantons which mediate such a process have O(3) symmetry (in four dimensions, rather than the usual O(4) symmetry of homogeneous vacuum decay), and have been called ‘barnacles’; previously they have been studied in flat space, in the thin wall limit, and this paper extends the analysis to include gravity. It is found that there are regions of parameter space in which, givenmore » an initial bubble, barnacles are the favoured subsequent decay process, and that the inclusion of gravity can enlarge this region. The relation to other heterogeneous vacuum decay scenarios, as well as some of the phenomenological implications of barnacles are briefly discussed.« less

The Infinitesimal Moduli Space of Heterotic G 2 Systems

NASA Astrophysics Data System (ADS)

de la Ossa, Xenia; Larfors, Magdalena; Svanes, Eirik E.

2018-06-01

Heterotic string compactifications on integrable G 2 structure manifolds Y with instanton bundles {(V,A), (TY,\\tilde{θ})} yield supersymmetric three-dimensional vacua that are of interest in physics. In this paper, we define a covariant exterior derivative D and show that it is equivalent to a heterotic G 2 system encoding the geometry of the heterotic string compactifications. This operator D acts on a bundle Q}=T^*Y \\oplus End(V) \\oplus End(TY)} and satisfies a nilpotency condition \\check{{D^2=0} , for an appropriate projection of D. Furthermore, we determine the infinitesimal moduli space of these systems and show that it corresponds to the finite-dimensional cohomology group H^1_{D}(Q). We comment on the similarities and differences of our result with Atiyah's well-known analysis of deformations of holomorphic vector bundles over complex manifolds. Our analysis leads to results that are of relevance to all orders in the {α'} expansion.

Four-dimensional gravity as an almost-Poisson system

NASA Astrophysics Data System (ADS)

Ita, Eyo Eyo

2015-04-01

In this paper, we examine the phase space structure of a noncanonical formulation of four-dimensional gravity referred to as the Instanton representation of Plebanski gravity (IRPG). The typical Hamiltonian (symplectic) approach leads to an obstruction to the definition of a symplectic structure on the full phase space of the IRPG. We circumvent this obstruction, using the Lagrange equations of motion, to find the appropriate generalization of the Poisson bracket. It is shown that the IRPG does not support a Poisson bracket except on the vector constraint surface. Yet there exists a fundamental bilinear operation on its phase space which produces the correct equations of motion and induces the correct transformation properties of the basic fields. This bilinear operation is known as the almost-Poisson bracket, which fails to satisfy the Jacobi identity and in this case also the condition of antisymmetry. We place these results into the overall context of nonsymplectic systems.

Exact semiclassical expansions for one-dimensional quantum oscillators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Delabaere, E.; Dillinger, H.; Pham, F.

1997-12-01

A set of rules is given for dealing with WKB expansions in the one-dimensional analytic case, whereby such expansions are not considered as approximations but as exact encodings of wave functions, thus allowing for analytic continuation with respect to whichever parameters the potential function depends on, with an exact control of small exponential effects. These rules, which include also the case when there are double turning points, are illustrated on various examples, and applied to the study of bound state or resonance spectra. In the case of simple oscillators, it is thus shown that the Rayleigh{endash}Schr{umlt o}dinger series is Borelmore » resummable, yielding the exact energy levels. In the case of the symmetrical anharmonic oscillator, one gets a simple and rigorous justification of the Zinn-Justin quantization condition, and of its solution in terms of {open_quotes}multi-instanton expansions.{close_quotes} {copyright} {ital 1997 American Institute of Physics.}« less

Identification of structural motifs as tunneling two-level systems in amorphous alumina at low temperatures

NASA Astrophysics Data System (ADS)

Paz, Alejandro Pérez; Lebedeva, Irina V.; Tokatly, Ilya V.; Rubio, Angel

2014-12-01

One of the most accepted models that describe the anomalous thermal behavior of amorphous materials at temperatures below 1 K relies on the quantum mechanical tunneling of atoms between two nearly equivalent potential energy wells forming a two-level system (TLS). Indirect evidence for TLSs is widely available. However, the atomistic structure of these TLSs remains an unsolved topic in the physics of amorphous materials. Here, using classical molecular dynamics, we found several hitherto unknown bistable structural motifs that may be key to understanding the anomalous thermal properties of amorphous alumina at low temperatures. We show through free energy profiles that the complex potential energy surface can be reduced to canonical TLSs. The tunnel splitting predicted from instanton theory, the number density, dipole moment, and coupling to external strain of the discovered motifs are consistent with experiments.

Transdimensional tunneling in the multiverse

DOE Office of Scientific and Technical Information (OSTI.GOV)

Blanco-Pillado, Jose J.; Schwartz-Perlov, Delia; Vilenkin, Alexander, E-mail: jose@cosmos.phy.tufts.edu, E-mail: dperlov@cosmos.phy.tufts.edu, E-mail: vilenkin@cosmos.phy.tufts.edu

2010-05-01

Topology-changing transitions between vacua of different effective dimensionality are studied in the context of a 6-dimensional Einstein-Maxwell theory. The landscape of this theory includes a 6d de Sitter vacuum (dS{sub 6}), a number of dS{sub 4} × S{sub 2} and AdS{sub 4} × S{sub 2} vacua, and a number of AdS{sub 2} × S{sub 4} vacua. We find that compactification transitions dS{sub 6} → AdS{sub 2} × S{sub 4} occur through the nucleation of electrically charged black hole pairs, and transitions from dS{sub 6} to dS{sub 4} × S{sub 2} and AdS{sub 4} × S{sub 2} occur through the nucleationmore » of magnetically charged spherical black branes. We identify the appropriate instantons and describe the spacetime structure resulting from brane nucleation.« less

Understanding Quantum Tunneling through Quantum Monte Carlo Simulations.

PubMed

Isakov, Sergei V; Mazzola, Guglielmo; Smelyanskiy, Vadim N; Jiang, Zhang; Boixo, Sergio; Neven, Hartmut; Troyer, Matthias

2016-10-28

The tunneling between the two ground states of an Ising ferromagnet is a typical example of many-body tunneling processes between two local minima, as they occur during quantum annealing. Performing quantum Monte Carlo (QMC) simulations we find that the QMC tunneling rate displays the same scaling with system size, as the rate of incoherent tunneling. The scaling in both cases is O(Δ^{2}), where Δ is the tunneling splitting (or equivalently the minimum spectral gap). An important consequence is that QMC simulations can be used to predict the performance of a quantum annealer for tunneling through a barrier. Furthermore, by using open instead of periodic boundary conditions in imaginary time, equivalent to a projector QMC algorithm, we obtain a quadratic speedup for QMC simulations, and achieve linear scaling in Δ. We provide a physical understanding of these results and their range of applicability based on an instanton picture.

Ubiquity of non-geometry in heterotic compactifications

DOE PAGES

García-Etxebarria, Iñaki; Lüst, Dieter; Massai, Stefano; ...

2017-03-08

Here, we study the effect of quantum corrections on heterotic compactifications on elliptic fibrations away from the stable degeneration limit, elaborating on a recent observation by Malmendier and Morrison. We show that already for the simplest nontrivial elliptic fibration the effect is quite dramatic: the I 1 degeneration with trivial gauge background dynamically splits into two T-fects with monodromy around each T-fect being (conjugate to) T-duality along one of the legs of the T 2. This implies that almost every elliptic heterotic compactification becomes a non-geometric T-fold away from the stable degeneration limit. We also point out a subtlety duemore » to this non-geometric splitting at finite fiber size. It arises when determining, via heterotic/F-theory duality, the SCFTs associated to a small number of pointlike instantons probing heterotic ADE singularities. Along the way we resolve various puzzles in the literature.« less

Pair creation of higher dimensional black holes on a de Sitter background

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dias, Oscar J.C.; Lemos, Jose P.S.; CENTRA, Departamento de Fisica, F.C.T., Universidade do Algarve, Campus de Gambelas, 8005-139 Faro

We study in detail the quantum process in which a pair of black holes is created in a higher D-dimensional de Sitter (dS) background. The energy to materialize and accelerate the pair comes from the positive cosmological constant. The instantons that describe the process are obtained from the Tangherlini black hole solutions. Our pair creation rates reduce to the pair creation rate for Reissner-Nordstroem-dS solutions when D=4. Pair creation of black holes in the dS background becomes less suppressed when the dimension of the spacetime increases. The dS space is the only background in which we can discuss analytically themore » pair creation process of higher dimensional black holes, since the C-metric and the Ernst solutions, which describe, respectively, a pair accelerated by a string and by an electromagnetic field, are not known yet in a higher dimensional spacetime.« less

Reaction rates and kinetic isotope effects of H{sub 2} + OH → H{sub 2}O + H

DOE Office of Scientific and Technical Information (OSTI.GOV)

Meisner, Jan; Kästner, Johannes, E-mail: kaestner@theochem.uni-stuttgart.de

2016-05-07

We calculated reaction rate constants including atom tunneling of the reaction of dihydrogen with the hydroxy radical down to a temperature of 50 K. Instanton theory and canonical variational theory with microcanonical optimized multidimensional tunneling were applied using a fitted potential energy surface [J. Chen et al., J. Chem. Phys. 138, 154301 (2013)]. All possible protium/deuterium isotopologues were considered. Atom tunneling increases at about 250 K (200 K for deuterium transfer). Even at 50 K the rate constants of all isotopologues remain in the interval 4 ⋅ 10{sup −20} to 4 ⋅ 10{sup −17} cm{sup 3} s{sup −1}, demonstrating thatmore » even deuterated versions of the title reaction are possibly relevant to astrochemical processes in molecular clouds. The transferred hydrogen atom dominates the kinetic isotope effect at all temperatures.« less

Black hole attractors and gauge theories

NASA Astrophysics Data System (ADS)

Huang, Lisa Li Fang

2007-12-01

This thesis is devoted to the study of supersymmetric black holes that arise from string compactifications. We begin by studying the R 2 corrections to the entropy of two solutions of five dimensional supergravity, the supersymmetric black ring and the spinning black hole. Using Wald's formula we compute the R2 corrections to the entropy of the black ring and BMPV black hole. We study N D4-branes wrapping a 4 cycle and M DO-branes on the quintic. For N D4-branes, we resolve the naive mismatch between the moduli space of the Higgs branch of the gauge theory and the moduli of a degree N hypersurface which the D4-brane wraps. The degree N surface must admit a holomorphic divisor and is a determinantal variety. Adding a single DO brane to probe the deformed geometry, we recover the determinant equation from F and D flatness condition which was previously discovered from a classical geometry approach. We next generalize the qunitic story for Calabi-Yau manifolds arising from complete intersections in toric varieties. We recover the moduli space of N D4-branes in terms of the moduli space of a U( N) x U(N) gauge theory with bi-fundamentals com ing from a D6 - D6 system. We also recast the tachyon condensation of the D6 - D6 system in the language of open string gauged linear sigma model. We obtain the determinant equation from F-term constraints arising from a boundary coupling. We set out to understand the Ooguri-Strominger-Vafa conjecture directly in the D4-DO black hole attractor geometry. We show that the lift to the euclidean IIA attractor geometry gives a complexified M-theory geometry whose asymptotic boundary is a torus. Employing AdS3/CFT 2 duality, we argue that the string partition function computes the elliptic genus of the Maldacena-Strominger-Witten conformal field theory. We evaluate the IIA partition function using the Green-Schwarz formalism and show that it gives ZtopZ top, coming from instantons and anti-instantons respectively. Finally, we determine the spectrum of free, large N, SU( N) Yang Mills theory on S3 by decomposing its thermal partition function into characters of the irreducible representations of the conformal group SO(4, 2).

Negative branes, supergroups and the signature of spacetime

NASA Astrophysics Data System (ADS)

Dijkgraaf, Robbert; Heidenreich, Ben; Jefferson, Patrick; Vafa, Cumrun

2018-02-01

We study the realization of supergroup gauge theories using negative branes in string theory. We show that negative branes are intimately connected with the possibility of timelike compactification and exotic spacetime signatures previously studied by Hull. Isolated negative branes dynamically generate a change in spacetime signature near their worldvolumes, and are related by string dualities to a smooth M-theory geometry with closed timelike curves. Using negative D3-branes, we show that SU(0| N) supergroup theories are holographically dual to an exotic variant of type IIB string theory on {dS}_{3,2}× {\\overline{S}}^5 , for which the emergent dimensions are timelike. Using branes, mirror symmetry and Nekrasov's instanton calculus, all of which agree, we derive the Seiberg-Witten curve for N=2 SU( N | M ) gauge theories. Together with our exploration of holography and string dualities for negative branes, this suggests that supergroup gauge theories may be non-perturbatively well-defined objects, though several puzzles remain.

Elliptic genus of E-strings

NASA Astrophysics Data System (ADS)

Kim, Joonho; Kim, Seok; Lee, Kimyeong; Park, Jaemo; Vafa, Cumrun

2017-09-01

We study a family of 2d N=(0, 4) gauge theories which describes at low energy the dynamics of E-strings, the M2-branes suspended between a pair of M5 and M9 branes. The gauge theory is engineered using a duality with type IIA theory, leading to the D2-branes suspended between an NS5-brane and 8 D8-branes on an O8-plane. We compute the elliptic genus of this family of theories, and find agreement with the known results for single and two E-strings. The partition function can in principle be computed for arbitrary number of E-strings, and we compute them explicitly for low numbers. We test our predictions against the partially known results from topological strings, as well as from the instanton calculus of 5d Sp(1) gauge theory. Given the relation to topological strings, our computation provides the all genus partition function of the refined topological strings on the canonical bundle over 1/2K3.

Weak-noise limit of a piecewise-smooth stochastic differential equation.

PubMed

Chen, Yaming; Baule, Adrian; Touchette, Hugo; Just, Wolfram

2013-11-01

We investigate the validity and accuracy of weak-noise (saddle-point or instanton) approximations for piecewise-smooth stochastic differential equations (SDEs), taking as an illustrative example a piecewise-constant SDE, which serves as a simple model of Brownian motion with solid friction. For this model, we show that the weak-noise approximation of the path integral correctly reproduces the known propagator of the SDE at lowest order in the noise power, as well as the main features of the exact propagator with higher-order corrections, provided the singularity of the path integral associated with the nonsmooth SDE is treated with some heuristics. We also show that, as in the case of smooth SDEs, the deterministic paths of the noiseless system correctly describe the behavior of the nonsmooth SDE in the low-noise limit. Finally, we consider a smooth regularization of the piecewise-constant SDE and study to what extent this regularization can rectify some of the problems encountered when dealing with discontinuous drifts and singularities in SDEs.

Orientifolding of the ABJ Fermi gas

NASA Astrophysics Data System (ADS)

Okuyama, Kazumi

2016-03-01

The grand partition functions of ABJ theory can be factorized into even and odd parts under the reflection of fermion coordinate in the Fermi gas approach. In some cases, the even/odd part of ABJ grand partition function is equal to that of {N}=5O(n)× USp({n}^') theory, hence it is natural to think of the even/odd projection of grand partition function as an orientifolding of ABJ Fermi gas system. By a systematic WKB analysis, we determine the coefficients in the perturbative part of grand potential of such orientifold ABJ theory. We also find the exact form of the first few "half-instanton" corrections coming from the twisted sector of the reflection of fermion coordinate. For the Chern-Simons level k = 2 ,4 ,8 we find closed form expressions of the grand partition functions of orientifold ABJ theory, and for k = 2 , 4 we prove the functional relations among the grand partition functions conjectured in arXiv:1410.7658.

Confinement and Mayer cluster expansions

NASA Astrophysics Data System (ADS)

Bourgine, Jean-Emile

2014-05-01

In this paper, we study a class of grand-canonical partition functions with a kernel depending on a small parameter ɛ. This class is directly relevant to Nekrasov partition functions of 𝒩 = 2 SUSY gauge theories on the 4d Ω-background, for which ɛ is identified with one of the equivariant deformation parameter. In the Nekrasov-Shatashvili limit ɛ→0, we show that the free energy is given by an on-shell effective action. The equations of motion take the form of a TBA equation. The free energy is identified with the Yang-Yang functional of the corresponding system of Bethe roots. We further study the associated canonical model that takes the form of a generalized matrix model. Confinement of the eigenvalues by the short-range potential is observed. In the limit where this confining potential becomes weak, the collective field theory formulation is recovered. Finally, we discuss the connection with the alternative expression of instanton partition functions as sums over Young tableaux.

PSEUDO-CODEWORD LANDSCAPE

DOE Office of Scientific and Technical Information (OSTI.GOV)

CHERTKOV, MICHAEL; STEPANOV, MIKHAIL

2007-01-10

The authors discuss performance of Low-Density-Parity-Check (LDPC) codes decoded by Linear Programming (LP) decoding at moderate and large Signal-to-Noise-Ratios (SNR). Frame-Error-Rate (FER) dependence on SNR and the noise space landscape of the coding/decoding scheme are analyzed by a combination of the previously introduced instanton/pseudo-codeword-search method and a new 'dendro' trick. To reduce complexity of the LP decoding for a code with high-degree checks, {ge} 5, they introduce its dendro-LDPC counterpart, that is the code performing identifically to the original one under Maximum-A-Posteriori (MAP) decoding but having reduced (down to three) check connectivity degree. Analyzing number of popular LDPC codes andmore » their dendro versions performing over the Additive-White-Gaussian-Noise (AWGN) channel, they observed two qualitatively different regimes: (i) error-floor sets early, at relatively low SNR, and (ii) FER decays with SNR increase faster at moderate SNR than at the largest SNR. They explain these regimes in terms of the pseudo-codeword spectra of the codes.« less

Tunnelling with a negative cosmological constant

NASA Astrophysics Data System (ADS)

Gibbons, G. W.

1996-02-01

The point of this paper is to see what light new results in hyperbolic geometry may throw on gravitational entropy and whether gravitational entropy is relevant for the quantum origin of the universe. We introduce some new gravitational instantons which mediate the birth from nothing of closed universes containing wormholes and suggest that they may contribute to the density matrix of the universe. We also discuss the connection between their gravitational action and the topological and volumetric entropies introduced in hyperbolic geometry. These coincide for hyperbolic 4-manifolds, and increase with increasing topological complexity of the 4-manifold. We raise the question of whether the action also increases with the topological complexity of the initial 3-geometry, measured either by its 3-volume or its Matveev complexity. We point out, in distinction to the non-supergravity case, that universes with domains of negative cosmological constant separated by supergravity domain walls cannot be born from nothing. Finally we point out that our wormholes provide examples of the type of Perpetual Motion machines envisaged by Frolov and Novikov.

Gravitational decoupling and the Picard-Lefschetz approach

NASA Astrophysics Data System (ADS)

Brown, Jon; Cole, Alex; Shiu, Gary; Cottrell, William

2018-01-01

In this work, we consider tunneling between nonmetastable states in gravitational theories. Such processes arise in various contexts, e.g., in inflationary scenarios where the inflaton potential involves multiple fields or multiple branches. They are also relevant for bubble wall nucleation in some cosmological settings. However, we show that the transition amplitudes computed using the Euclidean method generally do not approach the corresponding field theory limit as Mp→∞ . This implies that in the Euclidean framework, there is no systematic expansion in powers of GN for such processes. Such considerations also carry over directly to no-boundary scenarios involving Hawking-Turok instantons. In this note, we illustrate this failure of decoupling in the Euclidean approach with a simple model of axion monodromy and then argue that the situation can be remedied with a Lorentzian prescription such as the Picard-Lefschetz theory. As a proof of concept, we illustrate with a simple model how tunneling transition amplitudes can be calculated using the Picard-Lefschetz approach.

The problems in quantum foundations in the light of gauge theories

NASA Astrophysics Data System (ADS)

Ne'Eman, Yuval

1986-04-01

We review the issues of nonseparability and seemingly acausal propagation of information in EPR, as displayed by experiments and the failure of Bell's inequalities. We show that global effects are in the very nature of the geometric structure of modern physical theories, occurring even at the classical level. The Aharonov-Bohm effect, magnetic monopoles, instantons, etc. result from the topology and homotopy features of the fiber bundle manifolds of gauge theories. The conservation of probabilities, a supposedly highly quantum effect, is also achieved through global geometry equations. The EPR observables all fit in such geometries, and space-time is a truncated representation and is not the correct arena for their understanding. Relativistic quantum field theory represents the global action of the measurement operators as the zero-momentum (and therefore spatially infinitely spread) limit of their wave functions (form factors). We also analyze the collapse of the state vector as a case of spontaneous symmetry breakdown in the apparatus-observed state interaction.

Quantum Monte Carlo tunneling from quantum chemistry to quantum annealing

NASA Astrophysics Data System (ADS)

Mazzola, Guglielmo; Smelyanskiy, Vadim N.; Troyer, Matthias

2017-10-01

Quantum tunneling is ubiquitous across different fields, from quantum chemical reactions and magnetic materials to quantum simulators and quantum computers. While simulating the real-time quantum dynamics of tunneling is infeasible for high-dimensional systems, quantum tunneling also shows up in quantum Monte Carlo (QMC) simulations, which aim to simulate quantum statistics with resources growing only polynomially with the system size. Here we extend the recent results obtained for quantum spin models [Phys. Rev. Lett. 117, 180402 (2016), 10.1103/PhysRevLett.117.180402], and we study continuous-variable models for proton transfer reactions. We demonstrate that QMC simulations efficiently recover the scaling of ground-state tunneling rates due to the existence of an instanton path, which always connects the reactant state with the product. We discuss the implications of our results in the context of quantum chemical reactions and quantum annealing, where quantum tunneling is expected to be a valuable resource for solving combinatorial optimization problems.

Duality between electric and magnetic black holes

NASA Astrophysics Data System (ADS)

Hawking, S. W.; Ross, Simon F.

1995-11-01

A number of attempts have recently been made to extend the conjectured S duality of Yang-Mills theory to gravity. Central to these speculations has been the belief that electrically and magnetically charged black holes, the solitons of quantum gravity, have identical quantum properties. This is not obvious, because, although duality is a symmetry of the classical equations of motion, it changes the sign of the Maxwell action. Nevertheless, we show that the chemical potential and charge projection that one has to introduce for electric but not magnetic black holes exactly compensate for the difference in action in the semiclassical approximation. In particular, we show that the pair production of electric black holes is not a runaway process, as one might think if one just went by the action of the relevant instanton. We also comment on the definition of the entropy in cosmological situations, and show that we need to be more careful when defining the entropy than we are in an asymptotically flat case.

A Deconstruction Lattice Description of the D1/D5 Brane World-Volume Gauge Theory

DOE PAGES

Giedt, Joel

2011-01-01

I genermore » alize the deconstruction lattice formulation of Endres and Kaplan to two-dimensional super-QCD with eight supercharges, denoted by (4,4), and bifundamental matter. I specialize to a particularly interesting (4,4) gauge theory, with gauge group U ( N c ) × U ( N f ) , and U ( N f ) being weakly gauged. It describes the infrared limit of the D1/D5 brane system, which has been studied extensively as an example of the AdS 3 /CFT 2 correspondence. The construction here preserves two supercharges exactly and has a lattice structure quite similar to that which has previously appeared in the deconstruction approach, that is, site, link, and diagonal fields with both the Bose and Fermi statistics. I remark on possible applications of the lattice theory that would test the AdS 3 /CFT 2 correspondence, particularly one that would exploit the recent worldsheet instanton analysis of Chen and Tong.« less

E(lementary)-strings in six-dimensional heterotic F-theory

NASA Astrophysics Data System (ADS)

Choi, Kang-Sin; Rey, Soo-Jong

2017-09-01

Using E-strings, we can analyze not only six-dimensional superconformal field theories but also probe vacua of non-perturabative heterotic string. We study strings made of D3-branes wrapped on various two-cycles in the global F-theory setup. We claim that E-strings are elementary in the sense that various combinations of E-strings can form M-strings as well as heterotic strings and new kind of strings, called G-strings. Using them, we show that emissions and combinations of heterotic small instantons generate most of known six-dimensional superconformal theories, their affinizations and little string theories. Taking account of global structure of compact internal geometry, we also show that special combinations of E-strings play an important role in constructing six-dimensional theories of D- and E-types. We check global consistency conditions from anomaly cancellation conditions, both from five-branes and strings, and show that they are given in terms of elementary E-string combinations.

B-branes and supersymmetric quivers in 2d

NASA Astrophysics Data System (ADS)

Closset, Cyril; Guo, Jirui; Sharpe, Eric

2018-02-01

We study 2d N = (0, 2) supersymmetric quiver gauge theories that describe the low-energy dynamics of D1-branes at Calabi-Yau fourfold (CY4) singularities. On general grounds, the holomorphic sector of these theories — matter content and (classical) superpotential interactions — should be fully captured by the topological B-model on the CY4. By studying a number of examples, we confirm this expectation and flesh out the dictionary between B-brane category and supersymmetric quiver: the matter content of the supersymmetric quiver is encoded in morphisms between B-branes (that is, Ext groups of coherent sheaves), while the superpotential interactions are encoded in the A ∞ algebra satisfied by the morphisms. This provides us with a derivation of the supersymmetric quiver directly from the CY4 geometry. We also suggest a relation between triality of N = (0 ,2) gauge theories and certain mutations of exceptional collections of sheaves. 0d N = 1 supersymmetric quivers, corresponding to D-instantons probing CY5 singularities, can be discussed similarly.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nekrasov, Nikita; ITEP, Moscow; Shatashvili, Samson

Supersymmetric vacua of two dimensional N = 4 gauge theories with matter, softly broken by the twisted masses down to N = 2, are shown to be in one-to-one correspondence with the eigenstates of integrable spin chain Hamiltonians. Examples include: the Heisenberg SU(2)XXX spin chain which is mapped to the two dimensional U(N) theory with fundamental hypermultiplets, the XXZ spin chain which is mapped to the analogous three dimensional super-Yang-Mills theory compactified on a circle, the XYZ spin chain and eight-vertex model which are related to the four dimensional theory compactified on T{sup 2}. A consequence of our correspondence ismore » the isomorphism of the quantum cohomology ring of various quiver varieties, such as cotangent bundles to (partial) flag varieties and the ring of quantum integrals of motion of various spin chains. The correspondence extends to any spin group, representations, boundary conditions, and inhomogeneity, it includes Sinh-Gordon and non-linear Schroedinger models as well as the dynamical spin chains like Hubbard model. Compactifications of four dimensional N = 2 theories on a two-sphere lead to the instanton-corrected Bethe equations.« less

Twistor theory at fifty: from contour integrals to twistor strings

NASA Astrophysics Data System (ADS)

Atiyah, Michael; Dunajski, Maciej; Mason, Lionel J.

2017-10-01

We review aspects of twistor theory, its aims and achievements spanning the last five decades. In the twistor approach, space-time is secondary with events being derived objects that correspond to compact holomorphic curves in a complex threefold-the twistor space. After giving an elementary construction of this space, we demonstrate how solutions to linear and nonlinear equations of mathematical physics-anti-self-duality equations on Yang-Mills or conformal curvature-can be encoded into twistor cohomology. These twistor correspondences yield explicit examples of Yang-Mills and gravitational instantons, which we review. They also underlie the twistor approach to integrability: the solitonic systems arise as symmetry reductions of anti-self-dual (ASD) Yang-Mills equations, and Einstein-Weyl dispersionless systems are reductions of ASD conformal equations. We then review the holomorphic string theories in twistor and ambitwistor spaces, and explain how these theories give rise to remarkable new formulae for the computation of quantum scattering amplitudes. Finally, we discuss the Newtonian limit of twistor theory and its possible role in Penrose's proposal for a role of gravity in quantum collapse of a wave function.

Twistor theory at fifty: from contour integrals to twistor strings.

PubMed

Atiyah, Michael; Dunajski, Maciej; Mason, Lionel J

2017-10-01

We review aspects of twistor theory, its aims and achievements spanning the last five decades. In the twistor approach, space-time is secondary with events being derived objects that correspond to compact holomorphic curves in a complex threefold-the twistor space. After giving an elementary construction of this space, we demonstrate how solutions to linear and nonlinear equations of mathematical physics-anti-self-duality equations on Yang-Mills or conformal curvature-can be encoded into twistor cohomology. These twistor correspondences yield explicit examples of Yang-Mills and gravitational instantons, which we review. They also underlie the twistor approach to integrability: the solitonic systems arise as symmetry reductions of anti-self-dual (ASD) Yang-Mills equations, and Einstein-Weyl dispersionless systems are reductions of ASD conformal equations. We then review the holomorphic string theories in twistor and ambitwistor spaces, and explain how these theories give rise to remarkable new formulae for the computation of quantum scattering amplitudes. Finally, we discuss the Newtonian limit of twistor theory and its possible role in Penrose's proposal for a role of gravity in quantum collapse of a wave function.

Strangeness production in deep-inelastic positron-proton scattering at HERA

NASA Astrophysics Data System (ADS)

Aid, S.; Anderson, M.; Andreev, V.; Andrieu, B.; Appuhn, R.-D.; Babaev, A.; Bähr, J.; Bán, J.; Ban, Y.; Baranov, P.; Barrelet, E.; Barschke, R.; Bartel, W.; Barth, M.; Bassler, U.; Behrend, H.-J.; Belousov, A.; Berger, Ch.; Bernardi, G.; Bertrand-Coremans, G.; Besançon, M.; Beyer, R.; Biddulph, P.; Bispham, P.; Bizot, J. C.; Blobel, V.; Borras, K.; Botterweck, F.; Boudry, V.; Braemer, A.; Braunschweig, W.; Brisson, V.; Bruel, P.; Bruncko, D.; Brune, C.; Buchholz, R.; Büngener, L.; Bürger, J.; Büsser, F. W.; Buniatian, A.; Burke, S.; Burton, M. J.; Calvet, D.; Campbell, A. J.; Carli, T.; Charlet, M.; Clarke, D.; Clegg, A. B.; Clerbaux, B.; Cocks, S.; Contreras, J. G.; Cormack, C.; Coughlan, J. A.; Courau, A.; Cousinou, M.-C.; Cozzika, G.; Criegee, L.; Cussans, D. G.; Cvach, J.; Dagoret, S.; Dainton, J. B.; Dau, W. D.; Daum, K.; David, M.; Davis, C. L.; De Roeck, A.; De Wolf, E. A.; Delcourt, B.; Di Nezza, P.; Dirkmann, M.; Dixon, P.; Dlugosz, W.; Dollfus, C.; Dowell, J. D.; Dreis, H. B.; Droutskoi, A.; Dünger, O.; Duhm, H.; Ebert, J.; Ebert, T. R.; Eckerlin, G.; Efremenko, V.; Egli, S.; Eichler, R.; Eisele, F.; Eisenhandler, E.; Elsen, E.; Erdmann, M.; Erdmann, W.; Evrard, E.; Fahr, A. B.; Favart, L.; Fedotov, A.; Feeken, D.; Felst, R.; Feltesse, J.; Ferencei, J.; Ferrarotto, F.; Flamm, K.; Fleischer, M.; Flieseer, M.; Flügge, G.; Fomenko, A.; Fominykh, B.; Formánek, J.; Foster, J. M.; Franke, G.; Fretwurst, E.; Gabathuler, E.; Gabathuler, K.; Gaede, F.; Garvey, J.; Gayler, J.; Gebauer, M.; Genzel, H.; Gerhards, R.; Glazov, A.; Goerlach, U.; Goerlich, L.; Gogitidze, N.; Goldberg, M.; Goldner, D.; Golec-Biernat, K.; Gonzalez-Pineiro, B.; Gorelov, I.; Grab, C.; Grässler, H.; Greenshaw, T.; Griffiths, R. K.; Grindhammer, G.; Gruber, A.; Gruber, C.; Haack, J.; Hadig, T.; Haidt, D.; Haiduk, L.; Hampel, M.; Haynes, W. J.; Heinzelmann, G.; Henderson, R. C. M.; Henschel, H.; Herynek, I.; Hess, M. F.; Hewitt, K.; Hildesheim, W.; Hiller, K. H.; Hilton, C. D.; Hladký, J.; Hoeger, K. C.; Höppner, M.; Hoffmann, D.; Holtom, T.; Horisberger, R.; Hudgson, V. L.; Hütte, M.; Ibbotson, M.; Itterbeck, H.; Jacholkowska, A.; Jacobsson, C.; Jaffre, M.; Janoth, J.; Jansen, T.; Jönsson, L.; Johnson, D. P.; Jung, H.; Kalmus, P. I. P.; Kander, M.; Kant, D.; Kaschowitz, R.; Kathage, U.; Katzy, J.; Kaufmann, H. H.; Kaufmann, O.; Kazarian, S.; Kenyon, I. R.; Kermiche, S.; Keuker, C.; Kiesling, C.; Klein, M.; Kleinwort, C.; Knies, G.; Köhler, T.; Köhne, J. H.; Kole, F.; Kolya, S. D.; Korbel, V.; Korn, M.; Kostka, P.; Kotelnikov, S. K.; Krämerkämper, T.; Krasny, M. W.; Krehbiel, H.; Krücker, D.; Küster, H.; Kuhlen, M.; Kurča, T.; Kurzhöfer, J.; Lacour, D.; Laforge, B.; Lander, R.; Landon, M. P. J.; Lange, W.; Langenegger, U.; Laporte, J.-F.; Lebedev, A.; Lehner, F.; Levonian, S.; Lindström, G.; Lindstroem, M.; Link, J.; Linsel, F.; Lipinski, J.; List, B.; Lobo, G.; Lomas, J. W.; Lopez, G. C.; Lubimov, V.; Lüke, D.; Magnussen, N.; Malinovski, E.; Mani, S.; Maraček, R.; Marage, P.; Marks, J.; Marshall, R.; Martens, J.; Martin, G.; Martin, R.; Martyn, H.-U.; Martyniak, J.; Mavroidis, T.; Maxfield, S. J.; McMahon, S. J.; Mehta, A.; Meier, K.; Meyer, A.; Meyer, A.; Meyer, H.; Meyer, J.; Meyer, P.-O.; Megliori, A.; Mikocki, S.; Milstead, D.; Moeck, J.; Moreau, F.; Morris, J. V.; Mroczko, E.; Müller, D.; Müller, G.; Müller, M.; Müller, M.; Murín, P.; Nagovizin, V.; Nahnhauer, R.; Naroska, B.; Naumann, Th.; Négri, I.; Newman, P. R.; Newton, D.; Nguyen, H. K.; Nicholls, T. C.; Niebergall, F.; Niebuhr, C.; Niedzballa, Ch.; Niggli, H.; Nisius, R.; Nowak, G.; Noyes, G. W.; Nyberg-Werther, M.; Oakden, M.; Oberlack, H.; Olsson, J. E.; Ozerov, D.; Palmen, P.; Panaro, E.; Panitch, A.; Pascaud, C.; Patel, G. D.; Pawletta, H.; Peppel, E.; Perez, E.; Phillips, J. P.; Pieuchot, A.; Pitzl, D.; Pope, G.; Prell, S.; Rabbertz, K.; Rädel, G.; Reimer, P.; Reinshagen, S.; Rick, H.; Riech, V.; Riedlberger, J.; Riepenhausen, F.; Riess, S.; Rizvi, E.; Robertson, S. M.; Robmann, P.; Roloff, H. E.; Roosen, R.; Rosenbauer, K.; Rostovtsev, A.; Rouse, F.; Royon, C.; Rüter, K.; Rusakov, S.; Rybicki, K.; Sankey, D. P. C.; Schacht, P.; Schiek, S.; Schleif, S.; Schleper, P.; von Schlippe, W.; Schmidt, D.; Schmidt, G.; Schöning, A.; Schröder, V.; Schuhmann, E.; Schwab, B.; Sefkow, F.; Seidel, M.; Sell, R.; Semenov, A.; Shekelyan, V.; Sheviakov, I.; Shtarkov, L. N.; Siegmon, G.; Siewert, U.; Sirois, Y.; Skillicorn, I. O.; Smirnov, P.; Smith, J. R.; Solochenko, V.; Soloviev, Y.; Specka, A.; Spiekermann, J.; Spielman, S.; Spitzer, H.; Squinabol, F.; Steenbock, M.; Steffen, P.; Steinberg, R.; Steiner, H.; Steinhart, J.; Stella, B.; Stellberger, A.; Stier, J.; Stiewe, J.; Stößlein, U.; Stolze, K.; Straumann, U.; Struczinski, W.; Sutton, J. P.; Tapprogge, S.; Taševský, M.; Tchernyshov, V.; Tchetchelnitski, S.; Theissen, J.; Thiebaux, C.; Thompson, G.; Truöl, P.; Tsipolitis, G.; Turnau, J.; Tutas, J.; Uelkes, P.; Usik, A.; Valkár, S.; Valkárová, A.; Vallée, C.; Van Esch, P.; Van Mechelen, P.; Vandenplas, D.; Vazdik, Y.; Verrecchia, P.; Villet, G.; Wacker, K.; Wagener, A.; Wagener, M.; Walther, A.; Waugh, B.; Weber, G.; Weber, M.; Wegener, D.; Wegner, A.; Wengler, T.; Werner, M.; West, L. R.; Wilksen, T.; Willard, S.; Winde, M.; Winter, G.-G.; Wittek, C.; Wobisch, M.; Wünsch, E.; Žáček, J.; Zarbock, D.; Zhang, Z.; Zhokin, A.; Zini, P.; Zomer, F.; Zsembery, J.; Zuber, K.; zurNedden, M.; H1 Collaboration

1996-02-01

Measurements of K0 meson and Λ baryon production in deep-inelastic positron-proton scattering (DIS) are presented in the kinematic range 10 < Q2 < 70 GeV 2 and 10 -4 < x < 10 -2. The measurements, obtained using the H1 detector at the HEPA collider, are discussed in the light of possible mechanisms for increased strangeness production at low Bjorken- x. Comparisons of the xF spectra, where xF is the fractional longitudinal momentum in the hadronic centre-of-mass frame, are made with results from electron-positron annihilation. The xF spectra and the K0 "seagull" plot are compared with previous DIS results. The mean K0 and Λ multiplicities are studied as a function of the centre-of-mass energy W and are observed to be consistent with a logarithmic increase with W when compared with previous measurements. A comparison of strangeness production in diffractive and non-diffractive DIS is made. An upper limit of 0.9 nb, at the 95% confidence level, is placed on the cross section for QCD instanton induced events.

Surface operators, chiral rings and localization in N =2 gauge theories

NASA Astrophysics Data System (ADS)

Ashok, S. K.; Billò, M.; Dell'Aquila, E.; Frau, M.; Gupta, V.; John, R. R.; Lerda, A.

2017-11-01

We study half-BPS surface operators in supersymmetric gauge theories in four and five dimensions following two different approaches. In the first approach we analyze the chiral ring equations for certain quiver theories in two and three dimensions, coupled respectively to four- and five-dimensional gauge theories. The chiral ring equations, which arise from extremizing a twisted chiral superpotential, are solved as power series in the infrared scales of the quiver theories. In the second approach we use equivariant localization and obtain the twisted chiral superpotential as a function of the Coulomb moduli of the four- and five-dimensional gauge theories, and find a perfect match with the results obtained from the chiral ring equations. In the five-dimensional case this match is achieved after solving a number of subtleties in the localization formulas which amounts to choosing a particular residue prescription in the integrals that yield the Nekrasov-like partition functions for ramified instantons. We also comment on the necessity of including Chern-Simons terms in order to match the superpotentials obtained from dual quiver descriptions of a given surface operator.

Fermion-number violation in regularizations that preserve fermion-number symmetry

NASA Astrophysics Data System (ADS)

Golterman, Maarten; Shamir, Yigal

2003-01-01

There exist both continuum and lattice regularizations of gauge theories with fermions which preserve chiral U(1) invariance (“fermion number”). Such regularizations necessarily break gauge invariance but, in a covariant gauge, one recovers gauge invariance to all orders in perturbation theory by including suitable counterterms. At the nonperturbative level, an apparent conflict then arises between the chiral U(1) symmetry of the regularized theory and the existence of ’t Hooft vertices in the renormalized theory. The only possible resolution of the paradox is that the chiral U(1) symmetry is broken spontaneously in the enlarged Hilbert space of the covariantly gauge-fixed theory. The corresponding Goldstone pole is unphysical. The theory must therefore be defined by introducing a small fermion-mass term that breaks explicitly the chiral U(1) invariance and is sent to zero after the infinite-volume limit has been taken. Using this careful definition (and a lattice regularization) for the calculation of correlation functions in the one-instanton sector, we show that the ’t Hooft vertices are recovered as expected.

Computation of rare transitions in the barotropic quasi-geostrophic equations

NASA Astrophysics Data System (ADS)

Laurie, Jason; Bouchet, Freddy

2015-01-01

We investigate the theoretical and numerical computation of rare transitions in simple geophysical turbulent models. We consider the barotropic quasi-geostrophic and two-dimensional Navier-Stokes equations in regimes where bistability between two coexisting large-scale attractors exist. By means of large deviations and instanton theory with the use of an Onsager-Machlup path integral formalism for the transition probability, we show how one can directly compute the most probable transition path between two coexisting attractors analytically in an equilibrium (Langevin) framework and numerically otherwise. We adapt a class of numerical optimization algorithms known as minimum action methods to simple geophysical turbulent models. We show that by numerically minimizing an appropriate action functional in a large deviation limit, one can predict the most likely transition path for a rare transition between two states. By considering examples where theoretical predictions can be made, we show that the minimum action method successfully predicts the most likely transition path. Finally, we discuss the application and extension of such numerical optimization schemes to the computation of rare transitions observed in direct numerical simulations and experiments and to other, more complex, turbulent systems.

Stabilizing all geometric moduli in heterotic Calabi-Yau vacua

DOE PAGES

Anderson, Lara B.; Gray, James; Lukas, Andre; ...

2011-05-27

We propose a scenario to stabilize all geometric moduli - that is, the complex structure, Kähler moduli and the dilaton - in smooth heterotic Calabi-Yau compactifications without Neveu-Schwarz three-form flux. This is accomplished using the gauge bundle required in any heterotic compactification, whose perturbative effects on the moduli are combined with non-perturbative corrections. We argue that, for appropriate gauge bundles, all complex structure and a large number of other moduli can be perturbatively stabilized - in the most restrictive case, leaving only one combination of Kähler moduli and the dilaton as a flat direction. At this stage, the remaining modulimore » space consists of Minkowski vacua. That is, the perturbative superpotential vanishes in the vacuum without the necessity to fine-tune flux. Finally, we incorporate non-perturbative effects such as gaugino condensation and/or instantons. These are strongly constrained by the anomalous U(1) symmetries which arise from the required bundle constructions. We present a specific example, with a consistent choice of non-perturbative effects, where all remaining flat directions are stabilized in an AdS vacuum.« less

Twistor theory at fifty: from contour integrals to twistor strings

PubMed Central

Atiyah, Michael; Mason, Lionel J.

2017-01-01

We review aspects of twistor theory, its aims and achievements spanning the last five decades. In the twistor approach, space–time is secondary with events being derived objects that correspond to compact holomorphic curves in a complex threefold—the twistor space. After giving an elementary construction of this space, we demonstrate how solutions to linear and nonlinear equations of mathematical physics—anti-self-duality equations on Yang–Mills or conformal curvature—can be encoded into twistor cohomology. These twistor correspondences yield explicit examples of Yang–Mills and gravitational instantons, which we review. They also underlie the twistor approach to integrability: the solitonic systems arise as symmetry reductions of anti-self-dual (ASD) Yang–Mills equations, and Einstein–Weyl dispersionless systems are reductions of ASD conformal equations. We then review the holomorphic string theories in twistor and ambitwistor spaces, and explain how these theories give rise to remarkable new formulae for the computation of quantum scattering amplitudes. Finally, we discuss the Newtonian limit of twistor theory and its possible role in Penrose’s proposal for a role of gravity in quantum collapse of a wave function. PMID:29118667

Fast summation of divergent series and resurgent transseries from Meijer-G approximants

NASA Astrophysics Data System (ADS)

Mera, Héctor; Pedersen, Thomas G.; Nikolić, Branislav K.

2018-05-01

We develop a resummation approach based on Meijer-G functions and apply it to approximate the Borel sum of divergent series and the Borel-Écalle sum of resurgent transseries in quantum mechanics and quantum field theory (QFT). The proposed method is shown to vastly outperform the conventional Borel-Padé and Borel-Padé-Écalle summation methods. The resulting Meijer-G approximants are easily parametrized by means of a hypergeometric ansatz and can be thought of as a generalization to arbitrary order of the Borel-hypergeometric method [Mera et al., Phys. Rev. Lett. 115, 143001 (2015), 10.1103/PhysRevLett.115.143001]. Here we demonstrate the accuracy of this technique in various examples from quantum mechanics and QFT, traditionally employed as benchmark models for resummation, such as zero-dimensional ϕ4 theory; the quartic anharmonic oscillator; the calculation of critical exponents for the N -vector model; ϕ4 with degenerate minima; self-interacting QFT in zero dimensions; and the summation of one- and two-instanton contributions in the quantum-mechanical double-well problem.

Statistical Physics of Population Genetics in the Low Population Size Limit

NASA Astrophysics Data System (ADS)

Atwal, Gurinder

The understanding of evolutionary processes lends itself naturally to theory and computation, and the entire field of population genetics has benefited greatly from the influx of methods from applied mathematics for decades. However, in spite of all this effort, there are a number of key dynamical models of evolution that have resisted analytical treatment. In addition, modern DNA sequencing technologies have magnified the amount of genetic data available, revealing an excess of rare genetic variants in human genomes, challenging the predictions of conventional theory. Here I will show that methods from statistical physics can be used to model the distribution of genetic variants, incorporating selection and spatial degrees of freedom. In particular, a functional path-integral formulation of the Wright-Fisher process maps exactly to the dynamics of a particle in an effective potential, beyond the mean field approximation. In the small population size limit, the dynamics are dominated by instanton-like solutions which determine the probability of fixation in short timescales. These results are directly relevant for understanding the unusual genetic variant distribution at moving frontiers of populations.

The ground state tunneling splitting and the zero point energy of malonaldehyde: a quantum Monte Carlo determination.

PubMed

Viel, Alexandra; Coutinho-Neto, Maurício D; Manthe, Uwe

2007-01-14

Quantum dynamics calculations of the ground state tunneling splitting and of the zero point energy of malonaldehyde on the full dimensional potential energy surface proposed by Yagi et al. [J. Chem. Phys. 1154, 10647 (2001)] are reported. The exact diffusion Monte Carlo and the projection operator imaginary time spectral evolution methods are used to compute accurate benchmark results for this 21-dimensional ab initio potential energy surface. A tunneling splitting of 25.7+/-0.3 cm-1 is obtained, and the vibrational ground state energy is found to be 15 122+/-4 cm-1. Isotopic substitution of the tunneling hydrogen modifies the tunneling splitting down to 3.21+/-0.09 cm-1 and the vibrational ground state energy to 14 385+/-2 cm-1. The computed tunneling splittings are slightly higher than the experimental values as expected from the potential energy surface which slightly underestimates the barrier height, and they are slightly lower than the results from the instanton theory obtained using the same potential energy surface.

Anomalies, renormalization group flows, and the a-theorem in six-dimensional (1, 0) theories

DOE PAGES

Córdova, Clay; Dumitrescu, Thomas T.; Intriligator, Kenneth

2016-10-17

We establish a linear relation between the a-type Weyl anomaly and the ’t Hooft anomaly coeffcients for the R-symmetry and gravitational anomalies in sixdimensional (1,0) superconformal field theories. For RG flows onto the tensor branch, where conformal symmetry is spontaneously broken, supersymmetry relates the anomaly mismatch Δa to the square of a four-derivative interaction for the dilaton. This establishes the a-theorem for all such flows. The four-derivative dilaton interaction is in turn related to the Green-Schwarz-like terms that are needed to match the ’t Hooft anomalies on the tensor branch, thus fixing their relation to Δa. We use our formulamore » to obtain exact expressions for the a-anomaly of N small E 8 instantons, as well as N M 5-branes probing an orbifold singularity, and verify the a-theorem for RG flows onto their Higgs branches. We also discuss aspects of supersymmetric RG flows that terminate in scale but not conformally invariant theories with massless gauge fields.« less

Oscillations in the CMB from Axion Monodromy Inflation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Flauger, Raphael; /Texas U.; McAllister, Liam

2011-12-01

We study the CMB observables in axion monodromy inflation. These well-motivated scenarios for inflation in string theory have monomial potentials over super-Planckian field ranges, with superimposed sinusoidal modulations from instanton effects. Such periodic modulations of the potential can drive resonant enhancements of the correlation functions of cosmological perturbations, with characteristic modulations of the amplitude as a function of wavenumber. We give an analytical result for the scalar power spectrum in this class of models, and we determine the limits that present data places on the amplitude and frequency of modulations. Then, incorporating an improved understanding of the realization of axionmore » monodromy inflation in string theory, we perform a careful study of microphysical constraints in this scenario. We find that detectable modulations of the scalar power spectrum are commonplace in well-controlled examples, while resonant contributions to the bispectrum are undetectable in some classes of examples and detectable in others. We conclude that resonant contributions to the spectrum and bispectrum are a characteristic signature of axion monodromy inflation that, in favorable cases, could be detected in near-future experiments.« less

Efficient evaluation of atom tunneling combined with electronic structure calculations.

PubMed

Ásgeirsson, Vilhjálmur; Arnaldsson, Andri; Jónsson, Hannes

2018-03-14

Methodology for finding optimal tunneling paths and evaluating tunneling rates for atomic rearrangements is described. First, an optimal JWKB tunneling path for a system with fixed energy is obtained using a line integral extension of the nudged elastic band method. Then, a calculation of the dynamics along the path is used to determine the temperature at which it corresponds to an optimal Feynman path for thermally activated tunneling (instanton) and a harmonic approximation is used to estimate the transition rate. The method is illustrated with calculations for a modified two-dimensional Müller-Brown surface but is efficient enough to be used in combination with electronic structure calculations of the energy and atomic forces in systems containing many atoms. An example is presented where tunneling is the dominant mechanism well above room temperature as an H 3 BNH 3 molecule dissociates to form H 2 . Also, a solid-state example is presented where density functional theory calculations of H atom tunneling in a Ta crystal give close agreement with experimental measurements on hydrogen diffusion over a wide range in temperature.

Toward one-loop tunneling rates of near-extremal magnetic black hole pair production

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yi, P.

Pair production of magnetic Reissner-Nordstroem black holes (of charges [plus minus][ital q]) was recently studied in the leading WKB approximation. Here we consider generic quantum fluctuations in the corresponding instanton geometry given by the Euclidean Ernst metric, in order to simulate the behavior of the one-loop tunneling rate. A detailed study of the Ernst metric suggests that for a sufficiently weak field [ital B], the problem can be reduced to that of quantum fluctuations around a single near-extremal Euclidean black hole in thermal equilibrium with a heat bath of finite size. After appropriate renormalization procedures, typical one-loop contributions to themore » WKB exponent are shown to be inversely proportional to [ital B], as [ital B][r arrow]0, indicating that the leading Schwinger term is corrected by a small fraction [similar to][h bar]/[ital q][sup 2]. We demonstrate that this correction to the Schwinger term is actually due to a semiclassical shift of the black hole mass-to-charge ratio that persists even in the extremal limit. Finally we discuss a few loose ends.« less

Thermodynamic limit of random partitions and dispersionless Toda hierarchy

NASA Astrophysics Data System (ADS)

Takasaki, Kanehisa; Nakatsu, Toshio

2012-01-01

We study the thermodynamic limit of random partition models for the instanton sum of 4D and 5D supersymmetric U(1) gauge theories deformed by some physical observables. The physical observables correspond to external potentials in the statistical model. The partition function is reformulated in terms of the density function of Maya diagrams. The thermodynamic limit is governed by a limit shape of Young diagrams associated with dominant terms in the partition function. The limit shape is characterized by a variational problem, which is further converted to a scalar-valued Riemann-Hilbert problem. This Riemann-Hilbert problem is solved with the aid of a complex curve, which may be thought of as the Seiberg-Witten curve of the deformed U(1) gauge theory. This solution of the Riemann-Hilbert problem is identified with a special solution of the dispersionless Toda hierarchy that satisfies a pair of generalized string equations. The generalized string equations for the 5D gauge theory are shown to be related to hidden symmetries of the statistical model. The prepotential and the Seiberg-Witten differential are also considered.

Kinetic isotope effect in malonaldehyde determined from path integral Monte Carlo simulations.

PubMed

Huang, Jing; Buchowiecki, Marcin; Nagy, Tibor; Vaníček, Jiří; Meuwly, Markus

2014-01-07

The primary H/D kinetic isotope effect on the intramolecular proton transfer in malonaldehyde is determined from quantum instanton path integral Monte Carlo simulations on a fully dimensional and validated potential energy surface for temperatures between 250 and 1500 K. Our calculations, based on thermodynamic integration with respect to the mass of the transferring particle, are significantly accelerated by the direct evaluation of the kinetic isotope effect instead of computing it as a ratio of two rate constants. At room temperature, the KIE from the present simulations is 5.2 ± 0.4. The KIE is found to vary considerably as a function of temperature and the low-T behaviour is dominated by the fact that the free energy derivative in the reactant state increases more rapidly than in the transition state. Detailed analysis of the various contributions to the quantum rate constant together with estimates for rates from conventional transition state theory and from periodic orbit theory suggest that the KIE in malonaldehyde is dominated by zero point energy effects and that tunneling plays a minor role at room temperature.

Semiclassical theory of the tunneling anomaly in partially spin-polarized compressible quantum Hall states

NASA Astrophysics Data System (ADS)

Chowdhury, Debanjan; Skinner, Brian; Lee, Patrick A.

2018-05-01

Electron tunneling into a system with strong interactions is known to exhibit an anomaly, in which the tunneling conductance vanishes continuously at low energy due to many-body interactions. Recent measurements have probed this anomaly in a quantum Hall bilayer of the half-filled Landau level, and shown that the anomaly apparently gets stronger as the half-filled Landau level is increasingly spin polarized. Motivated by this result, we construct a semiclassical hydrodynamic theory of the tunneling anomaly in terms of the charge-spreading action associated with tunneling between two copies of the Halperin-Lee-Read state with partial spin polarization. This theory is complementary to our recent work (D. Chowdhury, B. Skinner, and P. A. Lee, arXiv:1709.06091) where the electron spectral function was computed directly using an instanton-based approach. Our results show that the experimental observation cannot be understood within conventional theories of the tunneling anomaly, in which the spreading of the injected charge is driven by the mean-field Coulomb energy. However, we identify a qualitatively new regime, in which the mean-field Coulomb energy is effectively quenched and the tunneling anomaly is dominated by the finite compressibility of the composite Fermion liquid.

Effects of the regularization on the restoration of chiral and axial symmetries

NASA Astrophysics Data System (ADS)

Costa, P.; Ruivo, M. C.; de Sousa, C. A.

2008-05-01

The effects of a type of regularization for finite temperatures on the restoration of chiral and axial symmetries are investigated within the SU(3) Nambu-Jona-Lasinio model. The regularization consists in using an infinite cutoff in the integrals that are convergent at finite temperature, a procedure that allows one to take into account the effects of high momentum quarks at high temperatures. It is found that the critical temperature for the phase transition is closer to lattice results than the one obtained with the conventional regularization, and the restoration of chiral and axial symmetries, signaled by the behavior of several observables, occurs simultaneously and at a higher temperature. The restoration of the axial symmetry appears as a natural consequence of the full recovering of the chiral symmetry that was dynamically broken. By using an additional ansatz that simulates instanton suppression effects, by means of a convenient temperature dependence of the anomaly coefficient, we found that the restoration of U(2) symmetry is shifted to lower values, but the dominant effect at high temperatures comes from the new regularization that enhances the decrease of quark condensates, especially in the strange sector.

Floquet Engineering in Quantum Chains

NASA Astrophysics Data System (ADS)

Kennes, D. M.; de la Torre, A.; Ron, A.; Hsieh, D.; Millis, A. J.

2018-03-01

We consider a one-dimensional interacting spinless fermion model, which displays the well-known Luttinger liquid (LL) to charge density wave (CDW) transition as a function of the ratio between the strength of the interaction U and the hopping J . We subject this system to a spatially uniform drive which is ramped up over a finite time interval and becomes time periodic in the long-time limit. We show that by using a density matrix renormalization group approach formulated for infinite system sizes, we can access the large-time limit even when the drive induces finite heating. When both the initial and long-time states are in the gapless (LL) phase, the final state has power-law correlations for all ramp speeds. However, when the initial and final state are gapped (CDW phase), we find a pseudothermal state with an effective temperature that depends on the ramp rate, both for the Magnus regime in which the drive frequency is very large compared to other scales in the system and in the opposite limit where the drive frequency is less than the gap. Remarkably, quantum defects (instantons) appear when the drive tunes the system through the quantum critical point, in a realization of the Kibble-Zurek mechanism.

M-theory through the looking glass: Tachyon condensation in the E8 heterotic string

DOE Office of Scientific and Technical Information (OSTI.GOV)

Horava, Petr; Horava, Petr; Keeler, Cynthia A.

2007-09-20

We study the spacetime decay to nothing in string theory and M-theory. First we recall a nonsupersymmetric version of heterotic M-theory, in which bubbles of nothing -- connecting the two E_8 boundaries by a throat -- are expected to be nucleated. We argue that the fate of this system should be addressed at weak string coupling, where the nonperturbative instanton instability is expected to turn into a perturbative tachyonic one. We identify the unique string theory that could describe this process: The heterotic model with one E_8 gauge group and a singlet tachyon. We then use worldsheet methods to studymore » the tachyon condensation in the NSR formulation of this model, and show that it induces a worldsheet super-Higgs effect. The main theme of our analysis is the possibility of making meaningful alternative gauge choices for worldsheet supersymmetry, in place of the conventional superconformal gauge. We show in a version of unitary gauge how the worldsheet gravitino assimilates the goldstino and becomes dynamical. This picture clarifies recent results of Hellerman and Swanson. We also present analogs of R_\\xi gauges, and note the importance of logarithmic CFT in the context of tachyon condensation.« less

Population extinction under bursty reproduction in a time-modulated environment

NASA Astrophysics Data System (ADS)

Vilk, Ohad; Assaf, Michael

2018-06-01

In recent years nondemographic variability has been shown to greatly affect dynamics of stochastic populations. For example, nondemographic noise in the form of a bursty reproduction process with an a priori unknown burst size, or environmental variability in the form of time-varying reaction rates, have been separately found to dramatically impact the extinction risk of isolated populations. In this work we investigate the extinction risk of an isolated population under the combined influence of these two types of nondemographic variation. Using the so-called momentum-space Wentzel-Kramers-Brillouin (WKB) approach and accounting for the explicit time dependence in the reaction rates, we arrive at a set of time-dependent Hamilton equations. To this end, we evaluate the population's extinction risk by finding the instanton of the time-perturbed Hamiltonian numerically, whereas analytical expressions are presented in particular limits using various perturbation techniques. We focus on two classes of time-varying environments: periodically varying rates corresponding to seasonal effects and a sudden decrease in the birth rate corresponding to a catastrophe. All our theoretical results are tested against numerical Monte Carlo simulations with time-dependent rates and also against a numerical solution of the corresponding time-dependent Hamilton equations.

Non-Abelian black string solutions of N = (2,0) , d = 6 supergravity

NASA Astrophysics Data System (ADS)

Cano, Pablo A.; Ortín, Tomás; Santoli, Camilla

2016-12-01

We show that, when compactified on a circle, N = (2, 0), d = 6 supergravity coupled to 1 tensor multiplet and n V vector multiplets is dual to N = (2 , 0) , d = 6 supergravity coupled to just n T = n V + 1 tensor multiplets and no vector multiplets. Both theories reduce to the same models of N = 2 , d = 5 supergravity coupled to n V 5 = n V + 2 vector fields. We derive Buscher rules that relate solutions of these theories (and of the theory that one obtains by dualizing the 3-form field strength) admitting an isometry. Since the relations between the fields of N = 2 , d = 5 supergravity and those of the 6-dimensional theories are the same with or without gaugings, we construct supersymmetric non-Abelian solutions of the 6-dimensional gauged theories by uplifting the recently found 5-dimensional supersymmetric non-Abelian black-hole solutions. The solutions describe the usual superpositions of strings and waves supplemented by a BPST instanton in the transverse directions, similar to the gauge dyonic string of Duff, Lü and Pope. One of the solutions obtained interpolates smoothly between two AdS3× S3 geometries with different radii.

A Hybrid Monte Carlo importance sampling of rare events in Turbulence and in Turbulent Models

NASA Astrophysics Data System (ADS)

Margazoglou, Georgios; Biferale, Luca; Grauer, Rainer; Jansen, Karl; Mesterhazy, David; Rosenow, Tillmann; Tripiccione, Raffaele

2017-11-01

Extreme and rare events is a challenging topic in the field of turbulence. Trying to investigate those instances through the use of traditional numerical tools turns to be a notorious task, as they fail to systematically sample the fluctuations around them. On the other hand, we propose that an importance sampling Monte Carlo method can selectively highlight extreme events in remote areas of the phase space and induce their occurrence. We present a brand new computational approach, based on the path integral formulation of stochastic dynamics, and employ an accelerated Hybrid Monte Carlo (HMC) algorithm for this purpose. Through the paradigm of stochastic one-dimensional Burgers' equation, subjected to a random noise that is white-in-time and power-law correlated in Fourier space, we will prove our concept and benchmark our results with standard CFD methods. Furthermore, we will present our first results of constrained sampling around saddle-point instanton configurations (optimal fluctuations). The research leading to these results has received funding from the EU Horizon 2020 research and innovation programme under Grant Agreement No. 642069, and from the EU Seventh Framework Programme (FP7/2007-2013) under ERC Grant Agreement No. 339032.

FRW and domain walls in higher spin gravity

NASA Astrophysics Data System (ADS)

Aros, R.; Iazeolla, C.; Noreña, J.; Sezgin, E.; Sundell, P.; Yin, Y.

2018-03-01

We present exact solutions to Vasiliev's bosonic higher spin gravity equations in four dimensions with positive and negative cosmological constant that admit an interpretation in terms of domain walls, quasi-instantons and Friedman-Robertson-Walker (FRW) backgrounds. Their isometry algebras are infinite dimensional higher-spin extensions of spacetime isometries generated by six Killing vectors. The solutions presented are obtained by using a method of holomorphic factorization in noncommutative twistor space and gauge functions. In interpreting the solutions in terms of Fronsdal-type fields in space-time, a field-dependent higher spin transformation is required, which is implemented at leading order. To this order, the scalar field solves Klein-Gordon equation with conformal mass in ( A) dS 4 . We interpret the FRW solution with de Sitter asymptotics in the context of inflationary cosmology and we expect that the domain wall and FRW solutions are associated with spontaneously broken scaling symmetries in their holographic description. We observe that the factorization method provides a convenient framework for setting up a perturbation theory around the exact solutions, and we propose that the nonlinear completion of particle excitations over FRW and domain wall solutions requires black hole-like states.

Finite-action solutions of Yang-Mills equations on de Sitter dS4 and anti-de Sitter AdS4 spaces

NASA Astrophysics Data System (ADS)

Ivanova, Tatiana A.; Lechtenfeld, Olaf; Popov, Alexander D.

2017-11-01

We consider pure SU(2) Yang-Mills theory on four-dimensional de Sitter dS4 and anti-de Sitter AdS4 spaces and construct various solutions to the Yang-Mills equations. On de Sitter space we reduce the Yang-Mills equations via an SU(2)-equivariant ansatz to Newtonian mechanics of a particle moving in R^3 under the influence of a quartic potential. Then we describe magnetic and electric-magnetic solutions, both Abelian and non-Abelian, all having finite energy and finite action. A similar reduction on anti-de Sitter space also yields Yang-Mills solutions with finite energy and action. We propose a lower bound for the action on both backgrounds. Employing another metric on AdS4, the SU(2) Yang-Mills equations are reduced to an analytic continuation of the above particle mechanics from R^3 to R^{2,1} . We discuss analytical solutions to these equations, which produce infinite-action configurations. After a Euclidean continuation of dS4 and AdS4 we also present self-dual (instanton-type) Yang-Mills solutions on these backgrounds.

A Flavorful Factoring of the Strong CP Problem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Agrawal, Prateek; Howe, Kiel

Motivated by the intimate connection between the strong CP problem and the flavor structure of the Standard Model, we present a flavor model that revives and extends the classicmore » $${m_u=0}$$ solution to the strong CP problem. QCD is embedded into a $$SU(3)_1\\times SU(3)_2 \\times SU(3)_3$$ gauge group, with each generation of quarks charged under the respective $SU(3)$. The non-zero value of the up-quark Yukawa coupling (along with the strange quark and bottom-quark Yukawas) is generated by contributions from small instantons at a new scale $$M \\gg \\Lambda_{QCD}$$. The Higgsing of $$SU(3)^3\\to SU(3)_c$$ allows dimension-5 operators that generate the Standard Model flavor structure and can be completed in a simple renormalizable theory. The smallness of the third generation mixing angles can naturally emerge in this picture, and is connected to the smallness of threshold corrections to $$\\bar\\theta$$. Remarkably, $$\\bar\\theta$$ is essentially fixed by the measured quark masses and mixings, and is estimated to be close to the current experimental bound and well within reach of the next generation of neutron and proton EDM experiments.« less

2d affine XY-spin model/4d gauge theory duality and deconfinement

NASA Astrophysics Data System (ADS)

Anber, Mohamed M.; Poppitz, Erich; Ünsal, Mithat

2012-04-01

We introduce a duality between two-dimensional XY-spin models with symmetry-breaking perturbations and certain four-dimensional SU(2) and SU(2)/ {{Z}_2} gauge theories, compactified on a small spatial circle {{R}^{{^{{{1},{2}}}}}} × {{S}^{{^{{1}}}}} , and considered at temperatures near the deconfinement transition. In a Euclidean set up, the theory is defined on {{R}^{{^{{2}}}}} × {{T}^{{^{{2}}}}} . Similarly, thermal gauge theories of higher rank are dual to new families of "affine" XY-spin models with perturbations. For rank two, these are related to models used to describe the melting of a 2d crystal with a triangular lattice. The connection is made through a multi-component electric-magnetic Coulomb gas representation for both systems. Perturbations in the spin system map to topological defects in the gauge theory, such as monopole-instantons or magnetic bions, and the vortices in the spin system map to the electrically charged W-bosons in field theory (or vice versa, depending on the duality frame). The duality permits one to use the two-dimensional technology of spin systems to study the thermal deconfinement and discrete chiral transitions in four-dimensional SU( N c ) gauge theories with n f ≥1 adjoint Weyl fermions.

Quantum geometry of resurgent perturbative/nonperturbative relations

NASA Astrophysics Data System (ADS)

Basar, Gökçe; Dunne, Gerald V.; Ünsal, Mithat

2017-05-01

For a wide variety of quantum potentials, including the textbook `instanton' examples of the periodic cosine and symmetric double-well potentials, the perturbative data coming from fluctuations about the vacuum saddle encodes all non-perturbative data in all higher non-perturbative sectors. Here we unify these examples in geometric terms, arguing that the all-orders quantum action determines the all-orders quantum dual action for quantum spectral problems associated with a classical genus one elliptic curve. Furthermore, for a special class of genus one potentials this relation is particularly simple: this class includes the cubic oscillator, symmetric double-well, symmetric degenerate triple-well, and periodic cosine potential. These are related to the Chebyshev potentials, which are in turn related to certain \\mathcal{N} = 2 supersymmetric quantum field theories, to mirror maps for hypersurfaces in projective spaces, and also to topological c = 3 Landau-Ginzburg models and `special geometry'. These systems inherit a natural modular structure corresponding to Ramanujan's theory of elliptic functions in alternative bases, which is especially important for the quantization. Insights from supersymmetric quantum field theory suggest similar structures for more complicated potentials, corresponding to higher genus. Our approach is very elementary, using basic classical geometry combined with all-orders WKB.

Supersymmetric solutions of the cosmological, gauged, ℂ magic model

NASA Astrophysics Data System (ADS)

Chimento, Samuele; Ortín, Tomás; Ruipérez, Alejandro

2018-05-01

We construct supersymmetric solutions of theories of gauged N = 1 , d = 5 supergravity coupled to vector multiplets with a U(1)R Abelian (Fayet-Iliopoulos) gauging and an independent SU(2) gauging associated to an SU(2) isometry group of the Real Special scalar manifold. These theories provide minimal supersymmetrizations of 5-dimensional SU(2) Einstein-Yang-Mills theories with negative cosmological constant. We consider a minimal model with these gauge groups and the "magic model" based on the Jordan algebra J 3 ℂ with gauge group SU(3) × U(1)R, which is a consistent truncation of maximal SO(6)-gauged supergravity in d = 5 and whose solutions can be embedded in Type IIB Superstring Theory. We find several solutions containing selfdual SU(2) instantons, some of which asymptote to AdS5 and some of which are very small, supersymmetric, deformations of AdS5. We also show how some of those solutions can be embedded in Romans' SU(2) × U(1)-gauged half-maximal supergravity, which was obtained by Lu, Pope and Tran by compactification of the Type IIB Superstring effective action. This provides another way of uplifting those solutions to 10 dimensions.

Schwinger effect in de Sitter space

NASA Astrophysics Data System (ADS)

Fröb, Markus B.; Garriga, Jaume; Kanno, Sugumi; Sasaki, Misao; Soda, Jiro; Tanaka, Takahiro; Vilenkin, Alexander

2014-04-01

We consider Schwinger pair production in 1+1 dimensional de Sitter space, filled with a constant electric field E. This can be thought of as a model for describing false vacuum decay beyond the semiclassical approximation, where pairs of a quantum field phi of mass m and charge e play the role of vacuum bubbles. We find that the adiabatic ``in" vacuum associated with the flat chart develops a space-like expectation value for the current J, which manifestly breaks the de Sitter invariance of the background fields. We derive a simple expression for J(E), showing that both ``upward" and ``downward" tunneling contribute to the build-up of the current. For heavy fields, with m2 gg eE,H2, the current is exponentially suppressed, in agreement with the results of semiclassical instanton methods. Here, H is the inverse de Sitter radius. On the other hand, light fields with m ll H lead to a phenomenon of infrared hyperconductivity, where a very small electric field mHlesssimeE ll H2 leads to a very large current J ~ H3/E. We also show that all Hadamard states for phi necessarily break de Sitter invariance. Finally, we comment on the role of initial conditions, and ``persistence of memory" effects.

Nonperturbative Time Dependent Solution of a Simple Ionization Model

NASA Astrophysics Data System (ADS)

Costin, Ovidiu; Costin, Rodica D.; Lebowitz, Joel L.

2018-02-01

We present a non-perturbative solution of the Schrödinger equation {iψ_t(t,x)=-ψ_{xx}(t,x)-2(1 +α sinω t) δ(x)ψ(t,x)} , written in units in which \\hbar=2m=1, describing the ionization of a model atom by a parametric oscillating potential. This model has been studied extensively by many authors, including us. It has surprisingly many features in common with those observed in the ionization of real atoms and emission by solids, subjected to microwave or laser radiation. Here we use new mathematical methods to go beyond previous investigations and to provide a complete and rigorous analysis of this system. We obtain the Borel-resummed transseries (multi-instanton expansion) valid for all values of α, ω, t for the wave function, ionization probability, and energy distribution of the emitted electrons, the latter not studied previously for this model. We show that for large t and small α the energy distribution has sharp peaks at energies which are multiples of ω, corresponding to photon capture. We obtain small α expansions that converge for all t, unlike those of standard perturbation theory. We expect that our analysis will serve as a basis for treating more realistic systems revealing a form of universality in different emission processes.

M theory through the looking glass: Tachyon condensation in the E{sub 8} heterotic string

DOE Office of Scientific and Technical Information (OSTI.GOV)

Horava, Petr; Keeler, Cynthia A.

2008-03-15

We study the spacetime decay to nothing in string theory and M-theory. First we recall a nonsupersymmetric version of heterotic M-theory, in which bubbles of nothing--connecting the two E{sub 8} boundaries by a throat--are expected to be nucleated. We argue that the fate of this system should be addressed at weak string coupling, where the nonperturbative instanton instability is expected to turn into a perturbative tachyonic one. We identify the unique string theory that could describe this process: The heterotic model with one E{sub 8} gauge group and a singlet tachyon. We then use world sheet methods to study themore » tachyon condensation in the Neveu-Schwarz-Ramond formulation of this model, and show that it induces a world sheet super-Higgs effect. The main theme of our analysis is the possibility of making meaningful alternative gauge choices for world sheet supersymmetry, in place of the conventional superconformal gauge. We show in a version of unitary gauge how the world sheet gravitino assimilates the Goldstino and becomes dynamical. This picture clarifies recent results of Hellerman and Swanson. We also present analogs of R{sub {xi}} gauges, and note the importance of logarithmic conformal field theories in the context of tachyon condensation.« less

Fuzzy Dark Matter from Infrared Confining Dynamics

NASA Astrophysics Data System (ADS)

Davoudiasl, Hooman; Murphy, Christopher W.

2017-04-01

A very light boson of mass O (10-22) eV may potentially be a viable dark matter (DM) candidate, which can avoid phenomenological problems associated with cold DM. Such "fuzzy DM (FDM)" may naturally be an axion with a decay constant fa˜1 016- 1 018 GeV and a mass ma˜μ2/fa with μ ˜1 02 eV . Here, we propose a concrete model, where μ arises as a dynamical scale from infrared confining dynamics, analogous to QCD. Our model is an alternative to the usual approach of generating μ through string theoretic instanton effects. We outline the features of this scenario that result from various cosmological constraints. We find that those constraints are suggestive of a period of mild of inflation, perhaps from a strong first order phase transition, that reheats the standard model (SM) sector only. A typical prediction of our scenario, broadly speaking, is a larger effective number of neutrinos compared to the SM value Neff≈3 , as inferred from precision measurements of the cosmic microwave background. Some of the new degrees of freedom may be identified as "sterile neutrinos," which may be required to explain certain neutrino oscillation anomalies. Hence, aspects of our scenario could be testable in terrestrial experiments, which is a novelty of our FDM model.

Hyperkahler metrics on focus-focus fibrations

NASA Astrophysics Data System (ADS)

Zhao, Jie

In this thesis, we focus on the study of hyperkahler metric in four dimensional cases, and practice GMN's construction of hyperkahler metric on focus-focus fibrations. We explicitly compute the action-angle coordinates on the local model of focus-focus fibration, and show its semi-global invariant should be harmonic to admit a compatible holomorphic 2-form. Then we study the canonical semi-flat metric on it. After the instanton correction inspired by physics, we get a family of the generalized Ooguri-Vafa metric on focus-focus fibrations, which becomes more local examples of explicit hyperkahler metric in four dimensional cases. In addition, we also make some exploration of the Ooguri-Vafa metric in the thesis. We study the potential function of the Ooguri-Vafa metric, and prove that its nodal set is a cylinder of bounded radius 1 < R < 1. As a result, we get that only on a finite neighborhood of the singular fibre the Ooguri-Vafa metric is a hyperkahler metric. Finally, we give some estimates for the diameter of the fibration under the Oogui-Vafa metric, which confirms that the Oogui-Vafa metric is not complete. The new family of metric constructed in the thesis, we think, will provide more examples to further study of Lagrangian fibrations and mirror symmetry in future.

New type of hill-top inflation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barvinsky, A.O.; Department of Physics, Tomsk State University,Lenin Ave. 36, Tomsk 634050; Department of Physics and Astronomy, Pacific Institue for Theoretical Physics,University of British Columbia, 6224 Agricultural Road, Vancouver, BC V6T 1Z1

2016-01-20

We suggest a new type of hill-top inflation originating from the initial conditions in the form of the microcanonical density matrix for the cosmological model with a large number of quantum fields conformally coupled to gravity. Initial conditions for inflation are set up by cosmological instantons describing underbarrier oscillations in the vicinity of the inflaton potential maximum. These periodic oscillations of the inflaton field and cosmological scale factor are obtained within the approximation of two coupled oscillators subject to the slow roll regime in the Euclidean time. This regime is characterized by rapid oscillations of the scale factor on themore » background of a slowly varying inflaton, which guarantees smallness of slow roll parameters ϵ and η of the following inflation stage. A hill-like shape of the inflaton potential is shown to be generated by logarithmic loop corrections to the tree-level asymptotically shift-invariant potential in the non-minimal Higgs inflation model and R{sup 2}-gravity. The solution to the problem of hierarchy between the Planckian scale and the inflation scale is discussed within the concept of conformal higher spin fields, which also suggests the mechanism bringing the model below the gravitational cutoff and, thus, protecting it from large graviton loop corrections.« less

New type of hill-top inflation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barvinsky, A.O.; Nesterov, D.V.; Kamenshchik, A.Yu., E-mail: barvin@td.lpi.ru, E-mail: Alexander.Kamenshchik@bo.infn.it, E-mail: nesterov@td.lpi.ru

2016-01-01

We suggest a new type of hill-top inflation originating from the initial conditions in the form of the microcanonical density matrix for the cosmological model with a large number of quantum fields conformally coupled to gravity. Initial conditions for inflation are set up by cosmological instantons describing underbarrier oscillations in the vicinity of the inflaton potential maximum. These periodic oscillations of the inflaton field and cosmological scale factor are obtained within the approximation of two coupled oscillators subject to the slow roll regime in the Euclidean time. This regime is characterized by rapid oscillations of the scale factor on themore » background of a slowly varying inflaton, which guarantees smallness of slow roll parameters ε and η of the following inflation stage. A hill-like shape of the inflaton potential is shown to be generated by logarithmic loop corrections to the tree-level asymptotically shift-invariant potential in the non-minimal Higgs inflation model and R{sup 2}-gravity. The solution to the problem of hierarchy between the Planckian scale and the inflation scale is discussed within the concept of conformal higher spin fields, which also suggests the mechanism bringing the model below the gravitational cutoff and, thus, protecting it from large graviton loop corrections.« less

Probable or improbable universe? Correlating electroweak vacuum instability with the scale of inflation

DOE PAGES

Hook, Anson; Kearney, John; Shakya, Bibhushan; ...

2015-01-13

Measurements of the Higgs boson and top quark masses indicate that the Standard Model Higgs potential becomes unstable around Λ I ~ 10 11 GeV. This instability is cosmologically relevant since quantum fluctuations during inflation can easily destabilize the electroweak vacuum if the Hubble parameter during inflation is larger than Λ I (as preferred by the recent BICEP 2 measurement). Here, we perform a careful study of the evolution of the Higgs field during inflation, obtaining different results from those currently in the literature. We consider both tunneling via a Coleman-de Luccia or Hawking-Moss instanton, valid when the scale ofmore » inflation is below the instability scale, as well as a statistical treatment via the Fokker-Planck equation appropriate in the opposite regime. We show that a better understanding of the post-inflation evolution of the unstable AdS vacuum regions is crucial for determining the eventual fate of the universe. If these AdS regions devour all of space, a universe like ours is indeed extremely unlikely without new physics to stabilize the Higgs potential; however, if these regions crunch, our universe survives, but inflation must last a few e-folds longer to compensate for the lost AdS regions. Lastly, we examine the effects of generic Planck-suppressed corrections to the Higgs potential, which can be sufficient to stabilize the electroweak vacuum during inflation.« less

Phases of kinky holographic nuclear matter

NASA Astrophysics Data System (ADS)

Elliot-Ripley, Matthew; Sutcliffe, Paul; Zamaklar, Marija

2016-10-01

Holographic QCD at finite baryon number density and zero temperature is studied within the five-dimensional Sakai-Sugimoto model. We introduce a new approximation that models a smeared crystal of solitonic baryons by assuming spatial homogeneity to obtain an effective kink theory in the holographic direction. The kink theory correctly reproduces a first order phase transition to lightly bound nuclear matter. As the density is further increased the kink splits into a pair of half-kink constituents, providing a concrete realization of the previously suggested dyonic salt phase, where the bulk soliton splits into constituents at high density. The kink model also captures the phenomenon of baryonic popcorn, in which a first order phase transition generates an additional soliton layer in the holographic direction. We find that this popcorn transition takes place at a density below the dyonic salt phase, making the latter energetically unfavourable. However, the kink model predicts only one pop, rather than the sequence of pops suggested by previous approximations. In the kink model the two layers produced by the single pop form the surface of a soliton bag that increases in size as the baryon chemical potential is increased. The interior of the bag is filled with abelian electric potential and the instanton charge density is localized on the surface of the bag. The soliton bag may provide a holographic description of a quarkyonic phase.

Fuzzy Dark Matter from Infrared Confining Dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Davoudiasl, Hooman; Murphy, Christopher W.

A very light boson of mass O ( 10 - 22 ) eV may potentially be a viable dark matter (DM) candidate, which can avoid phenomenological problems associated with cold DM. Such “fuzzy DM (FDM)” may naturally be an axion with a decay constant f a ~ 1 0 16 – 1 0 18 GeV and a mass m a ~ μ 2 / f a with μ ~ 1 0 2 eV . Here, we propose a concrete model, where μ arises as a dynamical scale from infrared confining dynamics, analogous to QCD. This model is an alternative tomore » the usual approach of generating μ through string theoretic instanton effects. We outline the features of this scenario that result from various cosmological constraints. We also found that those constraints are suggestive of a period of mild of inflation, perhaps from a strong first order phase transition, that reheats the standard model (SM) sector only. A typical prediction of our scenario, broadly speaking, is a larger effective number of neutrinos compared to the SM value N eff ≈ 3 , as inferred from precision measurements of the cosmic microwave background. Some of the new degrees of freedom may be identified as “sterile neutrinos,” which may be required to explain certain neutrino oscillation anomalies. Thus, aspects of our scenario could be testable in terrestrial experiments, which is a novelty of our FDM model.« less

Superfluid--Solid Quantum Phase Transitions and Landau-Ginzburg-Wilson Paradigm

NASA Astrophysics Data System (ADS)

Kuklov, A. B.; Prokof'ev, N. V.

2005-03-01

We study superfluid (SF)--solid zero-temperature transitions in 2d lattice boson/spin models by Worm-Algorithm Monte Carlo simulations. The SF -- Valence Bond Solid (VBS) transition was recently argued to be generically of II order in violation of the Ginzburg-Landau- Wilson (GLW) paradigm [1]. We simulate the J-current model on lattices up to 64x64x64, and observe that SF- columnar VBS and SF-checkerboard solid transitions are typically weak I-order ones and in small systems they may be confused with the continuous or high-symmetry points [2]. Thus, in the simulated model, the SF-VBS transition proceeds in agreement with the GLW paradigm. We explain this by dominance of standard particle and hole excitations, as opposed to fractionalized (spinon) excitations [1]. We developed a technique based on tunneling events (instantons) in the insulating phase which reveals charges of the revelant long-wave modes. While in 1d systems spinons are clearly seen in tunneling events, in two spatial dimensions tunneling is solely controlled by particles and holes in our system. This work is supported by NSF grant ITR-405460001 and PSC-CUNY- 665560035. [1] T. Senthil, A. Vishwanath, L. Balents, S. Sachdev, and M.P.A. Fisher, Science 303, 1490 (2004); [2] A.B. Kuklov, N.V. Prokof'ev, B.V. Svistunov, condmat/0406061; PRL, to be published.

Higher winding strings and confined monopoles in N=2 supersymmetric QCD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Auzzi, R.; Bolognesi, S.; Shifman, M.

2010-04-15

We consider composite string solutions in N=2 SQCD with the gauge group U(N), the Fayet-Iliopoulos term {xi}{ne}0 and N (s)quark flavors. These bulk theories support non-Abelian strings and confined monopoles identified with kinks in the two-dimensional world-sheet theory. Similar and more complicated kinks (corresponding to composite confined monopoles) must exist in the world-sheet theories on composite strings. In a bid to detect them we analyze the Hanany-Tong (HT) model, focusing on a particular example of N=2. Unequal quark mass terms in the bulk theory result in the twisted masses in the N=(2,2) HT model. For spatially coinciding 2-strings, we findmore » three distinct minima of potential energy, corresponding to three different 2-strings. Then we find BPS-saturated kinks interpolating between each pair of vacua. Two kinks can be called elementary. They emanate one unit of the magnetic flux and have the same mass as the conventional 't Hooft-Polyakov monopole on the Coulomb branch of the bulk theory ({xi}=0). The third kink represents a composite bimonopole, with twice the minimal magnetic flux. Its mass is twice the mass of the elementary confined monopole. We find instantons in the HT model, and discuss quantum effects in composite strings at strong coupling. In addition, we study the renormalization group flow in this model.« less

Fuzzy Dark Matter from Infrared Confining Dynamics

DOE PAGES

Davoudiasl, Hooman; Murphy, Christopher W.

2017-04-03

A very light boson of mass O ( 10 - 22 ) eV may potentially be a viable dark matter (DM) candidate, which can avoid phenomenological problems associated with cold DM. Such “fuzzy DM (FDM)” may naturally be an axion with a decay constant f a ~ 1 0 16 – 1 0 18 GeV and a mass m a ~ μ 2 / f a with μ ~ 1 0 2 eV . Here, we propose a concrete model, where μ arises as a dynamical scale from infrared confining dynamics, analogous to QCD. This model is an alternative tomore » the usual approach of generating μ through string theoretic instanton effects. We outline the features of this scenario that result from various cosmological constraints. We also found that those constraints are suggestive of a period of mild of inflation, perhaps from a strong first order phase transition, that reheats the standard model (SM) sector only. A typical prediction of our scenario, broadly speaking, is a larger effective number of neutrinos compared to the SM value N eff ≈ 3 , as inferred from precision measurements of the cosmic microwave background. Some of the new degrees of freedom may be identified as “sterile neutrinos,” which may be required to explain certain neutrino oscillation anomalies. Thus, aspects of our scenario could be testable in terrestrial experiments, which is a novelty of our FDM model.« less

Emergent universe with wormholes in massive gravity

NASA Astrophysics Data System (ADS)

Paul, B. C.; Majumdar, A. S.

2018-03-01

An emergent universe (EU) scenario is proposed to obtain a universe free from big-bang singularity. In this framework the present universe emerged from a static Einstein universe phase in the infinite past. A flat EU scenario is found to exist in Einstein’s gravity with a non-linear equation of state (EoS). It has been shown subsequently that a physically realistic EU model can be obtained considering cosmic fluid composed of interacting fluids with a non-linear equation of state. It results a viable cosmological model accommodating both early inflation and present accelerating phases. In the present paper, the origin of an initial static Einstein universe needed in the EU model is explored in a massive gravity theory which subsequently emerged to be a dynamically evolving universe. A new gravitational instanton solution in a flat universe is obtained in the massive gravity theory which is a dynamical wormhole that might play an important role in realizing the origin of the initial state of the emergent universe. The emergence of a Lorentzian universe from a Euclidean gravity is understood by a Wick rotation τ = i t . A universe with radiation at the beginning finally transits into the present observed universe with a non-linear EoS as the interactions among the fluids set in. Thus a viable flat EU scenario where the universe stretches back into time infinitely, with no big bang is permitted in a massive gravity.

Optical knots and contact geometry II. From Ranada dyons to transverse and cosmetic knots

NASA Astrophysics Data System (ADS)

Kholodenko, Arkady L.

2016-08-01

Some time ago Ranada (1989) obtained new nontrivial solutions of the Maxwellian gauge fields without sources. These were reinterpreted in Kholodenko (2015) [10] (part I) as particle-like (monopoles, dyons, etc.). They were obtained by the method of Abelian reduction of the non-Abelian Yang-Mills functional. The developed method uses instanton-type calculations normally employed for the non-Abelian gauge fields. By invoking the electric-magnetic duality it then becomes possible to replace all known charges/masses by the particle-like solutions of the source-free Abelian gauge fields. To employ these results in high energy physics, it is essential to extend Ranada's results by carefully analyzing and classifying all dynamically generated knotted/linked structures in gauge fields, including those discovered by Ranada. This task is completed in this work. The study is facilitated by the recent progress made in solving the Moffatt conjecture. Its essence is stated as follows: in steady incompressible Euler-type fluids the streamlines could have knots/links of all types. By employing the correspondence between the ideal hydrodynamics and electrodynamics discussed in part I and by superimposing it with the already mentioned method of Abelian reduction, it is demonstrated that in the absence of boundaries only the iterated torus knots and links could be dynamically generated. Obtained results allow to develop further particle-knot/link correspondence studied in Kholodenko (2015) [13].

BOOK REVIEW: Classical Solutions in Quantum Field Theory Classical Solutions in Quantum Field Theory

NASA Astrophysics Data System (ADS)

Mann, Robert

2013-02-01

Quantum field theory has evolved from its early beginnings as a tool for understanding the interaction of light with matter into a rather formidable technical paradigm, one that has successfully provided the mathematical underpinnings of all non-gravitational interactions. Over the eight decades since it was first contemplated the methods have become increasingly more streamlined and sophisticated, yielding new insights into our understanding of the subatomic world and our abilities to make clear and precise predictions. Some of the more elegant methods have to do with non-perturbative and semiclassical approaches to the subject. The chief players here are solitons, instantons, and anomalies. Over the past three decades there has been a steady rise in our understanding of these objects and of our ability to calculate their effects and implications for the rest of quantum field theory. This book is a welcome contribution to this subject. In 12 chapters it provides a clear synthesis of the key developments in these subjects at a level accessible to graduate students that have had an introductory course to quantum field theory. In the author's own words it provides both 'a survey and an overview of this field'. The first half of the book concentrates on solitons--kinks, vortices, and magnetic monopoles--and their implications for the subject. The reader is led first through the simplest models in one spatial dimension, into more sophisticated cases that required more advanced topological methods. The author does quite a nice job of introducing the various concepts as required, and beginning students should be able to get a good grasp of the subject directly from the text without having to first go through the primary literature. The middle part of the book deals with the implications of these solitons for both cosmology and for duality. While the cosmological discussion is quite nice, the discussion on BPS solitons, supersymmetry and duality is rather condensed. It is a tall order for a single chapter, relying rather heavily on additional background knowledge (for example supersymmetry) that students will not have unless they have already studied these topics in some depth. At this point students will need to be content with either appreciating the results as presented or else going to the original source material. The last four chapters of the book deal with anomalies and instantons, and again the reader is led from the simple material to the complex in a straightforward manner. Students should be able to follow the discussion both quantitatively and qualitatively, and become well-versed in understanding the 'big picture' provided they work through the material. The discussion on vacuum decay near the end of the book is quite timely given recent developments in eternal inflations, cosmic bubbles, and the like. The book contains a nice appendix that introduces students to the elements of Lie groups and Lie algebras that are required to understand a number of the ideas presented in various places in the book. There is also a short appendix on index theorems that should at least given students a basic sense of how these methods are employed in the subject at hand. This book would make a useful textbook for a mid-level graduate course. Though a bit terse in places, all of the main elements are there, in terms of both concept and methodology. It would make a fine addition to the library of any theorist in high-energy physics, gravitation, or cosmology.

Wormholes and Child Universes

NASA Astrophysics Data System (ADS)

Guendelman, E. I.

Evidence to the case that classical gravitation provides the clue to make sense out of quantum gravity is presented. The key observation is the existence in classical gravitation of child universe solutions or "almost" solutions, "almost" because of some singularity problems. The difficulties of these child universe solutions that are due to their generic singularity problems will be very likely be cured by quantum effects, just like for example "almost" instanton solutions are made relevant in gauge theories with the breaking of conformal invariance. Some well-motivated modifcations of general relativity where these singularity problems are absent even at the classical level are discussed. High energy density excitations, responsible for UV divergences in quantum field theories, including quantum gravity, are likely to be the source of child universes which carry them out of the original space-time. This decoupling could prevent these high UV excitations from having any influence on physical amplitudes. Child universe production could therefore be responsible for UV regularization in quantum field theories which take into account semiclassically gravitational effects. Child universe production in the last stages of black hole evaporation, the prediction of absence of trans-Planckian primordial perturbations, connection to the minimum length hypothesis, and in particular the connection to the maximal curvature hypothesis are discussed. Some discussion of superexcited states in the case these states such as Kaluza-Klein excitations are carried out. Finally, the possibility of obtaining "string like" effects from the wormholes associated with the child universes is discussed.

Dark matter as ultralight axion-like particle in E6 × U(1)X GUT with QCD axion

NASA Astrophysics Data System (ADS)

Corianò, Claudio; Frampton, Paul H.

2018-07-01

Axion-like fields are naturally generated by a mechanism of anomaly cancellation of one or more anomalous gauge abelian symmetries at the Planck scale, emerging as duals of a two-form from the massless bosonic sector of string theory. This suggests an analogy of the Green-Schwarz mechanism of anomaly cancellation, at field theory level, which results in one or more Stueckelberg pseudoscalars. In the case of a single Stueckelberg pseudoscalar b, vacuum misalignments at phase transitions in the early Universe at the GUT scale provide a small mass - due to instanton suppression of the periodic potential - for a component of b, denoted as χ and termed the "axi-Higgs", which is a physical axion-like particle. The coupling of the axi-Higgs to the gauge sector via Wess-Zumino terms is suppressed by the Planck mass, which guarantees its decoupling, while its angle of misalignment is related to MGUT. We build a gauged E6 × U (1) model with anomalous U (1). It contains both an automatic invisible QCD axion and an ultra-light axi-Higgs. The invisible axion present in the model solves the strong CP problem and has mass in the conventional range while the axi-Higgs, which can act as dark matter, is sufficiently light (10-22 eV

Light hadron spectra in the constituent quark model with the Kobayashi-Kondo-Maskawa-'t Hooft effective U {sub A} (1) symmetry breaking interaction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dmitrasinovic, V.; Toki, H.; Research Center for Nuclear Physics, Osaka University, Ibaraki, Osaka 567-0047

2006-02-15

We make a critical comparison of several versions of instanton-induced interactions present in the literature, all based on ITEP group's extension to three colours and flavours of 't Hooft's effective lagrangian, with the predictions of the phenomenological Kobayashi-Kondo-Maskawa (KKM) chiral quark lagrangian. We analyze the effects of all versions of the effective U {sub A} (1) symmetry breaking interactions on light hadron spectra in the non-relativistic constituent quark model. We show that the KKMT force, when used as a residual hyperfine interaction reproduces the correct ordering of pseudoscalar and vector mesons even without explicitly taking chiral symmetry into account. Moreover,more » the nucleon spectra are also correctly reproduced, only the Roper resonance remains too high, albeit lower than usual, at 1660 MeV. The latter's lower than expected mass is not due to a small excitation energy, as in the Glozman-Riska (GR) model, but to a combination of colour, flavour, and spatial wave function properties that enhance the relevant matrix elements. The KKMT interaction explicitly depends on flavour and spin of the quarks, but unlike the GR flavour-spin one it has a firm footing in QCD. In the process we provide several technical advances, in particular we show the first explicit derivation of the three-body Fierz transformation and apply it to the KKM interaction. We also discuss the ambiguities associated with the colour degree of freedom.« less

Topological susceptibility in finite temperature (2 +1 )-flavor QCD using gradient flow

NASA Astrophysics Data System (ADS)

Taniguchi, Yusuke; Kanaya, Kazuyuki; Suzuki, Hiroshi; Umeda, Takashi; WHOT-QCD Collaboration

2017-03-01

We compute the topological charge and its susceptibility in finite temperature (2 +1 )-flavor QCD on the lattice applying a gradient flow method. With the Iwasaki gauge action and nonperturbatively O (a ) -improved Wilson quarks, we perform simulations on a fine lattice with a ≃0.07 fm at a heavy u , d quark mass with mπ/mρ≃0.63 , but approximately physical s quark mass with mηss/mϕ≃0.74 . In a temperature range from T ≃174 MeV (Nt=16 ) to 697 MeV (Nt=4 ), we study two topics on the topological susceptibility. One is a comparison of gluonic and fermionic definitions of the topological susceptibility. Because the two definitions are related by chiral Ward-Takahashi identities, their equivalence is not trivial for lattice quarks which violate the chiral symmetry explicitly at finite lattice spacings. The gradient flow method enables us to compute them without being bothered by the chiral violation. We find a good agreement between the two definitions with Wilson quarks. The other is a comparison with a prediction of the dilute instanton gas approximation, which is relevant in a study of axions as a candidate of the dark matter in the evolution of the Universe. We find that the topological susceptibility shows a decrease in T which is consistent with the predicted χt(T )∝(T /Tpc)-8 for three-flavor QCD even at low temperature Tpc

Walls, anomalies, and deconfinement in quantum antiferromagnets

NASA Astrophysics Data System (ADS)

Komargodski, Zohar; Sulejmanpasic, Tin; Ünsal, Mithat

2018-02-01

We consider the Abelian-Higgs model in 2 +1 dimensions with instanton-monopole defects. This model is closely related to the phases of quantum antiferromagnets. In the presence of Z2 preserving monopole operators, there are two confining ground states in the monopole phase, corresponding to the valence bond solid (VBS) phase of quantum magnets. We show that the domain wall carries a 't Hooft anomaly in this case. The anomaly can be saturated by, e.g., charge-conjugation breaking on the wall or by the domain wall theory becoming gapless (a gapless model that saturates the anomaly is S U (2) 1 WZW). Either way the fundamental scalar particles (i.e., spinons) which are confined in the bulk are deconfined on the domain wall. This Z2 phase can be realized either with spin-1/2 on a rectangular lattice or spin-1 on a square lattice. In both cases the domain wall contains spin-1/2 particles (which are absent in the bulk). We discuss the possible relation to recent lattice simulations of domain walls in VBS. We further generalize the discussion to Abrikosov-Nielsen-Olsen (ANO) vortices in a dual superconductor of the Abelian-Higgs model in 3 +1 dimensions and to the easy-plane limit of antiferromagnets. In the latter case the wall can undergo a variant of the BKT transition (consistent with the anomalies) while the bulk is still gapped. The same is true for the easy-axis limit of antiferromagnets. We also touch upon some analogies to Yang-Mills theory.

Tunneling Rate Constants for H2CO+H on Amorphous Solid Water Surfaces

NASA Astrophysics Data System (ADS)

Song, Lei; Kästner, Johannes

2017-12-01

Formaldehyde (H2CO) is one of the most abundant molecules observed in the icy mantle covering interstellar grains. Studying its evolution can contribute to our understanding of the formation of complex organic molecules in various interstellar environments. In this work, we investigated the hydrogenation reactions of H2CO yielding CH3O, CH2OH, and the hydrogen abstraction resulting in H2+HCO on an amorphous solid water (ASW) surface using a quantum mechanics/molecular mechanics (QM/MM) model. The binding energies of H2CO on the ASW surface vary broadly, from 1000 to 9370 K. No correlation was found between binding energies and activation energies of hydrogenation reactions. Combining instanton theory with QM/MM modeling, we calculated rate constants for the Langmuir-Hinshelwood and the Eley-Rideal mechanisms for the three product channels of H+H2CO surface reactions down to 59 K. We found that the channel producing CH2OH can be ignored, owing to its high activation barrier leading to significantly lower rates than the other two channels. The ASW surface influences the reactivity in favor of formation of CH3O (branching ratio ˜80%) and hinders the H2CO dissociation into H2+HCO. In addition, kinetic isotope effects are strong in all reaction channels and vary strongly between the channels. Finally, we provide fits of the rate constants to be used in astrochemical models.

[Research in theoretical nuclear physics]. [Annual progress report, July 1992--June 1993

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kapusta, J.I.

1993-12-31

The main subject of research was the physics of matter at energy densities greater than 0.15 GeV/fm{sup 3}. Theory encompasses the relativistic many-body/quantum field theory aspects of QCD and the electroweak interactions at these high energy densities, both in and out of thermal equilibrium. Applications range from neutron stars/pulsars to QCD and electroweak phase transitions in the early universe, from baryon number violation in cosmology to the description of nucleus-nucleus collisions at CERN and at Brookhaven. Recent activity to understand the properties of matter at energy densities where the electroweak W and Z boson degrees of freedom are important ismore » reported. This problem has applications to cosmology and has the potential to explain the baryon asymmetry produced in the big bang at energies where the particle degrees of freedom will soon be experimentally, probed. This problem is interesting for nuclear physics because of the techniques used in many-body, physics of nuclei and the quark-gluon plasma may be extended to this new problem. The was also interested in problems related to multiparticle production. This includes work on production of particles in heavy-ion collisions, the small x part, of the nuclear and hadron wave function, and multiparticle production induced by instantons in weakly coupled theories. These problems have applications in the heavy ion program at RHIC and the deep inelastic scattering experiments at HERA.« less

Non Abelian T-duality in Gauged Linear Sigma Models

NASA Astrophysics Data System (ADS)

Bizet, Nana Cabo; Martínez-Merino, Aldo; Zayas, Leopoldo A. Pando; Santos-Silva, Roberto

2018-04-01

Abelian T-duality in Gauged Linear Sigma Models (GLSM) forms the basis of the physical understanding of Mirror Symmetry as presented by Hori and Vafa. We consider an alternative formulation of Abelian T-duality on GLSM's as a gauging of a global U(1) symmetry with the addition of appropriate Lagrange multipliers. For GLSMs with Abelian gauge groups and without superpotential we reproduce the dual models introduced by Hori and Vafa. We extend the construction to formulate non-Abelian T-duality on GLSMs with global non-Abelian symmetries. The equations of motion that lead to the dual model are obtained for a general group, they depend in general on semi-chiral superfields; for cases such as SU(2) they depend on twisted chiral superfields. We solve the equations of motion for an SU(2) gauged group with a choice of a particular Lie algebra direction of the vector superfield. This direction covers a non-Abelian sector that can be described by a family of Abelian dualities. The dual model Lagrangian depends on twisted chiral superfields and a twisted superpotential is generated. We explore some non-perturbative aspects by making an Ansatz for the instanton corrections in the dual theories. We verify that the effective potential for the U(1) field strength in a fixed configuration on the original theory matches the one of the dual theory. Imposing restrictions on the vector superfield, more general non-Abelian dual models are obtained. We analyze the dual models via the geometry of their susy vacua.

Cosmic bubble and domain wall instabilities III: the role of oscillons in three-dimensional bubble collisions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bond, J. Richard; Braden, Jonathan; Mersini-Houghton, Laura, E-mail: bond@cita.utoronto.ca, E-mail: j.braden@ucl.ac.uk, E-mail: mersini@physics.unc.edu

2015-09-01

We study collisions between pairs of bubbles nucleated in an ambient false vacuum. For the first time, we include the effects of small initial (quantum) fluctuations around the instanton profiles describing the most likely initial bubble profile. Past studies of this problem neglect these fluctuations and work under the assumption that the collisions posess an exact SO(2,1) symmetry. We use three-dimensional lattice simulations to demonstrate that for double-well potentials, small initial perturbations to this symmetry can be amplified as the system evolves. Initially the amplification is well-described by linear perturbation theory around the SO(2,1) background, but the onset of strongmore » nonlinearities amongst the fluctuations quickly leads to a drastic breaking of the original SO(2,1) symmetry and the production of oscillons in the collision region. We explore several single-field models, and we find it is hard to both realize inflation inside of a bubble and produce oscillons in a collision. Finally, we extend our results to a simple two-field model. The additional freedom allowed by the second field allows us to construct viable inflationary models that allow oscillon production in collisions. The breaking of the SO(2,1) symmetry allows for a new class of observational signatures from bubble collisions that do not posess azimuthal symmetry, including the production of gravitational waves which cannot be supported by an SO(2,1) spacetime.« less

Optical knots and contact geometry II. From Ranada dyons to transverse and cosmetic knots

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kholodenko, Arkady L., E-mail: string@clemson.edu

2016-08-15

Some time ago Ranada (1989) obtained new nontrivial solutions of the Maxwellian gauge fields without sources. These were reinterpreted in Kholodenko (2015) [10] (part I) as particle-like (monopoles, dyons, etc.). They were obtained by the method of Abelian reduction of the non-Abelian Yang–Mills functional. The developed method uses instanton-type calculations normally employed for the non-Abelian gauge fields. By invoking the electric–magnetic duality it then becomes possible to replace all known charges/masses by the particle-like solutions of the source-free Abelian gauge fields. To employ these results in high energy physics, it is essential to extend Ranada’s results by carefully analyzing and classifying all dynamicallymore » generated knotted/linked structures in gauge fields, including those discovered by Ranada. This task is completed in this work. The study is facilitated by the recent progress made in solving the Moffatt conjecture. Its essence is stated as follows: in steady incompressible Euler-type fluids the streamlines could have knots/links of all types. By employing the correspondence between the ideal hydrodynamics and electrodynamics discussed in part I and by superimposing it with the already mentioned method of Abelian reduction, it is demonstrated that in the absence of boundaries only the iterated torus knots and links could be dynamically generated. Obtained results allow to develop further particle-knot/link correspondence studied in Kholodenko (2015) [13].« less

Gapless bosonic excitation without symmetry breaking: An algebraic spin liquid with soft gravitons

NASA Astrophysics Data System (ADS)

Xu, Cenke

2006-12-01

A quantum ground state of matter is realized in a bosonic model on a three-dimensional fcc lattice with emergent low energy excitations. The phase obtained is a stable gapless boson liquid phase, with algebraic boson density correlations. The stability of this phase is protected against the instanton effect and superfluidity by self-duality and large gauge symmetries on both sides of the duality. The gapless collective excitations of this phase closely resemble the graviton, although they have a soft ω˜k2 dispersion relation. There are three branches of gapless excitations in this phase, one of which is gapless scalar trace mode, the other two have the same polarization and gauge symmetries as the gravitons. The dynamics of this phase is described by a set of Maxwell’s equations. The defects carrying gauge charges can drive the system into the superfluid order when the defects are condensed; also the topological defects are coupled to the dual gauge field in the same manner as the charge defects couple to the original gauge field, after the condensation of the topological defects, the system is driven into the Mott insulator phase. In the two-dimensional case, the gapless soft graviton as well as the algebraic liquid phase are destroyed by the vertex operators in the dual theory, and the stripe order is most likely to take place close to the two-dimensional quantum critical point at which the vertex operators are tuned to zero.

Hydrogen transfer reactions of interstellar Complex Organic Molecules

NASA Astrophysics Data System (ADS)

Álvarez-Barcia, S.; Russ, P.; Kästner, J.; Lamberts, T.

2018-06-01

Radical recombination has been proposed to lead to the formation of complex organic molecules (COMs) in CO-rich ices in the early stages of star formation. These COMs can then undergo hydrogen addition and abstraction reactions leading to a higher or lower degree of saturation. Here, we have studied 14 hydrogen transfer reactions for the molecules glyoxal, glycoaldehyde, ethylene glycol, and methylformate and an additional three reactions where CHnO fragments are involved. Over-the-barrier reactions are possible only if tunneling is invoked in the description at low temperature. Therefore the rate constants for the studied reactions are calculated using instanton theory that takes quantum effects into account inherently. The reactions were characterized in the gas phase, but this is expected to yield meaningful results for CO-rich ices due to the minimal alteration of reaction landscapes by the CO molecules. We found that rate constants should not be extrapolated based on the height of the barrier alone, since the shape of the barrier plays an increasingly larger role at decreasing temperature. It is neither possible to predict rate constants based only on considering the type of reaction, the specific reactants and functional groups play a crucial role. Within a single molecule, though, hydrogen abstraction from an aldehyde group seems to be always faster than hydrogen addition to the same carbon atom. Reactions that involve heavy-atom tunneling, e.g., breaking or forming a C-C or C-O bond, have rate constants that are much lower than those where H transfer is involved.

Importance of tunneling in H-abstraction reactions by OH radicals. The case of CH4 + OH studied through isotope-substituted analogs

NASA Astrophysics Data System (ADS)

Lamberts, T.; Fedoseev, G.; Kästner, J.; Ioppolo, S.; Linnartz, H.

2017-03-01

We present a combined experimental and theoretical study focussing on the quantum tunneling of atoms in the reaction between CH4 and OH. The importance of this reaction pathway is derived by investigating isotope substituted analogs. Quantitative reaction rates needed for astrochemical models at low temperature are currently unavailable both in the solid state and in the gas phase. Here, we study tunneling effects upon hydrogen abstraction in CH4 + OH by focusing on two reactions: CH4 + OD → CH3 + HDO and CD4 + OH → CD3 + HDO. The experimental study shows that the solid-state reaction rate RCH4 + OD is higher than RCD4 + OH at 15 K. Experimental results are accompanied by calculations of the corresponding unimolecular and bimolecular reaction rate constants using instanton theory taking into account surface effects. For the work presented here, the unimolecular reactions are particularly interesting as these provide insight into reactions following a Langmuir-Hinshelwood process. The resulting ratio of the rate constants shows that the H abstraction (kCH4 + OD) is approximately ten times faster than D-abstraction (kCD4 + OH) at 65 K. We conclude that tunneling is involved at low temperatures in the abstraction reactions studied here. The unimolecular rate constants can be used by the modeling community as a first approach to describe OH-mediated abstraction reactions in the solid phase. For this reason we provide fits of our calculated rate constants that allow the inclusion of these reactions in models in a straightforward fashion.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rossi, Mariana; Manolopoulos, David E.; Ceriotti, Michele

Two of the most successful methods that are presently available for simulating the quantum dynamics of condensed phase systems are centroid molecular dynamics (CMD) and ring polymer molecular dynamics (RPMD). Despite their conceptual differences, practical implementations of these methods differ in just two respects: the choice of the Parrinello-Rahman mass matrix and whether or not a thermostat is applied to the internal modes of the ring polymer during the dynamics. Here, we explore a method which is halfway between the two approximations: we keep the path integral bead masses equal to the physical particle masses but attach a Langevin thermostatmore » to the internal modes of the ring polymer during the dynamics. We justify this by showing analytically that the inclusion of an internal mode thermostat does not affect any of the established features of RPMD: thermostatted RPMD is equally valid with respect to everything that has actually been proven about the method as RPMD itself. In particular, because of the choice of bead masses, the resulting method is still optimum in the short-time limit, and the transition state approximation to its reaction rate theory remains closely related to the semiclassical instanton approximation in the deep quantum tunneling regime. In effect, there is a continuous family of methods with these properties, parameterised by the strength of the Langevin friction. Here, we explore numerically how the approximation to quantum dynamics depends on this friction, with a particular emphasis on vibrational spectroscopy. We find that a broad range of frictions approaching optimal damping give similar results, and that these results are immune to both the resonance problem of RPMD and the curvature problem of CMD.« less

Non Abelian T-duality in Gauged Linear Sigma Models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bizet, Nana Cabo; Martínez-Merino, Aldo; Zayas, Leopoldo A. Pando

Abelian T-duality in Gauged Linear Sigma Models (GLSM) forms the basis of the physical understanding of Mirror Symmetry as presented by Hori and Vafa. We consider an alternative formulation of Abelian T-duality on GLSM’s as a gauging of a global U(1) symmetry with the addition of appropriate Lagrange multipliers. For GLSMs with Abelian gauge groups and without superpotential we reproduce the dual models introduced by Hori and Vafa. We extend the construction to formulate non-Abelian T-duality on GLSMs with global non-Abelian symmetries. The equations of motion that lead to the dual model are obtained for a general group, they dependmore » in general on semi-chiral superfields; for cases such as SU(2) they depend on twisted chiral superfields. We solve the equations of motion for an SU(2) gauged group with a choice of a particular Lie algebra direction of the vector superfield. This direction covers a non-Abelian sector that can be described by a family of Abelian dualities. The dual model Lagrangian depends on twisted chiral superfields and a twisted superpotential is generated. We explore some non-perturbative aspects by making an Ansatz for the instanton corrections in the dual theories. We verify that the effective potential for the U(1) field strength in a fixed configuration on the original theory matches the one of the dual theory. Imposing restrictions on the vector superfield, more general non-Abelian dual models are obtained. We analyze the dual models via the geometry of their susy vacua.« less

Some finite terms from ladder diagrams in three and four loop maximal supergravity

NASA Astrophysics Data System (ADS)

Basu, Anirban

2015-10-01

We consider the finite part of the leading local interactions in the low energy expansion of the four graviton amplitude from the ladder skeleton diagrams in maximal supergravity on T 2, at three and four loops. At three loops, we express the {D}8{{R}}4 and {D}10{{R}}4 amplitudes as integrals over the moduli space of an underlying auxiliary geometry. These amplitudes are evaluated exactly for special values of the the moduli of the auxiliary geometry, where the integrand simplifies. We also perform a similar analysis for the {D}8{{R}}4 amplitude at four loops that arise from the ladder skeleton diagrams for a special value of a parameter in the moduli space of the auxiliary geometry. While the dependence of the amplitudes on the volume of the T 2 is very simple, the dependence on the complex structure of the T 2 is quite intricate. In some of the cases, the amplitude consists of terms each of which factorizes into a product of two {SL}(2,{{Z}}) invariant modular forms. While one of the factors is a non-holomorphic Eisenstein series, the other factor splits into a sum of modular forms each of which satisfies a Poisson equation on moduli space with source terms that are bilinear in the Eisenstein series. This leads to several possible perturbative contributions unto genus 5 in type II string theory on S1. Unlike the one and two loop supergravity analysis, these amplitudes also receive non-perturbative contributions from bound states of three D-(anti)instantons in the IIB theory.

The dissociation and recombination rates of CH4 through the Ni(111) surface: The effect of lattice motion

NASA Astrophysics Data System (ADS)

Wang, Wenji; Zhao, Yi

2017-07-01

Methane dissociation is a prototypical system for the study of surface reaction dynamics. The dissociation and recombination rates of CH4 through the Ni(111) surface are calculated by using the quantum instanton method with an analytical potential energy surface. The Ni(111) lattice is treated rigidly, classically, and quantum mechanically so as to reveal the effect of lattice motion. The results demonstrate that it is the lateral displacements rather than the upward and downward movements of the surface nickel atoms that affect the rates a lot. Compared with the rigid lattice, the classical relaxation of the lattice can increase the rates by lowering the free energy barriers. For instance, at 300 K, the dissociation and recombination rates with the classical lattice exceed the ones with the rigid lattice by 6 and 10 orders of magnitude, respectively. Compared with the classical lattice, the quantum delocalization rather than the zero-point energy of the Ni atoms further enhances the rates by widening the reaction path. For instance, the dissociation rate with the quantum lattice is about 10 times larger than that with the classical lattice at 300 K. On the rigid lattice, due to the zero-point energy difference between CH4 and CD4, the kinetic isotope effects are larger than 1 for the dissociation process, while they are smaller than 1 for the recombination process. The increasing kinetic isotope effect with decreasing temperature demonstrates that the quantum tunneling effect is remarkable for the dissociation process.

Transmutation of a trans-series: the Gross-Witten-Wadia phase transition

NASA Astrophysics Data System (ADS)

Ahmed, Anees; Dunne, Gerald V.

2017-11-01

We study the change in the resurgent asymptotic properties of a trans-series in two parameters, a coupling g 2 and a gauge index N, as a system passes through a large N phase transition, using the universal example of the Gross-Witten-Wadia third-order phase transition in the unitary matrix model. This transition is well-studied in the immediate vicinity of the transition point, where it is characterized by a double-scaling limit Painlevé II equation, and also away from the transition point using the pre-string difference equation. Here we present a complementary analysis of the transition at all coupling and all finite N, in terms of a differential equation, using the explicit Tracy-Widom mapping of the Gross-Witten-Wadia partition function to a solution of a Painlevé III equation. This mapping provides a simple method to generate trans-series expansions in all parameter regimes, and to study their transmutation as the parameters are varied. For example, at any finite N the weak coupling expansion is divergent, with a non-perturbative trans-series completion; on the other hand, the strong coupling expansion is convergent, and yet there is still a non-perturbative trans-series completion. We show how the different instanton terms `condense' at the transition point to match with the double-scaling limit trans-series. We also define a uniform large N strong-coupling expansion (a non-linear analogue of uniform WKB), which is much more precise than the conventional large N expansion through the transition region, and apply it to the evaluation of Wilson loops.

Formation of the prebiotic molecule NH2CHO on astronomical amorphous solid water surfaces: accurate tunneling rate calculations.

PubMed

Song, Lei; Kästner, Johannes

2016-10-26

Investigating how formamide forms in the interstellar medium is a hot topic in astrochemistry, which can contribute to our understanding of the origin of life on Earth. We have constructed a QM/MM model to simulate the hydrogenation of isocyanic acid on amorphous solid water surfaces to form formamide. The binding energy of HNCO on the ASW surface varies significantly between different binding sites, we found values between ∼0 and 100 kJ mol -1 . The barrier for the hydrogenation reaction is almost independent of the binding energy, though. We calculated tunneling rate constants of H + HNCO → NH 2 CO at temperatures down to 103 K combining QM/MM with instanton theory. Tunneling dominates the reaction at such low temperatures. The tunneling reaction is hardly accelerated by the amorphous solid water surface compared to the gas phase for this system, even though the activation energy of the surface reaction is lower than the one of the gas-phase reaction. Both the height and width of the barrier affect the tunneling rate in practice. Strong kinetic isotope effects were observed by comparing to rate constants of D + HNCO → NHDCO. At 103 K we found a KIE of 231 on the surface and 146 in the gas phase. Furthermore, we investigated the gas-phase reaction NH 2 + H 2 CO → NH 2 CHO + H and found it unlikely to occur at cryogenic temperatures. The data of our tunneling rate constants are expected to significantly influence astrochemical models.

Non Abelian T-duality in Gauged Linear Sigma Models

DOE PAGES

Bizet, Nana Cabo; Martínez-Merino, Aldo; Zayas, Leopoldo A. Pando; ...

2018-04-01

Abelian T-duality in Gauged Linear Sigma Models (GLSM) forms the basis of the physical understanding of Mirror Symmetry as presented by Hori and Vafa. We consider an alternative formulation of Abelian T-duality on GLSM’s as a gauging of a global U(1) symmetry with the addition of appropriate Lagrange multipliers. For GLSMs with Abelian gauge groups and without superpotential we reproduce the dual models introduced by Hori and Vafa. We extend the construction to formulate non-Abelian T-duality on GLSMs with global non-Abelian symmetries. The equations of motion that lead to the dual model are obtained for a general group, they dependmore » in general on semi-chiral superfields; for cases such as SU(2) they depend on twisted chiral superfields. We solve the equations of motion for an SU(2) gauged group with a choice of a particular Lie algebra direction of the vector superfield. This direction covers a non-Abelian sector that can be described by a family of Abelian dualities. The dual model Lagrangian depends on twisted chiral superfields and a twisted superpotential is generated. We explore some non-perturbative aspects by making an Ansatz for the instanton corrections in the dual theories. We verify that the effective potential for the U(1) field strength in a fixed configuration on the original theory matches the one of the dual theory. Imposing restrictions on the vector superfield, more general non-Abelian dual models are obtained. We analyze the dual models via the geometry of their susy vacua.« less

Entanglement and co-tunneling of two equivalent protons in hydrogen bond pairs

NASA Astrophysics Data System (ADS)

Smedarchina, Zorka; Siebrand, Willem; Fernández-Ramos, Antonio

2018-03-01

A theoretical study is reported of a system of two identical symmetric hydrogen bonds, weakly coupled such that the two mobile protons can move either separately (stepwise) or together (concerted). It is modeled by two equivalent quartic potentials interacting through dipolar and quadrupolar coupling terms. The tunneling Hamiltonian has two imaginary modes (reaction coordinates) and a potential with a single maximum that may turn into a saddle-point of second order and two sets of (inequivalent) minima. Diagonalization is achieved via a modified Jacobi-Davidson algorithm. From this Hamiltonian the mechanism of proton transfer is derived. To find out whether the two protons move stepwise or concerted, a new tool is introduced, based on the distribution of the probability flux in the dividing plane of the transfer mode. While stepwise transfer dominates for very weak coupling, it is found that concerted transfer (co-tunneling) always occurs, even when the coupling vanishes since the symmetry of the Hamiltonian imposes permanent entanglement on the motions of the two protons. We quantify this entanglement and show that, for a wide range of parameters of interest, the lowest pair of states of the Hamiltonian represents a perfect example of highly entangled quantum states in continuous variables. The method is applied to the molecule porphycene for which the observed tunneling splitting is calculated in satisfactory agreement with experiment, and the mechanism of double-proton tunneling is found to be predominantly concerted. We show that, under normal conditions, when they are in the ground state, the two porphycene protons are highly entangled, which may have interesting applications. The treatment also identifies the conditions under which such a system can be handled by conventional one-instanton techniques.

Predicted and Totally Unexpected in the Energy Frontier Opened by LHC

NASA Astrophysics Data System (ADS)

Zichichi, Antonino

2011-01-01

Opening lectures. Sid Coleman and Erice / A. Zichichi. Remembering Sidney Coleman / G.'t Hooft -- Predicted signals at LHC. From extra-dimensions: Multiple branes scenarios and their contenders / I. Antoniadis. Predicted signals at the LHC from technicolor / A. Martin. The one-parameter model at LHC / J. Maxin, E. Mayes and D. V. Nanopoulos. How supercritical string cosmology affects LHC / D. V. Nanopoulos. High scale physics connection to LHC data / P. Nath. Predicted signatures at the LHC from U(I) extensions of the standard model / P. Nath -- Hot theoretical topics. Progress on the ultraviolet finiteness of supergravity / Z. Bern. Status of supersymmetry: Foundations and applications / S. Ferrara and A. Marrani. Quantum gravity from dynamical triangulation / R. Loll. Status of superstring and M-theory / J. H. Schwarz. Some effects of instantons in QCD / G.'t Hooft. Crystalline gravity / G.'t Hooft -- QCD problems. Strongly coupled gauge theories / R. Kenway. Strongly interacting matter at high energy density / L. McLerran. Seminars on specialized topics. The nature and the mass of neutrinos. Majorana vs. Dirac / A. Bettini. The anomalous spin distributions in the nucleon / A. Deshpande. Results from PHENIX at RHIC / M. J. Tannenbaum -- Highlights from laboratories. Highlights from RHIC / Y. Akiba. News from the Gran Sasso Underground Laboratory / E. Coccia. Highlights from TRIUMF / N. S. Lockyer. Highlights from Superkamiokande / M. Koshiba. Highlights from Fermilab / P. J. Oddone. Highlights from IHEP / Y. Wang -- Special sessions for new talents. Fake supergravity and black hole evolution / A. Gnecchi. Track-based improvement in the jet transverse momentum resolution for ATLAS / Z. Marshall. Searches for supersymmetric dark matter with XENON / K. Ni. Running of Newton's constant and quantum gravitational effects / D. Reeb.

Detection and quantification of explosives and CWAs using a handheld widely tunable quantum cascade laser

NASA Astrophysics Data System (ADS)

Deutsch, Erik R.; Haibach, Frederick G.; Mazurenko, Alexander

2012-06-01

The requirements for standoff detection of Explosives and CWA/TICs on surfaces in the battlefield are challenging because of the low detection limits. The variety of targets, backgrounds and interferences increase the challenges. Infrared absorption spectroscopy with traditional infrared detection technologies, incandescent sources that offer broad wavelength range but poor spectral intensity, are particularly challenged in standoff applications because most photons are lost to the target, background and the environment. Using a brighter source for active infrared detection e.g. a widely-tunable quantum cascade laser (QCL) source, provides sufficient spectral intensity to achieve the needed sensitivity and selectivity for explosives, CWAs, and TICs on surfaces. Specific detection of 1-10 μg/cm2 is achieved within seconds. CWAs, and TICs in vapor and aerosol form present a different challenge. Vapors and aerosols are present at low concentrations, so long pathlengths are required to achieve the desired sensitivity. The collimated output beam from the QCL simplifies multi-reflection cells for vapor detection while also enabling large standoff distances. Results obtained by the QCL system indicate that <1 ppm for vapors can be achieved with specificity in a measurement time of seconds, and the QCL system was successfully able to detect agents in the presence of interferents. QCLs provide additional capabilities for the dismounted warfighter. Given the relatively low power consumption, small package, and instant-on capability of the QCL, a handheld device can provide field teams with early detection of toxic agents and energetic materials in standoff, vapor, or aerosol form using a single technology and device which makes it attractive compared other technologies.

Classification of compactified su( N c ) gauge theories with fermions in all representations

NASA Astrophysics Data System (ADS)

Anber, Mohamed M.; Vincent-Genod, Loïc

2017-12-01

We classify su( N c ) gauge theories on R^3× S^1 with massless fermions in higher representations obeying periodic boundary conditions along S^1 . In particular, we single out the class of theories that is asymptotically free and weakly coupled in the infrared, and therefore, is amenable to semi-classical treatment. Our study is conducted by carefully identifying the vacua inside the affine Weyl chamber using Verma bases and Frobenius formula techniques. Theories with fermions in pure representations are generally strongly coupled. The only exceptions are the four-index symmetric representation of su(2) and adjoint representation of su( N c ). However, we find a plethora of admissible theories with fermions in mixed representations. A sub-class of these theories have degenerate perturbative vacua separated by domain walls. In particular, su( N c ) theories with fermions in the mixed representations adjoint⊕fundamental and adjoint⊕two-index symmetric admit degenerate vacua that spontaneously break the parity P , charge conjugation C , and time reversal T symmetries. These are the first examples of strictly weakly coupled gauge theories on R^3× S^1 with spontaneously broken C , P , and T symmetries. We also compute the fermion zero modes in the background of monopole-instantons. The monopoles and their composites (topological molecules) proliferate in the vacuum leading to the confinement of electric charges. Interestingly enough, some theories have also accidental degenerate vacua, which are not related by any symmetry. These vacua admit different numbers of fermionic zero modes, and hence, different kinds of topological molecules. The lack of symmetry, however, indicates that such degeneracy might be lifted by higher order corrections. Finally, we study the general phase structure of adjoint⊕fundamental theories in the small circle and decompactification limits.

Towards a systematic construction of realistic D-brane models on a del Pezzo singularity

NASA Astrophysics Data System (ADS)

Dolan, Matthew J.; Krippendorf, Sven; Quevedo, Fernando

2011-10-01

A systematic approach is followed in order to identify realistic D-brane models at toric del Pezzo singularities. Requiring quark and lepton spectrum and Yukawas from D3 branes and massless hypercharge, we are led to Pati-Salam extensions of the Standard Model. Hierarchies of masses, flavour mixings and control of couplings select higher order del Pezzo singularities, minimising the Higgs sector prefers toric del Pezzos with dP 3 providing the most successful compromise. Then a supersymmetric local string model is presented with the following properties at low energies: (i) the MSSM spectrum plus a local B - L gauge field or additional Higgs fields depending on the breaking pattern, (ii) a realistic hierarchy of quark and lepton masses and (iii) realistic flavour mixing between quark and lepton families with computable CKM and PMNS matrices, and CP violation consistent with observations. In this construction, kinetic terms are diagonal and under calculational control suppressing standard FCNC contributions. Proton decay operators of dimension 4, 5, 6 are suppressed, and gauge couplings can unify depending on the breaking scales from string scales at energies in the range 1012-1016 GeV, consistent with TeV soft-masses from moduli mediated supersymmetry breaking. The GUT scale model corresponds to D3 branes at dP 3 with two copies of the Pati-Salam gauge symmetry SU(4) × SU(2) R × SU(2) L . D-brane instantons generate a non-vanishing μ-term. Right handed sneutrinos can break the B - L symmetry and induce a see-saw mechanism of neutrino masses and R-parity violating operators with observable low-energy implications.

A non-volatile flip-flop based on diode-selected PCM for ultra-low power systems

NASA Astrophysics Data System (ADS)

Ye, Yong; Du, Yuan; Gao, Dan; Kang, Yong; Song, Zhitang; Chen, Bomy

2016-10-01

As the process technology is continuously shrinking, low power consumption is a major issue in VLSI Systems-on-Chip (SoCs), especially for standby-power-critical applications. Recently, the emerging CMOS-compatible non-volatile memories (NVMs), such as Phase Change Memory (PCM), have been used as on-chip storage elements, which can obtain non-volatile processing, nearly-zero standby power and instant-on capability. PCM has been considered as the best candidate for the next generation of NVMs for its low cost, high density and high resistance transformation ratio. In this paper, for the first time, we present a diode-selected PCM based non-volatile flip-flop (NVFF) which is optimized for better power consumption and process variation tolerance. With dual trench isolation process, the diode-selected PCM realizes ultra small area, which is very suitable for multi-context configuration and large scale flip-flops matrix. Since the MOS-selected PCM is hard to shrink further due to large amount of PCM write current, the proposed NVFF achieves higher power efficiency without loss of current driving capability. Using the 40nm manufacturing process, the area of the cell (1D1R) is as small as 0.016 μm2. Simulation results show that the energy consumption during the recall operation is 62 fJ with 1.1 standard supply voltage, which is reduced by 54.9% compared to the previous 2T2R based NVFF. When the supply voltage reduces to 0.7 V, the recall energy is as low as 17 fJ. With the great advantages in cell size and energy, the proposed diode-selected NVFF is very applicable and cost-effective for ULP systems.

Effects of dynamical paths on the energy gap and the corrections to the free energy in path integrals of mean-field quantum spin systems

NASA Astrophysics Data System (ADS)

Koh, Yang Wei

2018-03-01

In current studies of mean-field quantum spin systems, much attention is placed on the calculation of the ground-state energy and the excitation gap, especially the latter, which plays an important role in quantum annealing. In pure systems, the finite gap can be obtained by various existing methods such as the Holstein-Primakoff transform, while the tunneling splitting at first-order phase transitions has also been studied in detail using instantons in many previous works. In disordered systems, however, it remains challenging to compute the gap of large-size systems with specific realization of disorder. Hitherto, only quantum Monte Carlo techniques are practical for such studies. Recently, Knysh [Nature Comm. 7, 12370 (2016), 10.1038/ncomms12370] proposed a method where the exponentially large dimensionality of such systems is condensed onto a random potential of much lower dimension, enabling efficient study of such systems. Here we propose a slightly different approach, building upon the method of static approximation of the partition function widely used for analyzing mean-field models. Quantum effects giving rise to the excitation gap and nonextensive corrections to the free energy are accounted for by incorporating dynamical paths into the path integral. The time-dependence of the trace of the time-ordered exponential of the effective Hamiltonian is calculated by solving a differential equation perturbatively, yielding a finite-size series expansion of the path integral. Formulae for the first excited-state energy are proposed to aid in computing the gap. We illustrate our approach using the infinite-range ferromagnetic Ising model and the Hopfield model, both in the presence of a transverse field.

Tunneling dynamics of double proton transfer in formic acid and benzoic acid dimers

NASA Astrophysics Data System (ADS)

Smedarchina, Zorka; Fernández-Ramos, Antonio; Siebrand, Willem

2005-04-01

Direct dynamics calculations based on instanton techniques are reported of tunneling splittings due to double proton transfer in formic and benzoic acid dimers. The results are used to assign the observed splittings to levels for which the authors of the high-resolution spectra could not provide a definitive assignment. In both cases the splitting is shown to be due mainly to the zero-point level rather than to the vibrationally or electronically excited level whose spectrum was investigated. This leads to zero-point splittings of 375MHz for (DCOOH)2 and 1107MHz for the benzoic acid dimer. Thus, contrary to earlier calculations, it is found that the splitting is considerably larger in the benzoic than in the formic acid dimer. The calculations are extended to solid benzoic acid where the asymmetry of the proton-transfer potential induced by the crystal can be overcome by suitable doping. This has allowed direct measurement of the interactions responsible for double proton transfer, which were found to be much larger than those in the isolated dimer. To account for this observation both static and dynamic effects of the crystal forces on the intradimer hydrogen bonds are included in the calculations. The same methodology, extended to higher temperatures, is used to calculate rate constants for HH, HD, and DD transfers in neat benzoic acid crystals. The results are in good agreement with reported experimental rate constants measured by NMR relaxometry and, if allowance is made for small structural changes induced by doping, with the transfer matrix elements observed in doped crystals. Hence the method used allows a unified description of tunneling splittings in the gas phase and in doped crystals as well as of transfer rates in neat crystals.

On the Large R-charge Expansion in N=2 Superconformal Field Theories

NASA Astrophysics Data System (ADS)

Hellerman, Simeon; Maeda, Shunsuke

2017-12-01

In this note we study two point functions of Coulomb branch chiral ring elements with large R-charge, in quantum field theories with N=2 superconformal symmetry in four spacetime dimensions. Focusing on the case of one-dimensional Coulomb branch, we use the effective-field-theoretic methods of [1], to estimate the two-point correlation function Y_n≡ {|x-y|}^{2n{Δ}_O}< {(O(x))}^n{(\\overlineO(y))}^n> in the limit where the operator insertion O^n has large total R-charge J=n{Δ}_O . We show that Y_n has a nontrivial but universal asymptotic expansion at large J , of the form Y_n from "Euclid Math One" (0x3D)J!{(|{N}_O|/2π)}^{2J}J^{α }{\\tildeY}_n, where {\\tildeY}_n approaches a constant as n → ∞, and {N}_O is an n-independent constant describing on the normalization of the operator relative to the effective Abelian gauge coupling. The exponent α is a positive number proportional to the difference between the a-anomaly coefficient of the underlying CFT and that of the effective theory of the Coulomb branch. For Lagrangian SCFT, we check our predictions for the logarithm B_n= log (Y_n) , up to and including order log J against exact results from supersymmetric localization [2-5]. In the case of N=4 we find precise agreement and in the case N=2 we find reasonably good numerical agreement at J˜eq 60 using the no-instanton approximation to the S 4 partition function. We also give predictions for the growth of two-point functions in all rank-one SCFT in the classification of [6-9]. In this way, we show the large- R-charge expansion serves as a bridge from the world of unbroken superconformal symmetry, OPE data, and bootstraps, to the world of the low-energy dynamics of the moduli space of vacua.

The infrared behaviour of QCD Green's functions. Confinement, dynamical symmetry breaking, and hadrons as relativistic bound states

NASA Astrophysics Data System (ADS)

Alkofer, Reinhard; von Smekal, Lorenz

2001-11-01

Recent studies of QCD Green's functions and their applications in hadronic physics are reviewed. We discuss the definition of the generating functional in gauge theories, in particular, the rôle of redundant degrees of freedom, possibilities of a complete gauge fixing versus gauge fixing in presence of Gribov copies, BRS invariance and positivity. The apparent contradiction between positivity and colour antiscreening in combination with BRS invariance in QCD is considered. Evidence for the violation of positivity by quarks and transverse gluons in the covariant gauge is collected, and it is argued that this is one manifestation of confinement. We summarise the derivation of the Dyson-Schwinger equations (DSEs) of QED and QCD. For the latter, the implications of BRS invariance on the Green's functions are explored. The possible influence of instantons on DSEs is discussed in a two-dimensional model. In QED in (2+1) and (3+1) dimensions, the solutions for Green's functions provide tests of truncation schemes which can under certain circumstances be extended to the DSEs of QCD. We discuss some limitations of such extensions and assess the validity of assumptions for QCD as motivated from studies in QED. Truncation schemes for DSEs are discussed in axial and related gauges, as well as in the Landau gauge. Furthermore, we review the available results from a systematic non-perturbative expansion scheme established for Landau gauge QCD. Comparisons to related lattice results, where available, are presented. The applications of QCD Green's functions to hadron physics are summarised. Properties of ground state mesons are discussed on the basis of the ladder Bethe-Salpeter equation for quarks and antiquarks. The Goldstone nature of pseudoscalar mesons and a mechanism for diquark confinement beyond the ladder approximation are reviewed. We discuss some properties of ground state baryons based on their description as Bethe-Salpeter/Faddeev bound states of quark-diquark correlations in the quantum field theory of confined quarks and gluons.

Perspective: Memcomputing: Leveraging memory and physics to compute efficiently

NASA Astrophysics Data System (ADS)

Di Ventra, Massimiliano; Traversa, Fabio L.

2018-05-01

It is well known that physical phenomena may be of great help in computing some difficult problems efficiently. A typical example is prime factorization that may be solved in polynomial time by exploiting quantum entanglement on a quantum computer. There are, however, other types of (non-quantum) physical properties that one may leverage to compute efficiently a wide range of hard problems. In this perspective, we discuss how to employ one such property, memory (time non-locality), in a novel physics-based approach to computation: Memcomputing. In particular, we focus on digital memcomputing machines (DMMs) that are scalable. DMMs can be realized with non-linear dynamical systems with memory. The latter property allows the realization of a new type of Boolean logic, one that is self-organizing. Self-organizing logic gates are "terminal-agnostic," namely, they do not distinguish between the input and output terminals. When appropriately assembled to represent a given combinatorial/optimization problem, the corresponding self-organizing circuit converges to the equilibrium points that express the solutions of the problem at hand. In doing so, DMMs take advantage of the long-range order that develops during the transient dynamics. This collective dynamical behavior, reminiscent of a phase transition, or even the "edge of chaos," is mediated by families of classical trajectories (instantons) that connect critical points of increasing stability in the system's phase space. The topological character of the solution search renders DMMs robust against noise and structural disorder. Since DMMs are non-quantum systems described by ordinary differential equations, not only can they be built in hardware with the available technology, they can also be simulated efficiently on modern classical computers. As an example, we will show the polynomial-time solution of the subset-sum problem for the worst cases, and point to other types of hard problems where simulations of DMMs' equations of motion on classical computers have already demonstrated substantial advantages over traditional approaches. We conclude this article by outlining further directions of study.

Emergent gauge fields and their nonperturbative effects in correlated electrons

NASA Astrophysics Data System (ADS)

Kim, Ki-Seok; Tanaka, Akihiro

2015-06-01

The history of modern condensed matter physics may be regarded as the competition and reconciliation between Stoner’s and Anderson’s physical pictures, where the former is based on momentum-space descriptions focusing on long wave-length fluctuations while the latter is based on real-space physics emphasizing emergent localized excitations. In particular, these two view points compete with each other in various nonperturbative phenomena, which range from the problem of high Tc superconductivity, quantum spin liquids in organic materials and frustrated spin systems, heavy-fermion quantum criticality, metal-insulator transitions in correlated electron systems such as doped silicons and two-dimensional electron systems, the fractional quantum Hall effect, to the recently discussed Fe-based superconductors. An approach to reconcile these competing frameworks is to introduce topologically nontrivial excitations into the Stoner’s description, which appear to be localized in either space or time and sometimes both, where scattering between itinerant electrons and topological excitations such as skyrmions, vortices, various forms of instantons, emergent magnetic monopoles, and etc. may catch nonperturbative local physics beyond the Stoner’s paradigm. In this review paper, we discuss nonperturbative effects of topological excitations on dynamics of correlated electrons. First, we focus on the problem of scattering between itinerant fermions and topological excitations in antiferromagnetic doped Mott insulators, expected to be relevant for the pseudogap phase of high Tc cuprates. We propose that nonperturbative effects of topological excitations can be incorporated within the perturbative framework, where an enhanced global symmetry with a topological term plays an essential role. In the second part, we go on to discuss the subject of symmetry protected topological states in a largely similar light. While we do not introduce itinerant fermions here, the nonperturbative dynamics of topological excitations is again seen to be crucial in classifying topologically nontrivial gapped systems. We point to some hidden links between several effective field theories with topological terms, starting with one-dimensional physics, and subsequently finding natural generalizations to higher dimensions.

Emergent Gauge Fields and Their Nonperturbative Effects in Correlated Electrons

NASA Astrophysics Data System (ADS)

Kim, Ki-Seok; Tanaka, Akihiro

The history of modern condensed matter physics may be regarded as the competition and reconciliation between Stoner's and Anderson's physical pictures, where the former is based on momentum-space descriptions focusing on long wave-length fluctuations while the latter is based on real-space physics emphasizing emergent localized excitations. In particular, these two view points compete with each other in various nonperturbative phenomena, which range from the problem of high Tc superconductivity, quantum spin liquids in organic materials and frustrated spin systems, heavy-fermion quantum criticality, metal-insulator transitions in correlated electron systems such as doped silicons and two-dimensional electron systems, the fractional quantum Hall effect, to the recently discussed Fe-based superconductors. An approach to reconcile these competing frameworks is to introduce topologically nontrivial excitations into the Stoner's description, which appear to be localized in either space or time and sometimes both, where scattering between itinerant electrons and topological excitations such as skyrmions, vortices, various forms of instantons, emergent magnetic monopoles, and etc. may catch nonperturbative local physics beyond the Stoner's paradigm. In this review article we discuss nonperturbative effects of topological excitations on dynamics of correlated electrons. First, we focus on the problem of scattering between itinerant fermions and topological excitations in antiferromagnetic doped Mott insulators, expected to be relevant for the pseudogap phase of high Tc cuprates. We propose that nonperturbative effects of topological excitations can be incorporated within the perturbative framework, where an enhanced global symmetry with a topological term plays an essential role. In the second part, we go on to discuss the subject of symmetry protected topological states in a largely similar light. While we do not introduce itinerant fermions here, the nonperturbative dynamics of topological excitations is again seen to be crucial in classifying topologically nontrivial gapped systems. We point to some hidden links between several effective field theories with topological terms, starting with one dimensional physics, and subsequently finding natural generalizations to higher dimensions.

Fluxes, holography and twistors: String theory paths to four dimensions

NASA Astrophysics Data System (ADS)

Gao, Peng

2007-12-01

There are presently three popular paths to obtain four dimensional physics from string theory: compactification, holography and twistor space. We present results in this thesis on each of them, discussing the geometric structure of flux compactifications, the interplay between holography and S -duality in M-theory and the perturbative amplitudes of the marginally deformed super-Yang-Mills theory obtained from topological string theory on a supertwistor space. First we analyze supersymmetric flux compactifications of ten dimensional string theories to four dimensions. Back reaction of the fluxes on the six dimensional internal geometry is characterized by G-structures. In type IIB compactification on SU(3)-structure manifold with N = 1 supersymmetry, we solve the equations dictating the five components of intrinsic torsion. We find that the six dimensional manifold always retains an integrable almost complex structure compatible with supersymmetry. In terms of the various vacuum fields, the axion/dilaton is found to be generically non-holomorphic, and the four dimensional cosmological constant is nonvanishing only if the SU(3) structure group is reduced to SU(2). The equations are solved by one holomorphic function. Around the poles and zeros of the holomorphic function, the geometry locally looks like the well known type-A and type-B solutions. When this function is a constant, the geometry can be viewed as a holographic RG flow. After classifying the type IIB SU(3)-structure flux vacua, we analyze the effect of non-perturbative corrections on the moduli space of N = 2 flux compactifications. At energy below the Kaluza-Klein scale, the four dimensional effective theory is a gauged supergravity theory with vanishing cosmological constant. The gauging of isometries on the hyper-multiplet moduli space is induced by the fluxes. We show that instanton corrections which could potentially lift the gauged isometries are in fact prohibited both in the type IIA and heterotic string theories by the inclusion of flux. Hence gauged supergravity is a robust framework for studying flux vacua even when these stringy effects are taken into account. The mechanisms which protect the gauged isometries are different in the two theories. Then we switch to the understanding of SL(2, Z ) duality transformations in asymptotically AdS4 x S7 spacetime with an Abelian gauge theory. The bulk duality acts non-trivially on the three-dimensional SCFT of coincident M2-branes on the conformal boundary. We develop a systematic method to holographically obtain the deformations of the boundary CFT manifested by generalized boundary conditions and show how SL(2, Z ) duality relates different deformations of the conformal vacuum. We analyze in detail marginal deformations and deformations by dimension 4 operators. In the case of massive deformations, the RG flow induces a Legendre transform as well as S-duality. Correlation functions in the CFT are computed by differentiating with respect to magnetic bulk sources, whereas correlation functions in the Legendre dual CFT are computed using electric bulk sources. Under massive deformations, the boundary effective action is generically minimized by massive self-dual configurations of the U(1) gauge field. We show that a massive and self-dual boundary condition corresponds to the unique self-dual topologically massive gauge theory in three dimensions. Thus, self-duality in three dimensions can be understood as a consequence of SL(2, Z ) invariance in the bulk of AdS4. We discuss various implications for understanding the strongly interacting worldvolume theory of M2-branes and more general dualities of the maximally supersymmetric AdS4 supergravity theory. Finally we study the twistor string theory whose D-instanton expansion gives the perturbative expansion of marginally deformed N = 4 super-Yang-Mills theories. More precisely this string theory is a topological B-model with both open and closed string sectors with target space CP3|4 , a super-Calabi-Yau manifold. The tree-level amplitudes in the N = 1 beta-deformed field theory are exactly reproduced by introducing non-anticommutative star-products among the D1 and D5 open strings. A related star-product gives the tree-level amplitudes of the non-supersymmetric gamma-deformed conformal field theory. The non-anticommutativity arises essentially from the deformation of the supertwistor space which reduces the amount of superconformal symmetries realized by the supertwistor space. The tree-level gluonic amplitudes in more general marginally deformed field theories are also discussed using twistor string theory.

Aspects of Chiral Symmetry Breaking in Lattice QCD

NASA Astrophysics Data System (ADS)

Horkel, Derek P.

In this thesis we describe two studies concerting lattice quantum chromodynamics (LQCD): first, an analysis of the phase structure of Wilson and twisted-mass fermions with isospin breaking effects, second a computational study measuring non-perturbative Greens functions. We open with a brief overview of the formalism of QCD and LQCD, focusing on the aspects necessary for understanding how a lattice computation is performed and how discretization effects can be understood. Our work in Wilson and twisted-mass fermions investigates an increasingly relevant regime where lattice simulations are performed with quarks at or near their physical masses and both the mass difference of the up and down quarks and their differing electric charges are included. Our computation of a non-perturbative Greens functions on the lattice serves as a first attempt to validate recent work by Dine et. al. [24] in which they calculate Greens functions which vanish in perturbation theory, yet have a contribution from the one instanton background. In chapter 2, we determine the phase diagram and pion spectrum for Wilson and twisted-mass fermions in the presence of non-degeneracy between the up and down quark and discretization errors, using Wilson and twisted-mass chiral perturbation theory. We find that the CP-violating phase of the continuum theory (which occurs for sufficiently large non-degeneracy) is continuously connected to the Aoki phase of the lattice theory with degenerate quarks. We show that discretization effects can, in some cases, push simulations with physical masses closer to either the CP-violating phase or another phase not present in the continuum, so that at sufficiently large lattice spacings physical-point simulations could lie in one of these phases. In chapter 3, we extend the work in chapter 2 to include the effects of electromagnetism, so that it is applicable to recent simulations incorporating all sources of isospin breaking. For Wilson fermions, we find that the phase diagram is unaffected by the inclusion of electromagnetism--the only effect is to raise the charged pion masses. For maximally twisted fermions, we previously took the twist and isospin-breaking directions to be different, in order that the fermion determinant is real and positive. However, this is incompatible with electromagnetic gauge invariance, and so here we take the twist to be in the isospin-breaking direction, following the RM123 collaboration. We map out the phase diagram in this case, which has not previously been studied. The results differ from those obtained with different twist and isospin directions. One practical issue when including electromagnetism is that the critical masses for up and down quarks differ. We show that one of the criteria suggested to determine these critical masses does not work, and propose an alternative. In chapter 4, we delve deeper into the technical details of the analysis in chapter 3. We determine the phase diagram and chiral condensate for lattice QCD with two flavors of twisted-mass fermions in the presence of nondegenerate up and down quarks, discretization errors and a nonzero value of thetaQCD. We find that, in general, the only phase structure is a first-order transition of finite length. Pion masses are nonvanishing throughout the phase plane except at the endpoints of the first-order line. Only for extremal values of the twist angle and thetaQCD (o = 0 or pi/2 and thetaQCD = 0 or pi) are there second-order transitions. In chapter 5 we move on to a new topic, working to make a first measurement of non-perturbative Greens functions which vanish in perturbation theory but have a non-vanishing one-instanton contribution, as suggested in recent work by Dine et. al. [24] using a semi- classical approach. This measurement was done using 163 x 48 configurations generated by the MILC collaboration, with coupling beta = 6.572, light quark mass m la = 0.0097, strange quark mass msa = 0.0484, lattice spacing a ≈ 0.14 fm and pion mass mpia = 0.2456. The analysis was done by separating the Green function of interest into pseudoscalar and scalar components. These are separately calculated on 440 configurations, using the Chroma software package. To improve statistics, we used the various reduction technique suggested in Ref. [13]. We subtracted out the long distance contributions from the pion, excited pion and a0 from the Green function, in the hope of obtaining the short distance form predicted by Ref. [24]. Unfortunately, after subtraction of the a0 and pion states only noise remained. While the results are not in themselves useful, we believe this approach will be worth repeating in the future with finer lattices with a fermion action with better chiral symmetry.

Measurements of d 2 n and A 1 n : Probing the neutron spin structure

DOE PAGES

Flay, D.; Posik, M.; Parno, D. S.; ...

2016-09-06

We report on the results of the E06-014 experiment performed at Jefferson Lab in Hall A, where a precision measurement of the twist-3 matrix elementmore » $$d_2$$ of the neutron ($$d_{2}^{n}$$) was conducted. This quantity represents the average color Lorentz force a struck quark experiences in a deep inelastic electron scattering event off a neutron due to its interaction with the hadronizing remnants. This color force was determined from a linear combination of the third moments of the spin structure functions $$g_1$$ and $$g_2$$ on $$^{3}$$He after nuclear corrections had been applied to these moments. The kinematics included two average $$Q^{2}$$ bins of $3.2$ GeV$$^{2}$$ and $4.3$ GeV$$^{2}$$, and Bjorken-$x$ $$0.25 \\leq x \\leq 0.90$$ covering the DIS and resonance regions. We found $$d_2^n$$ to be small and negative for $ = 3.2$ GeV$$^{2}$$, and smaller for $ = 4.3$ GeV$$^{2}$$, consistent with a lattice QCD calculation. The twist-4 matrix element $$f_{2}^{n}$$ was extracted by combining our $$d_{2}^{n}$$ with the world data on $$\\Gamma_{1}^{n} = \\int_{0}^{1} g_{1}^{n} dx$$. We found $$f_{2}^{n}$$ to be roughly an order of magnitude larger than $$d_{2}^{n}$$. Utilizing the extracted $$d_{2}^{n}$$ and $$f_{2}^{n}$$ data, we separated the color force into its electric and magnetic components, $$F_{E}^{y,n}$$ and $$F_{B}^{y,n}$$, and found them to be equal and opposite in magnitude, in agreement with instanton model predictions but not with those from QCD sum rules. Additionally, we have extracted the neutron virtual photon-nucleon asymmetry $$A_{1}^{n}$$, the structure function ratio $$g_{1}^{n}/F_{1}^{n}$$, and the quark ratios $$(\\Delta u + \\Delta \\bar{u})/(u + \\bar{u})$$ and $$(\\Delta d + \\Delta \\bar{d})/(d + \\bar{d})$$. Lastly, these results were found to be consistent with DIS world data and with the prediction of the constituent quark model but at odds with those of perturbative QCD at large $x$.« less

Quantum Rotational Effects in Nanomagnetic Systems

NASA Astrophysics Data System (ADS)

O'Keeffe, Michael F.

Quantum tunneling of the magnetic moment in a nanomagnet must conserve the total angular momentum. For a nanomagnet embedded in a rigid body, reversal of the magnetic moment will cause the body to rotate as a whole. When embedded in an elastic environment, tunneling of the magnetic moment will cause local elastic twists of the crystal structure. In this thesis, I will present a theoretical study of the interplay between magnetization and rotations in a variety of nanomagnetic systems which have some degree of rotational freedom. We investigate the effect of rotational freedom on the tunnel splitting of a nanomagnet which is free to rotate about its easy axis. Calculating the exact instanton of the coupled equations of motion shows that mechanical freedom of the particle renormalizes the easy axis anisotropy, increasing the tunnel splitting. To understand magnetization dynamics in free particles, we study a quantum mechanical model of a tunneling spin embedded in a rigid rotor. The exact energy levels for a symmetric rotor exhibit first and second order quantum phase transitions between states with different values the magnetic moment. A quantum phase diagram is obtained in which the magnetic moment depends strongly on the moments of inertia. An intrinsic contribution to decoherence of current oscillations of a flux qubit must come from the angular momentum it transfers to the surrounding body. Within exactly solvable models of a qubit embedded in a rigid body and an elastic medium, we show that slow decoherence is permitted if the solid is macroscopically large. The spin-boson model is one of the simplest representations of a two-level system interacting with a quantum harmonic oscillator, yet has eluded a closed-form solution. I investigate some possible approaches to understanding its spectrum. The Landau-Zener dynamics of a tunneling spin coupled to a torsional resonator show that for certain parameter ranges the system exhibits multiple Landau-Zener transitions. These transitions coincide in time with changes in the oscillator dynamics. A large number of spins on a single oscillator coupled only through the in-phase oscillations behaves as a single large spin, greatly enhancing the spin-phonon coupling.

Quantum cosmology of a conformal multiverse

NASA Astrophysics Data System (ADS)

Robles-Pérez, Salvador J.

2017-09-01

This paper studies the cosmology of a homogeneous and isotropic spacetime endorsed with a conformally coupled massless scalar field. We find six different solutions of the Friedmann equation that represent six different types of universes, and all of them are periodically distributed along the complex time axis. From a classical point of view, they are then isolated, separated by Euclidean regions that represent quantum mechanical barriers. Quantum mechanically, however, there is a nonzero probability for the state of the universes to tunnel out through a Euclidean instanton and suffer a sudden transition to another state of the spacetime. We compute the probability of transition for this and other nonlocal processes like the creation of universes in entangled pairs and, generally speaking, in multipartite entangled states. We obtain the quantum state of a single universe within the formalism of the Wheeler-DeWitt equation and give the semiclassical state of the universes that describes the quantum mechanics of a scalar field propagating in a de Sitter background spacetime. We show that the superposition principle of the quantum mechanics of matter fields alone is an emergent feature of the semiclassical description of the universe that is not valid, for instance, in the spacetime foam. We use the third quantization formalism to describe the creation of an entangled pair of universes with opposite signs of the momentum conjugated to the scale factor. Each universe of the entangled pair represents an expanding spacetime in terms of the Wentzel-Kramers-Brillouin (WKB) time experienced by internal observers in their particle physics experiments. We compute the effective value of the Friedmann equation of the background spacetime of the two entangled universes, and thus, the effect that the entanglement would have in their expansion rates. We analyze as well the effects of the interuniversal entanglement in the properties of the scalar fields that propagate in each spacetime of the entangled pair. We find that the largest modes of the scalar field are unaware of the entanglement between the universes, but the effects can be significant for the lowest modes, allowing us to compute, in principle, detailed observational imprints of the multiverse in the properties of a single universe like ours.

Unconventional phases in quantum spin and pseudospin systems in two dimensional and three dimensional lattices

NASA Astrophysics Data System (ADS)

Xu, Cenke

Several examples of quantum spin systems and pseudo spin systems have been studied, and unconventional states of matters and phase transitions have been realized in all these systems under consideration. In the p +/- ip superconductor Josephson lattice and the p--band cold atomic system trapped in optical lattices, novel phases which behave similarly to 1+1 dimensional systems are realized, despite the fact that the real physical systems are in two or three dimensional spaces. For instance, by employing a spin-wave analysis together with a new duality transformation, we establish the existence and stability of a novel gapless "critical phase", which we refer to as a "bond algebraic liquid". This novel critical phase is analogous to the 1+1 dimensional algebraic boson liquid phase. The reason for the novel physics is that there is a quasilocal gauge symmetry in the effective low energy Hamiltonian. In a spin-1 system on the kagome lattice, and a hard-core boson system on the honeycomb lattice, the low energy physics is controlled by two components of compact U(1) gauge symmetries that emerge at low energy. Making use of the confinement nature of the 2+1 dimensional compact gauge theories and the powerful duality between gauge theories and height field theories, the crystalline phase diagrams are studied for both systems, and the transitions to other phases are also considered. These phase diagrams might be accessible in strongly correlated materials, or atomic systems in optical lattices. A novel quantum ground state of matter is realized in a bosonic model on three dimensional fcc lattice with emergent low energy excitations. The novel phase obtained is a stable gapless boson liquid phase, with algebraic boson density correlations. The stability of this phase is protected against the instanton effect and superfluidity by self-duality and large gauge symmetries on both sides of the duality. The gapless collective excitations of this phase closely resemble the graviton, although they have a soft w ˜ k2 dispersion relation. The dynamics of this novel phase is described by a new set of Maxwell's equations.

Duality, Gauge Symmetries, Renormalization Groups and the BKT Transition

NASA Astrophysics Data System (ADS)

José, Jorge V.

2017-03-01

In this chapter, I will briefly review, from my own perspective, the situation within theoretical physics at the beginning of the 1970s, and the advances that played an important role in providing a solid theoretical and experimental foundation for the Berezinskii-Kosterlitz-Thouless theory (BKT). Over this period, it became clear that the Abelian gauge symmetry of the 2D-XY model had to be preserved to get the right phase structure of the model. In previous analyses, this symmetry was broken when using low order calculational approximations. Duality transformations at that time for two-dimensional models with compact gauge symmetries were introduced by José, Kadanoff, Nelson and Kirkpatrick (JKKN). Their goal was to analyze the phase structure and excitations of XY and related models, including symmetry breaking fields which are experimentally important. In a separate context, Migdal had earlier developed an approximate Renormalization Group (RG) algorithm to implement Wilson’s RG for lattice gauge theories. Although Migdal’s RG approach, later extended by Kadanoff, did not produce a true phase transition for the XY model, it almost did asymptotically in terms of a non-perturbative expansion in the coupling constant with an essential singularity. Using these advances, including work done on instantons (vortices), JKKN analyzed the behavior of the spin-spin correlation functions of the 2D XY-model in terms of an expansion in temperature and vortex-pair fugacity. Their analysis led to a perturbative derivation of RG equations for the XY model which are the same as those first derived by Kosterlitz for the two-dimensional Coulomb gas. JKKN’s results gave a theoretical formulation foundation and justification for BKT’s sound physical assumptions and for the validity of their calculational approximations that were, in principle, strictly valid only at very low temperatures, away from the critical TBKT temperature. The theoretical predictions were soon tested successfully against experimental results on superfluid helium films. The success of the BKT theory also gave one of the first quantitative proofs of the validity of the RG theory.

Duality, Gauge Symmetries, Renormalization Groups and the BKT Transition

NASA Astrophysics Data System (ADS)

José, Jorge V.

2013-06-01

In this chapter, I will briefly review, from my own perspective, the situation within theoretical physics at the beginning of the 1970s, and the advances that played an important role in providing a solid theoretical and experimental foundation for the Berezinskii-Kosterlitz-Thouless theory (BKT). Over this period, it became clear that the Abelian gauge symmetry of the 2D-XY model had to be preserved to get the right phase structure of the model. In previous analyses, this symmetry was broken when using low order calculational approximations. Duality transformations at that time for two-dimensional models with compact gauge symmetries were introduced by José, Kadanoff, Nelson and Kirkpatrick (JKKN). Their goal was to analyze the phase structure and excitations of XY and related models, including symmetry breaking fields which are experimentally important. In a separate context, Migdal had earlier developed an approximate Renormalization Group (RG) algorithm to implement Wilson's RG for lattice gauge theories. Although Migdal's RG approach, later extended by Kadanoff, did not produce a true phase transition for the XY model, it almost did asymptotically in terms of a non-perturbative expansion in the coupling constant with an essential singularity. Using these advances, including work done on instantons (vortices), JKKN analyzed the behavior of the spin-spin correlation functions of the 2D XY-model in terms of an expansion in temperature and vortex-pair fugacity. Their analysis led to a perturbative derivation of RG equations for the XY model which are the same as those first derived by Kosterlitz for the two-dimensional Coulomb gas. JKKN's results gave a theoretical formulation foundation and justification for BKT's sound physical assumptions and for the validity of their calculational approximations that were, in principle, strictly valid only at very low temperatures, away from the critical TBKT temperature. The theoretical predictions were soon tested successfully against experimental results on superfluid helium films. The success of the BKT theory also gave one of the first quantitative proofs of the validity of the RG theory...

Vacuum structure and string tension in Yang-Mills dimeron ensembles

NASA Astrophysics Data System (ADS)

Zimmermann, Falk; Forkel, Hilmar; Müller-Preußker, Michael

2012-11-01

We numerically simulate ensembles of SU(2) Yang-Mills dimeron solutions with a statistical weight determined by the classical action and perform a comprehensive analysis of their properties as a function of the bare coupling. In particular, we examine the extent to which these ensembles and their classical gauge interactions capture topological and confinement properties of the Yang-Mills vacuum. This also allows us to put the classic picture of meron-induced quark confinement, with the confinement-deconfinement transition triggered by dimeron dissociation, to stringent tests. In the first part of our analysis we study spacial, topological-charge and color correlations at the level of both the dimerons and their meron constituents. At small to moderate couplings, the dependence of the interactions between the dimerons on their relative color orientations is found to generate a strong attraction (repulsion) between nearest neighbors of opposite (equal) topological charge. Hence, the emerging short- to mid-range order in the gauge-field configurations screens topological charges. With increasing coupling this order weakens rapidly, however, in part because the dimerons gradually dissociate into their less localized meron constituents. Monitoring confinement properties by evaluating Wilson-loop expectation values, we find the growing disorder due to the long-range tails of these progressively liberated merons to generate a finite and (with the coupling) increasing string tension. The short-distance behavior of the static quark-antiquark potential, on the other hand, is dominated by small, “instantonlike” dimerons. String tension, action density and topological susceptibility of the dimeron ensembles in the physical coupling region turn out to be of the order of standard values. Hence, the above results demonstrate without reliance on weak-coupling or low-density approximations that the dissociating dimeron component in the Yang-Mills vacuum can indeed produce a meron-populated confining phase. The density of coexisting, hardly dissociated and thus instantonlike dimerons seems to remain large enough, on the other hand, to reproduce much of the additional phenomenology successfully accounted for by nonconfining instanton vacuum models. Hence, dimeron ensembles should provide an efficient basis for a more complete description of the Yang-Mills vacuum.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Flay, D.; Posik, M.; Parno, D. S.

We report on the results of the E06-014 experiment performed at Jefferson Lab in Hall A, where a precision measurement of the twist-3 matrix elementmore » $$d_2$$ of the neutron ($$d_{2}^{n}$$) was conducted. This quantity represents the average color Lorentz force a struck quark experiences in a deep inelastic electron scattering event off a neutron due to its interaction with the hadronizing remnants. This color force was determined from a linear combination of the third moments of the spin structure functions $$g_1$$ and $$g_2$$ on $$^{3}$$He after nuclear corrections had been applied to these moments. The kinematics included two average $$Q^{2}$$ bins of $3.2$ GeV$$^{2}$$ and $4.3$ GeV$$^{2}$$, and Bjorken-$x$ $$0.25 \\leq x \\leq 0.90$$ covering the DIS and resonance regions. We found $$d_2^n$$ to be small and negative for $ = 3.2$ GeV$$^{2}$$, and smaller for $ = 4.3$ GeV$$^{2}$$, consistent with a lattice QCD calculation. The twist-4 matrix element $$f_{2}^{n}$$ was extracted by combining our $$d_{2}^{n}$$ with the world data on $$\\Gamma_{1}^{n} = \\int_{0}^{1} g_{1}^{n} dx$$. We found $$f_{2}^{n}$$ to be roughly an order of magnitude larger than $$d_{2}^{n}$$. Utilizing the extracted $$d_{2}^{n}$$ and $$f_{2}^{n}$$ data, we separated the color force into its electric and magnetic components, $$F_{E}^{y,n}$$ and $$F_{B}^{y,n}$$, and found them to be equal and opposite in magnitude, in agreement with instanton model predictions but not with those from QCD sum rules. Additionally, we have extracted the neutron virtual photon-nucleon asymmetry $$A_{1}^{n}$$, the structure function ratio $$g_{1}^{n}/F_{1}^{n}$$, and the quark ratios $$(\\Delta u + \\Delta \\bar{u})/(u + \\bar{u})$$ and $$(\\Delta d + \\Delta \\bar{d})/(d + \\bar{d})$$. Lastly, these results were found to be consistent with DIS world data and with the prediction of the constituent quark model but at odds with those of perturbative QCD at large $x$.« less

Quarks, Symmetries and Strings - a Symposium in Honor of Bunji Sakita's 60th Birthday

NASA Astrophysics Data System (ADS)

Kaku, M.; Jevicki, A.; Kikkawa, K.

1991-04-01

The Table of Contents for the full book PDF is as follows: * Preface * Evening Banquet Speech * I. Quarks and Phenomenology * From the SU(6) Model to Uniqueness in the Standard Model * A Model for Higgs Mechanism in the Standard Model * Quark Mass Generation in QCD * Neutrino Masses in the Standard Model * Solar Neutrino Puzzle, Horizontal Symmetry of Electroweak Interactions and Fermion Mass Hierarchies * State of Chiral Symmetry Breaking at High Temperatures * Approximate |ΔI| = 1/2 Rule from a Perspective of Light-Cone Frame Physics * Positronium (and Some Other Systems) in a Strong Magnetic Field * Bosonic Technicolor and the Flavor Problem * II. Strings * Supersymmetry in String Theory * Collective Field Theory and Schwinger-Dyson Equations in Matrix Models * Non-Perturbative String Theory * The Structure of Non-Perturbative Quantum Gravity in One and Two Dimensions * Noncritical Virasoro Algebra of d < 1 Matrix Model and Quantized String Field * Chaos in Matrix Models ? * On the Non-Commutative Symmetry of Quantum Gravity in Two Dimensions * Matrix Model Formulation of String Field Theory in One Dimension * Geometry of the N = 2 String Theory * Modular Invariance form Gauge Invariance in the Non-Polynomial String Field Theory * Stringy Symmetry and Off-Shell Ward Identities * q-Virasoro Algebra and q-Strings * Self-Tuning Fields and Resonant Correlations in 2d-Gravity * III. Field Theory Methods * Linear Momentum and Angular Momentum in Quaternionic Quantum Mechanics * Some Comments on Real Clifford Algebras * On the Quantum Group p-adics Connection * Gravitational Instantons Revisited * A Generalized BBGKY Hierarchy from the Classical Path-Integral * A Quantum Generated Symmetry: Group-Level Duality in Conformal and Topological Field Theory * Gauge Symmetries in Extended Objects * Hidden BRST Symmetry and Collective Coordinates * Towards Stochastically Quantizing Topological Actions * IV. Statistical Methods * A Brief Summary of the s-Channel Theory of Superconductivity * Neural Networks and Models for the Brain * Relativistic One-Body Equations for Planar Particles with Arbitrary Spin * Chiral Property of Quarks and Hadron Spectrum in Lattice QCD * Scalar Lattice QCD * Semi-Superconductivity of a Charged Anyon Gas * Two-Fermion Theory of Strongly Correlated Electrons and Charge-Spin Separation * Statistical Mechanics and Error-Correcting Codes * Quantum Statistics

Anisotropic modulus stabilisation: strings at LHC scales with micron-sized extra dimensions

NASA Astrophysics Data System (ADS)

Cicoli, M.; Burgess, C. P.; Quevedo, F.

2011-10-01

We construct flux-stabilised Type IIB string compactifications whose extra dimensions have very different sizes, and use these to describe several types of vacua with a TeV string scale. Because we can access regimes where two dimensions are hierarchically larger than the other four, we find examples where two dimensions are micron-sized while the other four are at the weak scale in addition to more standard examples with all six extra dimensions equally large. Besides providing ultraviolet completeness, the phenomenology of these models is richer than vanilla large-dimensional models in several generic ways: ( i) they are supersymmetric, with supersymmetry broken at sub-eV scales in the bulk but only nonlinearly realised in the Standard Model sector, leading to no MSSM superpartners for ordinary particles and many more bulk missing-energy channels, as in supersymmetric large extra dimensions (SLED); ( ii) small cycles in the more complicated extra-dimensional geometry allow some KK states to reside at TeV scales even if all six extra dimensions are nominally much larger; ( iii) a rich spectrum of string and KK states at TeV scales; and ( iv) an equally rich spectrum of very light moduli exist having unusually small (but technically natural) masses, with potentially interesting implications for cosmology and astrophysics that nonetheless evade new-force constraints. The hierarchy problem is solved in these models because the extra-dimensional volume is naturally stabilised at exponentially large values: the extra dimensions are Calabi-Yau geometries with a 4D K3 or T 4-fibration over a 2D base, with moduli stabilised within the well-established LARGE-Volume scenario. The new technical step is the use of poly-instanton corrections to the superpotential (which, unlike for simpler models, are likely to be present on K3 or T 4-fibered Calabi-Yau compactifications) to obtain a large hierarchy between the sizes of different dimensions. For several scenarios we identify the low-energy spectrum and briefly discuss some of their astrophysical, cosmological and phenomenological implications.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Weinstein, Marvin; /SLAC

It is apparent to anyone who thinks about it that, to a large degree, the basic concepts of Newtonian physics are quite intuitive, but quantum mechanics is not. My purpose in this talk is to introduce you to a new, much more intuitive way to understand how quantum mechanics works. I begin with an incredibly easy way to derive the time evolution of a Gaussian wave-packet for the case free and harmonic motion without any need to know the eigenstates of the Hamiltonian. This discussion is completely analytic and I will later use it to relate the solution for themore » behavior of the Gaussian packet to the Feynman path-integral and stationary phase approximation. It will be clear that using the information about the evolution of the Gaussian in this way goes far beyond what the stationary phase approximation tells us. Next, I introduce the concept of the bucket brigade approach to dealing with problems that cannot be handled totally analytically. This approach combines the intuition obtained in the initial discussion, as well as the intuition obtained from the path-integral, with simple numerical tools. My goal is to show that, for any specific process, there is a simple Hilbert space interpretation of the stationary phase approximation. I will then argue that, from the point of view of numerical approximations, the trajectory obtained from my generalization of the stationary phase approximation specifies that subspace of the full Hilbert space that is needed to compute the time evolution of the particular state under the full Hamiltonian. The prescription I will give is totally non-perturbative and we will see, by the grace of Maple animations computed for the case of the anharmonic oscillator Hamiltonian, that this approach allows surprisingly accurate computations to be performed with very little work. I think of this approach to the path-integral as defining what I call a guided numerical approximation scheme. After the discussion of the anharmonic oscillator I will turn to tunneling problems and show that the instanton can also be though of in the same way. I will do this for the classic problem of a double well potential in the extreme limit when the splitting between the two lowest levels is extremely small and the tunneling rate from one well to another is also very small.« less

The Entropy of Non-Ergodic Complex Systems — a Derivation from First Principles

NASA Astrophysics Data System (ADS)

Thurner, Stefan; Hanel, Rudolf

In information theory the 4 Shannon-Khinchin1,2 (SK) axioms determine Boltzmann Gibbs entropy, S -∑i pilog pi, as the unique entropy. Physics is different from information in the sense that physical systems can be non-ergodic or non-Markovian. To characterize such strongly interacting, statistical systems - complex systems in particular - within a thermodynamical framework it might be necessary to introduce generalized entropies. A series of such entropies have been proposed in the past decades. Until now the understanding of their fundamental origin and their deeper relations to complex systems remains unclear. To clarify the situation we note that non-ergodicity explicitly violates the fourth SK axiom. We show that by relaxing this axiom the entropy generalizes to, S ∑i Γ(d + 1, 1 - c log pi), where Γ is the incomplete Gamma function, and c and d are scaling exponents. All recently proposed entropies compatible with the first 3 SK axioms appear to be special cases. We prove that each statistical system is uniquely characterized by the pair of the two scaling exponents (c, d), which defines equivalence classes for all systems. The corresponding distribution functions are special forms of Lambert-W exponentials containing, as special cases, Boltzmann, stretched exponential and Tsallis distributions (power-laws) - all widely abundant in nature. This derivation is the first ab initio justification for generalized entropies. We next show how the phasespace volume of a system is related to its generalized entropy, and provide a concise criterion when it is not of Boltzmann-Gibbs type but assumes a generalized form. We show that generalized entropies only become relevant when the dynamically (statistically) relevant fraction of degrees of freedom in a system vanishes in the thermodynamic limit. These are systems where the bulk of the degrees of freedom is frozen. Systems governed by generalized entropies are therefore systems whose phasespace volume effectively collapses to a lower-dimensional 'surface'. We explicitly illustrate the situation for accelerating random walks, and a spin system on a constant-conectancy network. We argue that generalized entropies should be relevant for self-organized critical systems such as sand piles, for spin systems which form meta-structures such as vortices, domains, instantons, etc., and for problems associated with anomalous diffusion.

Classification of Arnold-Beltrami flows and their hidden symmetries

NASA Astrophysics Data System (ADS)

Fré, P.; Sorin, A. S.

2015-07-01

In the context of mathematical hydrodynamics, we consider the group theory structure which underlies the so named ABC flows introduced by Beltrami, Arnold and Childress. Main reference points are Arnold's theorem stating that, for flows taking place on compact three manifolds ℳ3, the only velocity fields able to produce chaotic streamlines are those satisfying Beltrami equation and the modern topological conception of contact structures, each of which admits a representative contact one-form also satisfying Beltrami equation. We advocate that Beltrami equation is nothing else but the eigenstate equation for the first order Laplace-Beltrami operator ★ g d, which can be solved by using time-honored harmonic analysis. Taking for ℳ3, a torus T 3 constructed as ℝ3/Λ, where Λ is a crystallographic lattice, we present a general algorithm to construct solutions of the Beltrami equation which utilizes as main ingredient the orbits under the action of the point group B A of three-vectors in the momentum lattice *Λ. Inspired by the crystallographic construction of space groups, we introduce the new notion of a Universal Classifying Group which contains all space groups as proper subgroups. We show that the ★ g d eigenfunctions are naturally arranged into irreducible representations of and by means of a systematic use of the branching rules with respect to various possible subgroups we search and find Beltrami fields with non trivial hidden symmetries. In the case of the cubic lattice the point group is the proper octahedral group O24 and the Universal Classifying Group is a finite group G1536 of order |G1536| = 1536 which we study in full detail deriving all of its 37 irreducible representations and the associated character table. We show that the O24 orbits in the cubic lattice are arranged into 48 equivalence classes, the parameters of the corresponding Beltrami vector fields filling all the 37 irreducible representations of G1536. In this way we obtain an exhaustive classification of all generalized ABC- flows and of their hidden symmetries. We make several conceptual comments about the need of a field-theory yielding Beltrami equation as a field equation and/or an instanton equation and on the possible relation of Arnold-Beltrami flows with (supersymmetric) Chern-Simons gauge theories. We also suggest linear generalizations of Beltrami equation to higher odd-dimensions that are different from the non-linear one proposed by Arnold and possibly make contact with M-theory and the geometry of flux-compactifications.

Measurements of d 2 n and A 1 n : Probing the neutron spin structure

DOE Office of Scientific and Technical Information (OSTI.GOV)

Flay, D.; Posik, M.; Parno, D. S.

We report on the results of the E06-014 experiment performed at Jefferson Lab in Hall A, where a precision measurement of the twist-3 matrix element d(2) of the neutron (d(2)(n)) was conducted. The quantity d(2)(n) represents the average color Lorentz force a struck quark experiences in a deep inelastic electron scattering event off a neutron due to its interaction with the hadronizing remnants. This color force was determined from a linear combination of the third moments of the He-3 spin structure functions, g(1) and g(2), after nuclear corrections had been applied to these moments. The structure functions were obtained frommore » a measurement of the unpolarized cross section and of double-spin asymmetries in the scattering of a longitudinally polarized electron beam from a transversely and a longitudinally polarized He-3 target. The measurement kinematics included two average Q(2) bins of 3.2 GeV2 and 4.3 GeV2, and Bjorken-x 0.25 <= x <= 0.90 covering the deep inelastic and resonance regions. We have found that d(2)(n) is small and negative for < Q(2)> = 3.2 GeV2, and even smaller for < Q(2)> = 4.3 GeV2, consistent with the results of a lattice QCD calculation. The twist-4 matrix element f(2)(n) was extracted by combining our measured d(2)(n) with the world data on the first moment in x of g(1)(n), Gamma(n)(1). We found f(2)(n) to be roughly an order of magnitude larger than d(2)(n). Utilizing the extracted d(2)(n) and f(2)(n) data, we separated the Lorentz color force into its electric and magnetic components, F-E(y,n) and F-B(y,n), and found them to be equal and opposite in magnitude, in agreement with the predictions from an instanton model but not with those from QCD sum rules. Furthermore, using the measured double-spin asymmetries, we have extracted the virtual photon-nucleon asymmetry on the neutron A(1)(n), the structure function ratio g(1)(n)/F-1(n), and the quark ratios (Delta u + Delta(u) over bar)/(u + (u) over bar) and (Delta d + Delta(d) over bar)/(d + (d) over bar). These results were found to be consistent with deep-inelastic scattering world data and with the prediction of the constituent quark model but at odds with the perturbative quantum chromodynamics predictions at large x.« less

H2+, HeH and H2: Approximating potential curves, calculating rovibrational states

NASA Astrophysics Data System (ADS)

Olivares-Pilón, Horacio; Turbiner, Alexander V.

2018-06-01

Analytic consideration of the Bohr-Oppenheimer (BO) potential curves for diatomic molecules is proposed: accurate analytic interpolation for a potential curve consistent with its rovibrational spectra is found. It is shown that in the BO approximation for four lowest electronic states 1 sσg and 2 pσu, 2 pπu and 3 dπg of H2+, the ground state X2Σ+ of HeH and the two lowest states 1 Σg+ and 3 Σu+ of H2, the potential curves can be analytically interpolated in full range of internuclear distances R with not less than 4-5-6 s.d. Approximation based on matching the Laurant-type expansion at small R and a combination of the multipole expansion with one-instanton type contribution at large distances R is given by two-point Padé approximant. The position of minimum, when exists, is predicted within 1% or better. For the molecular ion H2+ in the Lagrange mesh method, the spectra of vibrational, rotational and rovibrational states (ν , L) associated with 1 sσg and 2 pσu, 2 pπu and 3 dπg potential curves are calculated. In general, it coincides with spectra found via numerical solution of the Schrödinger equation (when available) within six s.d. It is shown that 1 sσg curve contains 19 vibrational states (ν , 0) , while 2 pσu curve contains a single one (0 , 0) and 2 pπu state contains 12 vibrational states (ν , 0) . In general, 1 sσg electronic curve contains 420 rovibrational states, which increases up to 423 when we are beyond BO approximation. For the state 2 pσu the total number of rovibrational states (all with ν = 0) is equal to 3, within or beyond Bohr-Oppenheimer approximation. As for the state 2 pπu within the Bohr-Oppenheimer approximation the total number of the rovibrational bound states is equal to 284. The state 3 dπg is repulsive, no rovibrational state is found. It is confirmed in Lagrange mesh formalism the statement that the ground state potential curve of the heteronuclear molecule HeH does not support rovibrational states. Accurate analytical expression for the potential curves of the hydrogen molecule H2 for the states 1Σg+ and 3 Σu+ is presented. The ground state 1 Σg+ contains 15 vibrational states (ν , 0) , ν = 0- 14. In general, this state supports 301 rovibrational states. The potential curve of the state 3Σu+ has a shallow minimum: it does not support any rovibrational state, it is repulsive.

Continuous Advances in QCD 2008

NASA Astrophysics Data System (ADS)

Peloso, Marco M.

2008-12-01

1. High-order calculations in QCD and in general gauge theories. NLO evolution of color dipoles / I. Balitsky. Recent perturbative results on heavy quark decays / J. H. Piclum, M. Dowling, A. Pak. Leading and non-leading singularities in gauge theory hard scattering / G. Sterman. The space-cone gauge, Lorentz invariance and on-shell recursion for one-loop Yang-Mills amplitudes / D. Vaman, Y.-P. Yao -- 2. Heavy flavor physics. Exotic cc¯ mesons / E. Braaten. Search for new physics in B[symbol]-mixing / A. J. Lenz. Implications of D[symbol]-D[symbol] mixing for new physics / A. A. Petrov. Precise determinations of the charm quark mass / M. Steinhauser -- 3. Quark-gluon dynamics at high density and/or high temperature. Crystalline condensate in the chiral Gross-Neveu model / G. V. Dunne, G. Basar. The strong coupling constant at low and high energies / J. H. Kühn. Quarkyonic matter and the phase diagram of QCD / L. McLerran. Statistical QCD with non-positive measure / J. C. Osborn, K. Splittorff, J. J. M. Verbaarschot. From equilibrium to transport properties of strongly correlated fermi liquids / T. Schäfer. Lessons from random matrix theory for QCD at finite density / K. Splittorff, J. J. M. Verbaarschot -- 4. Methods and models of holographic correspondence. Soft-wall dynamics in AdS/QCD / B. Batell. Holographic QCD / N. Evans, E. Threlfall. QCD glueball sum rules and vacuum topology / H. Forkel. The pion form factor in AdS/QCD / H. J. Kwee, R. F. Lebed. The fast life of holographic mesons / R. C. Myers, A. Sinha. Properties of Baryons from D-branes and instantons / S. Sugimoto. The master space of N = 1 quiver gauge theories: counting BPS operators / A. Zaffaroni. Topological field congurations. Skyrmions in theories with massless adjoint quarks / R. Auzzi. Domain walls, localization and confinement: what binds strings inside walls / S. Bolognesi. Static interactions of non-abelian vortices / M. Eto. Vortices which do not abelianize dynamically: semi-classical origin of non-abelian monopoles / K. Konishi. A generalized construction for lumps and non-abelian vortices / W. Vinci -- 6. Dynamics in supersymmetric theories. Cusp anomalous dimension in planar maximally supersymmetric Yang-Mills theory / B. Basso. SO(2M) and USp(2M) (hyper)Kähler quotients and lumps / S. B. Gudnason -- 7. Other developments. Gluinos condensing at the CCNI: 4096 CPUs weigh in / J. Giedt ... [et al.]. Baryon Regge trajectories and the 1/N[symbol] expansion / J. L. Goity, N. Matagne. Infrared behavior of the fermion propagator in unquenched QED[symbol] with finite threshold effects / Y. Hoshino. Gauge fields in accelerated frames / F. Lenz. QCD at complex coupling, large order in perturbation theory and the gluon condensate / Y. Meurice. 511 KeV line and other diffuse emissions as a trace of the dark matter / A. R. Zhitnitsky -- 8. Glimpses of the conference.

BOOK REVIEW: Modern Supersymmetry

NASA Astrophysics Data System (ADS)

Kulish, Petr P.

2006-12-01

We have spent more than twenty years applying supersymmetry (SUSY) to elementary particle physics and attempting to find an experimental manifestation of this symmetry. Terning's monograph demonstrates the strong influence of SUSY on theoretical elaborations in the field of elementary particles. It gives both an overview of modern supersymmetry in elementary particle physics and calculation techniques. The author, trying to be closer to applications of SUSY in the real world of elementary particles, is also anticipating the importance of supersymmetry for rigorous study of nonperturbative phenomena in quantum field theory. In particular, he presents the `exact' SUSY β function using instanton methods, phenomena of anomalies and dualities. Supersymmetry algebra is introduced by adding two anticommuting spinor generators to Poincaré algebra and by presenting massive and massless supermultiplets of its representations. The author prefers to use mostly the component description of field contents of the theories in question rather than the superfield formalism. Such a style makes the account closer to physical chartacteristics. Relations required by SUSY among β functions of the gauge, Yukawa and quartic interactions are checked by direct calculations as well as to all orders in perturbation theory, thus demonstrating that SUSY survives quantization. A discussion is included of the hierarchy problem of different scales of weak and strong interactions and its possible solution by the minimal supersymmetric standard model. Different SUSY breaking mechanisms are presented corresponding to a realistic phenomenology. The monograph can also be considered as a guide to `duality' relations connecting different SUSY gauge theories, supergravities and superstrings. This is demonstrated referring to the particular properties and characteristics of these theories (field contents, scaling dimensions of appropriate operators etc). In particular, the last chapter deals with the AdS/CFT correspondence. The author explains clearly most of the arguments in discussions and refers for further details to original papers (with corresponding arXiv numbers), selected lists of which appear at the end of each chapter (there are more than 300 references in the book). Considered as a whole the book covers primers on quantum fields, Feynman diagrams, renormalization procedure and renormalization groups, as well as the representation theory of classical linear Lie algebras. Some necessary information on irreducible representations of su(N), so(N) and sp(2N) is given in an appendix. There are in the text short historical and biographical notes concerning those scientists who made important contributions to the subject of the monograph: S Coleman, Yu Golfand, E Witten and others. Most of the seventeen chapters contain a few exercises to check the reader's understanding of the corresponding material. This monograph will be useful for graduate students and researchers in the field of elementary particles.

Quark confinement: Dual superconductor picture based on a non-Abelian Stokes theorem and reformulations of Yang-Mills theory

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 confinement. The Wilson loop average is calculated according to the new reformulation written in terms of new field variables obtained from the original Yang-Mills field based on change of variables. The Maximally Abelian gauge in the original Yang-Mills theory is also reproduced by taking a specific gauge fixing in the reformulated Yang-Mills theory. This observation justifies the preceding results obtained in the maximal Abelian gauge at least for gauge-invariant quantities for SU(2) gauge group, which eliminates the criticism of gauge artifact raised for the Abelian projection. The claim has been confirmed based on the numerical simulations. However, for SU(N) (N ≥ 3), such a gauge-invariant reformulation is not unique, although the extension along the line proposed by Cho, Faddeev and Niemi is possible. In fact, we have found that there are a number of possible options of the reformulations, which are discriminated by the maximal stability group H ˜ of G, while there is a unique option of H ˜ = U(1) for G = SU(2) . The maximal stability group depends on the representation of the gauge group, to that the quark source belongs. For the fundamental quark for SU(3) , the maximal stability group is U(2) , which is different from the maximal torus group U(1) × U(1) suggested from the Abelian projection. Therefore, the chromomagnetic monopole inherent in the Wilson loop operator responsible for confinement of quarks in the fundamental representation for SU(3) is the non-Abelian magnetic monopole, which is distinct from the Abelian magnetic monopole for the SU(2) case. Therefore, we claim that the mechanism for quark confinement for SU(N) (N ≥ 3) is the non-Abelian dual superconductivity caused by condensation of non-Abelian magnetic monopoles. We give some theoretical considerations and numerical results supporting this picture. Finally, we discuss some issues to be investigated in future studies.

100th anniversary of the birth of I Ya Pomeranchuk (Extended session of the all-institute seminar at the Alikhanov Institute for Theoretical and Experimental Physics, 5 - 6 June 2013)

NASA Astrophysics Data System (ADS)

2014-02-01

On 5 - 6 June 2013, an extended session of the all-institute seminar was held at the Russian Federation State Scientific Center 'Alikhanov Institute for Theoretical and Experimental Physics' (ITEP). It was devoted to the 100th anniversary of the birth of Academician Isaak Yakovlevich Pomeranchuk, the founder of the Theory Department of ITEP. The announced agenda of the session on the ITEP website http://www.itep.ru/rus/Pomeranchuk100.html contained the following reports: (1) Gershtein S S (SRC 'Institute for High Energy Physics', Protvino, Moscow region) "I Ya Pomeranchuk and the large accelerator";(2) Keldysh L V (Lebedev Physical Institute, RAS (FIAN), Moscow) "Dynamic tunneling";(3) Vaks V G (National Research Centre 'Kurchatov Institute' (NRC KI), Moscow) "Brief reminiscences";(4) Smilga A V (Laboratoire Physique Subatomique et des technologies associées, Université de Nantes, France) "Vacuum structure in 3D supersymmetric gauge theories";(5) Khriplovich I B (Budker Institute of Nuclear Physics, SB RAS, Novosibirsk) "Gravitational four-fermion interaction and early Universe dynamics";(6) Dremin I M (FIAN, Moscow) "Elastic scattering of hadrons";(7) Belavin A A (Landau Institute of Theoretical Physics, RAS, Moscow) "Correlators in minimal string models";(8) Voloshin M B (Theoretical Physics Institute, University of Minnesota, USA) "Exotic quarkonium";(9) Nekrasov N A (Institut des hautes études scientifiques (IHES), France) "BPS/CFT correspondence";(10) Zarembo K (Uppsala Universitet, Sweden) "Exact results in supersymmetric theories and AdS/CFT correspondence";(11) Gorsky A S (ITEP, Moscow) "Baryon as a dyon instanton";(12) Blinnikov S I (ITEP, Moscow) "Mirror substance and other models for dark matter";(13) Rubakov V A (Institute for Nuclear Research, RAS, Moscow) "Test-tube Universe";(14) Kancheli O V (ITEP, Moscow) "50 years of reggistics";(15) Shevchenko V I (NRC KI) "In search of the chiral magnetic effect";(16) Kirilin V P (ITEP, Moscow) "Anomalies and long-range action";(17) Narozhny N B (National Research Nuclear University 'MEPhI', Moscow) "Superpower lasers as instruments for studying the properties of vacuum";(18) Kerbikov B O (ITEP, Moscow) "Hadrons in strong magnetic fields";(19) Neznamov V P, Safronov I I (Russian Federal Nuclear Center - All-Russian Scientific Research Institute of Experimental Physics (VNIIEF), Sarov, Nizhny Novgorod region) "A new method for solving the 'Z > 137' problem and determining hydrogen-like energy levels";(20) Vysotsky M I, Godunov S I (ITEP, Moscow) "Critical charge in a superstrong magnetic field";(21) Dolgov A D (Universitè degli Studi di Ferrara, Italy) "Cosmology: from Pomeranchuk to the present day".Papers written around the reports Nos 4, 5, 11, 12, 19 - 21 are published below. The content of report 6 in an extended form is reflected in I M Dremin's 2013 review of the same title published in Phys. Usp. 56 3 (2013). An extended version of report 13 is published in the present issue of Phys. Usp. 57 128 (2014). • Vacuum structure in 3D supersymmetric gauge theories, A V Smilga Physics-Uspekhi, 2014, Volume 57, Number 2, Pages 155-166 • Gravitational four-fermion interaction in the early Universe, A S Rudenko, I B Khriplovich Physics-Uspekhi, 2014, Volume 57, Number 2, Pages 167-170 • Limit cycles in renormalization group dynamics, K M Bulycheva, A S Gorsky Physics-Uspekhi, 2014, Volume 57, Number 2, Pages 171-182 • Mirror matter and other dark matter models, S I Blinnikov Physics-Uspekhi, 2014, Volume 57, Number 2, Pages 183-188 • New method for solving the Z>137 problem and determining hydrogen-like energy levels, V P Neznamov, I I Safronov Physics-Uspekhi, 2014, Volume 57, Number 2, Pages 189-193 • Critical charge in a superstrong magnetic field, M I Vysotskii, S I Godunov Physics-Uspekhi, 2014, Volume 57, Number 2, Pages 194-198 • Cosmology: from Pomeranchuk to the present day, A D Dolgov Physics-Uspekhi, 2014, Volume 57, Number 2, Pages 199-208

List of Posters

NASA Astrophysics Data System (ADS)

List of Posters: Dark matter annihilation in the Galactic galo, by Dokuchaev Vyacheslav, et al. NEMO developments towards km3 telescope in the Mediterranean Sea. The NEMO project. Neutrino Mediterranean Observatory By Antonio Capone, NEMO Collaboration. Alignment as a result from QCD jet production or new still unknown physics at LHC? By Alexander Snigirev. Small-scale fluctuations of extensive air showers: systematics in energy and muon density estimation By Grigory Rubtsov. SHINIE: Simulation of High-Energy Neutrino Interacting with the Earth By Lin Guey-Lin, et al.. Thermodynamics of rotating solutions in n+1 dimensional Einstein - Maxwell -dilation gravity By Ahmad Sheykhi, et al.. Supernova neutrino physics with future large Cherenkov detectors By Daniele Montanino. Crossing of the Cosmological Constant Barrier in the string Inspired Dark Energy Model By S. Yu. Vernov. Calculations of radio signals produced by ultra-high and extremely high energy neutrino induced cascades in Antarctic ice By D. Besson, et al.. Inflation, Cosmic Acceleration and string Gravity By Ischwaree Neupane. Neutrino Physics: Charm and J/Psi production in the atmosphere By Liudmila Volkova. Three generation flavor transitions and decays of supernova relic neutrinos By Daniele Montanino. Lattice calculations & computational quantum field theory: Sonification of Quark and Baryon Spectra By Markum Harald, et al.. Generalized Kramers-Wannier Duality for spin systems with non-commutative symmetry By V. M. Buchstaber, et al.. Heavy ion collisions & quark matter: Nuclear matter jets and multifragmentation By Danut Argintaru, et al.. QCD hard interactions: The qT-spectrum of the Higgs and Slepton-pairs at the LHC By Guiseppe Bozzi. QCD soft interactions: Nonperturbative effects in Single-Spin Asymmetries: Instantons and TMD-parton distributions By Igor Cherednikov, et al.. Gluon dominance model and high multiplicity By Elena Kokoulina. Resonances in eta pi- pi- pi+ system By Dmitry Ryabchikov. Saturation effects in diffractive scattering at LHC By Oleg Selugin. A nonperturbative expansion method in QCD and R-related quantities By Igor Solovtsov. Z-scaling and high multiplicity particle Production in bar pp/pp & AA collisions at Tevatron and RHIC By Mikhail Tokarev. Scaling behaviour of the reactionsdd - > p↑ /3H and pd - > pd with pT at energy I-2 GeV By Yuri Uzikov. [ADS Note: Title formula can not be rendered correctly in ASCII.] CP violation, rare decays, CKM: Precision Measurements of the Mass of the Top Quark at CDF (Precision Top Mass Measurements at CDF) By Daniel Whiteson. Measurement of the Bs Oscillation at CDF By Luciano Ristori. The Bs mixing phase at LHCb By J. J. van Hunen. ATLAS preparations for precise measurements of semileptonic rare B decays By K. Toms. Hadron spectroscopy & exotics: Searches for radial excited states of charmonium in experiments using cooled antiproton beams By M. Yu. Barabanov. Retardation effects in the rotating string model By Fabien Buisseret and Claude Semay. Final results from VEPP-2M (CMD-2 and SND) By G. V. Fedotovich. Heavy Quark Physics: Prospects for B physics measurements using the CMS detector at the LHC By Andreev Valery. Heavy flavour production at HERA-B By Andrey Bogatyrev. B-Meson subleading form factors in the Heavy Quark Effective Theory (HQET) By Frederic Jugeau. Beyond the Standard Model: Monopole Decay in a Variable External Field By Andrey Zayakin. Two-Loop matching coefficients for the strong coupling in the MSSM By Mihaila Luminita. Test of lepton flavour violation at LHC By Hidaka Keisho. Looking at New Physics through 4 jets and no ET By Maity Manas. Are Preons Dyons? Naturalness of Three Generations By Das Chitta Ranjan. SUSY Dark Matter at Linear Collider By Sezen Sekmen, Mehmet Zeyrek. MSSM light Higgs boson scenario and its test at hadron colliders By Alexander Belyaev. Antiscalar Approach to Gravity and Standard Model By E. Mychelkin. GRID distributed analysis in high energy physics: PAX: Physics Analysis Design and Application on the GRID By Martin Erdmann, et al.. D0 and the (SAM) GRID: An ongoing success story DO Collaboration. R & D for future accelerators, detectors & new facilities: High Level Trigger Selection in the CMS experiment By Monica Vazquez Acosta. R&D for a Helical Undulator Based Positron Source for the International Linear Collider By Phil Allport. Muon Detection, Reconstruction and Identification in CMS By Ivan Belotelov. Acoustic Measurements for EeV Neutrino Detection at the South Pole By Sebastian Böser. The PSI source of ultracold neutrons (UCN) By Manfred Daum. The LHCb Pixel Hybrid Photon Detectors (Characterization of Nybrig Photon Detectors for the LHCb experiment) By Neville Harnew, et al.. Semi-Insulating GaN-radiation hard semiconductor for ionizing radiation detectors By Juozas Vaitkus. Monitored Drift Tube end-cap spectrometer for the ATLAS detector By Dmitri Kotchetkov. Development of Focusing Aerogel RICH By Sergey Kononov, et al.. Electromagnetic Calibration of the Hadronic Tile Calorimeter Modules of the ATLAS detector at the LHC By Iouri Koultchitski. A Study of Proximity focusing RICH with Multiple Refractive Index Aerogel Radiator By Peter Krizan. The Heavy Flavor Tracker (HFT) for STAR By Vasil Kuspil. ATLAS Liquid Argon Calorimeter ATLAS Collaboration: Field Emission in HEP Colliders Initiated by a Relativistic Positively Charged Bunch of Particles By Boris Levchenko. MICE: the international Muon Ionization Cooling Experiment By Kenneth Long. In situ calibration of the CMS electromagnetic calorimeter By Augustino Lorenzo. The Transition Radiation Tracker for the ATLAS experiment at the LHC By Victor Maleev. Resonance depolarization and Compton-Backscattering technique for beam energy measurement of VEPP-4M collider By Ivan Nikolaev, et al.. CCD - based Pixel Detectors by LCFI By Andrei Nomerotski. The SiD Detector Concept for the International Linear Collider By Dmitry Onoprienko. CMS Hadron Calorimetry, Calibration, and Jets/Missing Transverse Energy Measurements By Sergey Petrushanko. The CMS Silicon Tracker By Oliver Pooth. Drift Chamber for CMD-3 detector By Alexandr Popov, et al.. Vacuum Phototriods for the CMS ECAL Endcap crystal calorimeter By Vladimir Postoev. CMS Silicon Tracker: Track Reconstruction and Alignment By Frank-Peter Schilling. eRHIC - A precision electron-proton/ion collider facility at Brookhaven National Laboratory By Bernd Surrow. Development of tracking detectors with industrially produced GEM foils By Bernd Surrow, et al.. A Linear Collider Facility with High Intensity e+e- beams (A high intensity e+e- Linear Collider Facility at low energy) By Andre Schoening. Construction of the BESIII detector for tau-charm physics By Yifang Wang. The HERMES Recoil Detector By Sergey Yashchenko. Simulation of MICE in G4 MICE MICE Experiment: The new DO Layer O silicon detector The DO trigger upgrade for RUNIIb The Do Collaboration. Operational experiences with the silicon detector at CDF By Jeannine Wagner. Mathematical aspects of QFT & string theory: Electron in superstrong Coulomb field By D. Gitman. Stability of a non-commutative Jackiw-Teitelboim gravity By Fresneda Rodrigo, et al.. 4d gravity localized on thick branes: the complete mass spectrum By Alfredo Herrera-Aguilar. On Emergence of Quantum Mechanics By L. V. Prokhorov.

PREFACE: Nonlinearity and Geometry: connections with integrability Nonlinearity and Geometry: connections with integrability

NASA Astrophysics Data System (ADS)

Cieslinski, Jan L.; Ferapontov, Eugene V.; Kitaev, Alexander V.; Nimmo, Jonathan J. C.

2009-10-01

Geometric ideas are present in many areas of modern theoretical physics and they are usually associated with the presence of nonlinear phenomena. Integrable nonlinear systems play a prime role both in geometry itself and in nonlinear physics. One can mention general relativity, exact solutions of the Einstein equations, string theory, Yang-Mills theory, instantons, solitons in nonlinear optics and hydrodynamics, vortex dynamics, solvable models of statistical physics, deformation quantization, and many others. Soliton theory now forms a beautiful part of mathematics with very strong physical motivations and numerous applications. Interactions between mathematics and physics associated with integrability issues are very fruitful and stimulating. For instance, spectral theories of linear quantum mechanics turned out to be crucial for studying nonlinear integrable systems. The modern theory of integrable nonlinear partial differential and difference equations, or the `theory of solitons', is deeply rooted in the achievements of outstanding geometers of the end of the 19th and the beginning of the 20th century, such as Luigi Bianchi (1856-1928) and Jean Gaston Darboux (1842-1917). Transformations of surfaces and explicit constructions developed by `old' geometers were often rediscovered or reinterpreted in a modern framework. The great progress of recent years in so-called discrete geometry is certainly due to strong integrable motivations. A very remarkable feature of the results of the classical integrable geometry is the quite natural (although nontrivial) possibility of their discretization. This special issue is dedicated to Jean Gaston Darboux and his pioneering role in the development of the geometric ideas of modern soliton theory. The most famous aspects of his work are probably Darboux transformations and triply orthogonal systems of surfaces, whose role in modern mathematical physics cannot be overestimated. Indeed, Darboux transformations play a central role in soliton theory unifying continuous, discrete and quantum integrable systems. Triply orthogonal coordinates proved to be of prime importance for the modern theory of Hamiltonian systems of hydrodynamic type and differential-geometric Poisson brackets, culminating in the construction of the rich and beautiful theory of Frobenius manifolds. The idea for this special issue developed out of the Second Workshop on Nonlinearity and Geometry, a successful conference held in the Mathematical Research and Conference Center at Będlewo, Poland, 13-19 April 2008 (http://wmii.uwm.edu.pl/˜doliwa/WNG-DD.html). However, there was an open call for papers for this issue and all contributions were peer reviewed according to the standards of the journal and taking into account their relevance to the subject of the planned issue. Among the 30 listed authors, 16 attended the conference and the remaining 14 submitted their papers in answer to this open call. The First School on Nolinearity and Geometry (`Bianchi Days') was organized by Antoni Sym and his students in 1995 at the Physics Faculty of Warsaw University, Poland. The proceedings of the workshop, edited by Daniel Wójcik and Jan Cieśliński, were published by Polish Scientific Publishers PWN (Warsaw, 1998). The Second Workshop (`Darboux Days') was organized in 2008 by Adam Doliwa and his coworkers, under the Honorary Chair of Antoni Sym, as a Banach Center Conference. Both workshops gathered around 50 participants. The purpose of these meetings was to bring together researchers with diverse backgrounds (e.g., mathematical physics and differential geometry), and to review the state of the art at the border between the two subjects: geometric inspirations in soliton theory and applications of soliton techniques in geometry. The format was designed to allow substantial time for interaction and research. The invited lectures were longer, intended to present the current trends and open problems in the fields, and to be accessible to younger researchers. It is not out of place to recall that earlier the Institute of Theoretical of Physics of Warsaw University organized two, now legendary, Jadwisin Soliton Workshops (1977 and 1979); see the short note in Physica D: Nonlinear Phenomena (1980 vol. 1, issue 1, pp 159-163) written by Antoni Sym who was deeply engaged in the organization of these conferences. In scale and scope both Jadwisin workshops preceded a series of very successful NEEDS conferences. Among the celebrated participants of the Jadwisin meeetings one can find names of great importance for the history of soliton theory: Martin Kruskal, Norman Zabuski, Mark Ablowitz, David Kaup, Allan Newell, Vladimir Zakharov, Sergei Manakov, Francesco Calogero, Antonio Degasperis and Ryogo Hirota. This special issue begins with an introductory historical article in which Antoni Sym presents the most important ideas in the scientific biography of Gaston Darboux. We encourage the readers discover the greatest (scientific!) love of Darboux. This is followed by five review papers. M Błaszak and B M Szablikowski discuss the general R-matrix formalism for the construction of integrable systems with infinitely many degrees of freedom. The general theory is applied to several infinite-dimensional Lie algebras leading to new examples of dispersionless and dispersive (soliton) integrable field systems in 1+1 and 2+1 dimensions. J L Cieśliński presents the Darboux-Bäcklund transformation for 1+1-dimensional integrable systems of PDEs. He compares existing approaches to the construction of multisoliton Darboux matrices, discusses the nonisospectral case and presents some new results on the linear and bilinear invariants of the Darboux-Bäcklund transformation. M Dunajski presents twistor theory as a geometric tool for solving nonlinear differential equations. Many soliton equations admit twistor interpretation in terms of holomophic vector bundles. A different approach is provided for dispersionless equations. Some integrable systems still await successful application of the twistor approach. This review, although concerned with advanced differential geometry, is quite elementary and self-contained. F Nijhoff, J Atkinson and J Hietarinta review the construction of soliton solutions for the KdV type lattice equations and derive N-soliton solutions for all lattice equations in the Adler-Bobenko-Suris list except for the generic elliptic case. The same problem is addressed in the contribution by J Hietarinta and D J Zhang based on the more traditional direct Hirota method. This leads to Casoratians and bilinear difference equations. Regular contributions include the following. H Baran and M Marvan launch a project to classify integrable classes of surfaces based on a novel deformation procedure of the equations of the embedding. This leads to a remarkable new integrable equation describing a class of Weingarten surfaces which seems to be overlooked in the literature. A Doliwa shows that the τ-function of the quadrilateral lattice can be identified with the Fredholm determinant of the integral equation inverting the nonlocal problem. This result is expected because its continuous counterpart (the case of conjugate nets, Darboux equations and the multicomponent KP hierarchy) is already known. Here one can find an explicit proof. P Gaillard and V B Matveev consider special reductions of the generic Darboux-Crum dressing procedure, leading to new formulas for Darboux-Pöschl-Teller potentials, their difference deformations and the related eigenfunctions. A Gouberman and K Leschke develop the theory of (generalized) Darboux transformations for conformal immersions of a Riemann surface into the 4-sphere. Applying this construction to the Clifford torus, they obtain a family of Willmore tori parametrized by Pythagorean triples. V Kiselev and J W van de Leur construct compatible nontrivial finite deformations of the Lie algebra structure in the symmetry algebra of the 3-component dispersionless Boussinesq-type system. T E Kouloukas and V G Papageorgiou introduce a family of nonparametric Yang-Baxter maps obtained by re-factorization of matrix polynomials of first degree. These maps are Poisson with respect to the Sklyanin bracket, and their degenerations are connected to known integrable systems on quad-graphs. S V Manakov and P M Santini apply a novel version of the inverse scattering transform based on Lax pairs in multidimensional commuting vector fields to the heavenly and Pavlov equations, establishing that their localized solutions evolve without breaking, and constructing the long-time behaviour of the corresponding Cauchy problems. Discretizations of integrable geometric models depend heavily on the coordinates used. M Nieszporski and A Sym show how to discretize Bianchi surfaces (associated with an elliptic version of the Ernst equation) in arbitrary parametrization. C Rogers and A Szereszewski study the Bäcklund transformation for L-isothermic surfaces in the original Bianchi formulation. They establish a connection between this transformation and a nonhomogeneous linear Schrödinger equation and construct a class of generalized Dupin cyclides. W K Schief, A Szereszewski and C Rogers study a classical system of equilibrium equations for shell membranes. Various examples of viable membrane geometries lead to remarkable geometric configurations such as generalized Dupin cyclides and L-minimal surfaces. A Sergyeyev constructs infinite hierarchies of nonlocal higher symmetries for the oriented associativity equations using the spectral problem. The hierarchies in question generalize those constructed by Chen, Kontsevich and Schwarz for the WDVV equations. J Shiraishi and Y Tutiya study an integro-differential equation which generalizes the periodic intermediate long wave equation. The kernel of the singular integral involved is a second order difference of the Weierstrass ζ-function. Using Sato's formulation, the authors demonstrate the integrability of the equation in question, and construct some special solutions. P H van der Kamp discusses general aspects of the Cauchy and Goursat problems for lattice equations focusing on their well-posedness, as well as on periodic and travelling wave reductions. We would like to express sincere thanks to all contributors, editorial staff and all involved in compiling this special issue. Jan L Cieśliński, Eugene V Ferapontov, Alexander V Kitaev and Jonathan J C Nimmo Guest Editors

PREFACE Integrability and nonlinear phenomena Integrability and nonlinear phenomena

NASA Astrophysics Data System (ADS)

Gómez-Ullate, David; Lombardo, Sara; Mañas, Manuel; Mazzocco, Marta; Nijhoff, Frank; Sommacal, Matteo

2010-10-01

Back in 1967, Clifford Gardner, John Greene, Martin Kruskal and Robert Miura published a seminal paper in Physical Review Letters which was to become a cornerstone in the theory of integrable systems. In 2006, the authors of this paper received the AMS Steele Prize. In this award the AMS pointed out that `In applications of mathematics, solitons and their descendants (kinks, anti-kinks, instantons, and breathers) have entered and changed such diverse fields as nonlinear optics, plasma physics, and ocean, atmospheric, and planetary sciences. Nonlinearity has undergone a revolution: from a nuisance to be eliminated, to a new tool to be exploited.' From this discovery the modern theory of integrability bloomed, leading scientists to a deep understanding of many nonlinear phenomena which is by no means reachable by perturbation methods or other previous tools from linear theories. Nonlinear phenomena appear everywhere in nature, their description and understanding is therefore of great interest both from the theoretical and applicative point of view. If a nonlinear phenomenon can be represented by an integrable system then we have at our disposal a variety of tools to achieve a better mathematical description of the phenomenon. This special issue is largely dedicated to investigations of nonlinear phenomena which are related to the concept of integrability, either involving integrable systems themselves or because they use techniques from the theory of integrability. The idea of this special issue originated during the 18th edition of the Nonlinear Evolution Equations and Dynamical Systems (NEEDS) workshop, held at Isola Rossa, Sardinia, Italy, 16-23 May 2009 (http://needs-conferences.net/2009/). The issue benefits from the occasion offered by the meeting, in particular by its mini-workshops programme, and contains invited review papers and contributed papers. It is worth pointing out that there was an open call for papers and all contributions were peer reviewed according to the standards of the journal. The selection of papers in this issue aims to bring together recent developments and findings, even though it consists of only a fraction of the impressive developments in recent years which have affected a broad range of fields, including the theory of special functions, quantum integrable systems, numerical analysis, cellular automata, representations of quantum groups, symmetries of difference equations, discrete geometry, among others. The special issue begins with four review papers: Integrable models in nonlinear optics and soliton solutions Degasperis [1] reviews integrable models in nonlinear optics. He presents a number of approximate models which are integrable and illustrates the links between the mathematical and applicative aspects of the theory of integrable dynamical systems. In particular he discusses the recent impact of boomeronic-type wave equations on applications arising in the context of the resonant interaction of three waves. Hamiltonian PDEs: deformations, integrability, solutions Dubrovin [2] presents classification results for systems of nonlinear Hamiltonian partial differential equations (PDEs) in one spatial dimension. In particular he uses a perturbative approach to the theory of integrability of these systems and discusses their solutions. He conjectures universality of the critical behaviour for the solutions, where the notion of universality refers to asymptotic independence of the structure of solutions (at the point of gradient catastrophe) from the choice of generic initial data as well as from the choice of a generic PDE. KP solitons in shallow water Kodama [3] presents a survey of recent studies on soliton solutions of the Kadomtsev-Petviashvili (KP) equation. A large variety of exact soliton solutions of the KP equation are presented and classified. The study includes numerical analysis of the stability of the found solution as well as numerical simulations of the initial value problems which indicate that a certain class of initial waves approach asymptotically these exact solutions of the KP equation. The author discusses an application of the theory to the problem of the resonant interaction of solitary waves appearing in the reflection of an obliquely incident wave onto a vertical wall, known as the Mach reflection problem in shallow water. A beautiful explanation of the problem was presented in a swimming pool experiment during NEEDS 2009. Smooth and peaked solitons of the CH equation Holm and Ivanov [4] discuss the relations between smooth and peaked soliton solutions for the Camassa-Holm (CH) shallow water wave equation in one spatial dimension. They first present the derivation of the soliton solution for the CH equation by means of inverse scattering transform (IST); the solution is obtained in a form that admits the peakon limit. The canonical Hamiltonian formulation of the CH equation in action-angle variables is recovered using the scattering data. The authors review some of the geometric properties of the CH equation and conclude their review with the higher dimensional generalization of the dispersionless CH equation, known as EPDiff. They also consider the possible extensions of their approach in three open problems. Regular contributions to this issue cover a wide range of topics related to integrable systems. Let us briefly illustrate some of the topics covered by this issue. One of the main topics is the study of hierarchies of integrable equations. The multifaceted idea of integrability of a particular PDE includes an approach whose aim is to find an infinite set of independent conserved quantities, much in the spirit of Liouville integrability in classical mechanics. The existence of these conserved quantities in involution, or of the corresponding infinite set of commuting symmetries, leads to an infinite set of commuting flows; i.e., to the construction of a hierarchy of compatible PDEs with respect to an infinite set of times. Obviously one can generalize or adapt this construction to different settings like the integro-differential, discrete or super-symmetric ones. The emphasis is usually to find auxiliary linear systems defining an infinite set of linear commuting flows whose solutions, if some asymptotic conditions are imposed, are named wave or Baker-Akhiezer functions. These linear flows determine the so called Lax equations, another infinite set of commuting equations whose compatibility leads to the so called Zakharov-Shabat system. An alternative description of the hierarchies is achieved with the use of the bilinear equations directly linked with the tau-function description of the hierarchy. There are two paradigmatic integrable hierarchies, namely the KP and 2-dimensional Toda lattice (2DTL). These hierarchies are treated within this volume in three contributions. In particular, Takasaki [5] reconsiders the extended Toda hierarchy of Carlet, Dubrovin and Zhang in the light of Ogawa's 2 + 1D extension of the 1D Toda hierarchy. It turns out that the former may be thought of as some sort of dimensional reduction of the latter. This explains the structure of the bilinear formalism proposed by Milanov. Carlet and Manas [6] study the 2-component KP and 2D Toda hierarchies and solve explicitly several implicit constraints present in the usual Lax formulation of the hierarchy, thus identifying a set of free dependent variables for such hierarchies. Finally, the KP hierarchy is considered in the paper by Lin et al [7], which explores the extended flows of a q-deformed modified KP hierarchy leading to the introduction of self-consistent sources. By a combination of the dressing method and the method of variation of constants, the authors are able through a dressing approach to find a scheme for the construction of solutions of the corresponding integrable equations with self-consistent sources. The study of dispersionless integrable hierarchies is an active field of research, and this special issue includes two papers devoted to the subject. Konopelchenko et al [8] describe critical and degenerate critical points of a scalar function which obeys the Euler-Poisson-Darboux equation in terms of the hodograph solutions of the dispersionless coupled Korteweg-de Vries hierarchies. Finally, Bogdanov [9] considers 2-component integrable generalizations of the dispersionless 2D Toda lattice hierarchy connected with non-Hamiltonian vector fields, similar to the Manakov-Santini hierarchy generalizing the dKP hierarchy. He presents the simplest 2-component generalization of the dispersionless 2DTL equation, being its differential reduction analogous to the Dunajski interpolating system. Some papers in the issue are concerned with methods to construct solutions of integrable systems, while others place more emphasis on studying properties of specific solutions of applicative interest. Among the first approach, the paper by Kaup and van Gorder [10] describes perturbation theory applied to the Inverse Scattering Transform in 3x eigenvalue problems of Zakharov-Shabat's type. Schiebold [11] studies a projection method to construct solutions of the Ablowitz-Kaup-Newell-Segur (AKNS) system, which enables her to write explicit N-soliton solutions in closed form. An example of the second kind is the paper by Biondini and Wang [12], who study in detail the behaviour of line soliton solutions of the 2DTL, describing their directions and amplitudes and also the richness of their interactions, which include resonant soliton interactions and web structure. An important field of study in integrable systems relates to the singularity structure of the solutions to nonlinear equations. When all movable singularities are poles, the system is said to have the Painleve property. The solutions may be multivalued but they can be analytically continued to meromorphic functions on the universal cover of the punctured Riemann sphere (the punctures being the fixed singularities) and the spectral curve is an affine algebraic curve. Benes and Previato [13] study the connection between the Painleve property and algebras of differential operators, extending an approach initiated by Flaschka. Solutions to some integrable systems can be constructed in terms of analytic objects associated to a spectral algebraic curve. It is therefore of interest to study the Riemann surfaces of algebraic functions, a program illustrated in the paper by Braden and Northover [14], who have implemented some algorithms for this purpose in a popular symbolic computation software. In the paper by Zhilinski [15], the critical points of the energy momentum map in classical Hamiltonian problems with nontrivial monodromy are shown to form regular lattices. The quantum mechanical counterpart has similar lattices for the joint spectrum of the commuting observables. Some examples are given in which these points form special geometric patterns. Claeys [16] uses analytic techniques and Riemann-Hilbert problems to study the asymptotic behaviour when x and t tend to infinity of a solution to the second member of the Painleve I hierarchy, which arises in multicritical string model theory and random matrix theory. This solution is conjectured to describe the universal asymptotics for Hamiltonian perturbations of hyperbolic equations near the point of gradient catastrophe for the unperturbed equation. Darboux and Backlund transformations were born more than a century ago in the context of the geometric theory of surfaces. In the past few decades they have become a useful element in the theory of integrability, with applications in different guises. Typically, they appear in dressing methods that show how to construct new interesting solutions from known simple ones. A few of the contributed papers to the issue make use of these transformations as one of their fundamental objects. Liu et al [17] use iterated Darboux transformations to construct compact representations of the multi-soliton solutions to the derivative nonlinear Schroedinger (DNLS) equation. Ragnisco and Zullo [18] construct Backlund transformations for the trigonometric classical Gaudin magnet in the partially anisotropic (xxz) case, identifying the subcase of transformations that preserve the real character of the variables. The recently discovered exceptional polynomials are complete polynomial systems that satisfy Sturm-Liouville problems but differ from the classical families of Hermite, Laguerre and Jacobi. Gomez-Ullate et al [19] prove that the families of exceptional orthogonal polynomials known to date can be obtained from the classical ones via a Darboux transformation, which becomes a useful tool to derive some of their properties. Integrability in the context of classical mechanics is associated to the existence of a sufficient number of conserved quantities, which allows sometimes an explicit integration of the equations of motion. This is the case for the motion of the Chaplygin sleigh, a rigid body motion on a fluid with nonholonomic constraints studied in the paper by Fedorov and Garcia-Naranjo [20], who derive explicit solutions and study their asymptotic behaviour. In connection with classical mechanics, some techniques of KAM theory have been used by Procesi [21] to derive normal forms for the NLS equation in its Hamiltonian formulation and prove existence and stability of quasi-periodic solutions in the case of periodic boundary conditions. Algebraic and group theoretic aspects of integrability are covered in a number of papers in the issue. The quest for symmetries of a system of differential equations usually allows us to reduce the order or the number of equations or to find special solutions possesing that symmetry, but algebraic aspects of integrable systems encompass a wide and rich spectrum of techniques, as evidenced by the following contributions. Muriel and Romero [22] perform a systematic study of all second order nonlinear ODEs that are linearizable by generalized Sundman and point transformations, showing that the two classes are inequivalent and providing an explicit characterization thereof. Lie algebras are also prominent in the work of Gerdjikov et al [23], where a class of integrable PDEs associated to symmetric spaces is studied in detail. In their approach, systems of nonlinear integrable PDEs are obtained as reductions of generic integrable systems corresponding to Lax operators with matrix coefficients. The reduction here is carried out using a reduction group which reflects symmetries of the Lax operator. These symmetries allow also a characterization of the corresponding Riemann-Hilbert data. Habibullin [24] employs algebraic techniques to study discrete chains of differential-difference equations that are Darboux integrable, i.e. that admit a certain number of nontrivial first integrals. Musso [25] provides a unified algebraic framework for the rational, trigonometric and elliptic Gaudin models. The results are achieved using a generalization of the Gaudin algebras and of the so-called coproduct method. Odesskii and Sokolov [26] present a classification of all infinite (1+1)-dimensional hydrodynamic-type chains of shift one. They establish a one-to-one correspondence between integrable chains and infinite triangular Gibbons-Tsarev (GT) systems and thus reduce the classification problem to a description of all GT-systems. In Korff's paper [27] we find a study of various algebraic and combinatorial structures that emerge in the statistical vertex model with infinite spin, an integrable model associated to a certain quantum affine algebra. In the crystal limit, this model is connected with the WZNW model in conformal field theory. The motivation for some of the submitted contributions arises also from field theories in theoretical physics. Ferreira et al [28] construct soliton solutions with non-zero topological charges to the Skyrme-Faddeev model in Yang-Mills theory. Using techniques of differential geometry and complex analysis, Manton and Rink [29] explore vortex solutions on hyperbolic surfaces extending an approach by Witten. These solutions can be interpreted as self-dual SU(2) Yang-Mills fields on R4. Shah and Woodhouse [30] use the Penrose-Ward correspondence from twistor theory to relate generalized anti self-duality equations to certain isomonodromic problems whose solutions are expressed in terms of generalized hypergeometric functions. Applications of integrable systems and nonlinear phenomena in other fields are also present in some of the papers. Kanna et al [31] study the collision of soliton solutions to coherently coupled NLS equations using a variant of the Hirota bilinearization method. Their results have applications in pulse shaping in nonlinear optics. Calogero et al [32] present examples of systems of ODEs with quadratic nonlinearities that could describe rate equations in chemical dynamics. They derive explicit conditions on the parameters of the problem for which the solutions are periodic and isochronous. Ablowitz and Haut [33] study the motion of large amplitude water waves with surface tension using asymptotic expansions and providing a comparison with experimental results. This issue is the result of the collaboration of many individuals. We would like to thank the editors and staff of the Journal of Physics A: Mathematical and Theoretical for their enthusiastic support and efficient help during the preparation of this issue. A key factor has been the work of many anonymous referees who performed careful analysis and scrutiny of the research papers submitted to this issue, often making remarks which helped to improve their quality and readability. They carried out dedicated, altruistic work with a very high standard and this issue would not exist without their contribution. Finally, we would like to thank the authors who responded to our open call, sending us their most recent results and sharing with us the enthusiasm and interest for this fascinating field of research. We hope that this collection of papers will provide a good overview for anyone interested in recent developments in the field of integrability and nonlinear phenomena. [1] Integrable models in nonlinear optics and soliton solutions Degasperis A [2] Hamiltonian PDEs: deformations, integrability, solutions Dubrovin B [3] Smooth and peaked solitons of the CH equation Holm D D and Ivanov R I [4] KP solitons in shallow water Kodama Y [5] Two extensions of 1D Toda hierarchy Takasaki K [6] On the Lax representation of the 2-component KP and 2D Toda hierarchies Guido Carlet and Manuel Manas [7] The q-deformed mKP hierarchy with self-consistent sources, Wronskian solutions and solitons Lin R L, Peng H and Manas M [8] Hodograph solutions of the dispersionless coupled KdV hierarchies, critical points and the Euler-Poisson-Darboux equation Konopelchenko B, Martinez Alonso L and E Medina [9] Non-Hamiltonian generalizations of the dispersionless 2DTL hierarchy Bogdanov L V [10] Squared eigenfunctions and the perturbation theory for the nondegenerate N x N operator: a general outline Kaup D J and Van Gorder R A [11] The noncommutative AKNS system: projection to matrix systems, countable superposition and soliton-like solutions Schiebold C [12] On the soliton solutions of the two-dimensional Toda lattice Biondini G and Wang D [13] Differential algebra of the Painleve property Benes G N and Previato E [14] Klein's curve Braden H W and Northover T P [15] Quantum monodromy and pattern formation Zhilinskii B [16] A symptotics for a special solution to the second member of the Painleve I hierarchy Claeys T [17] Darboux transformation for a two-component derivative nonlinear Schroedinger equation Ling L and Liu Q P [18] Backlund transformations as exact integrable time discretizations for the trigonometric Gaudin model Ragnisco O and Zullo F [19] Exceptional orthogonal polynomials and the Darboux transformation Gomez-Ullate D, Kamran N and Milson R [20] The hydrodynamic Chaplygin sleigh Fedorov Y N and Garcia-Naranjo L C [21] A normal form for beam and non-local nonlinear Schroedinger equations Procesi M [22] Nonlocal transformations and linearization of second-order ordinary differential equations Muriel and Romero J L [23] Reductions of integrable equations on A.III-type symmetric spaces Gerdjikov V S, Mikhailov A V and Valchev T I [24] On Darboux-integrable semi-discrete chains Habibullin I, Zheltukhina N and Sakieva A [25] Loop coproducts, Gaudin models and Poisson coalgebras Musso F [26] Classification of integrable hydrodynamic chains Odesskii A V and Sokolov V V [27] Noncommutative Schur polynomials and the crystal limit of the Uq sl(2)-vertex model Korff C [28] Axially symmetric soliton solutions in a Skyrme-Faddeev-type model with Gies's extension Ferreira L A, Sawado N and Toda K [29] Vortices on hyperbolic surfaces Manton N S and Rink N A [30] Multivariate hypergeometric cascades, isomonodromy problems and Ward ansatze Shah M R and Woodhouse N J M [31] Coherently coupled bright optical solitons and their collisions Kanna T, Vijayajayanthi M and Lakshmanan M [32] Isochronous rate equations describing chemical reactions Calogero F, Leyvraz F and Sommacal M [33] Asymptotic expansions for solitary gravity-capillary waves in two and three dimensions Ablowitz M J and Haut T S