Holomorphic Hartree-Fock Theory: The Nature of Two-Electron Problems.

PubMed

Burton, Hugh G A; Gross, Mark; Thom, Alex J W

2018-02-13

We explore the existence and behavior of holomorphic restricted Hartree-Fock (h-RHF) solutions for two-electron problems. Through algebraic geometry, the exact number of solutions with n basis functions is rigorously identified as 1 / 2 (3 n - 1), proving that states must exist for all molecular geometries. A detailed study on the h-RHF states of HZ (STO-3G) then demonstrates both the conservation of holomorphic solutions as geometry or atomic charges are varied and the emergence of complex h-RHF solutions at coalescence points. Using catastrophe theory, the nature of these coalescence points is described, highlighting the influence of molecular symmetry. The h-RHF states of HHeH 2+ and HHeH (STO-3G) are then compared, illustrating the isomorphism between systems with two electrons and two electron holes. Finally, we explore the h-RHF states of ethene (STO-3G) by considering the π electrons as a two-electron problem and employ NOCI to identify a crossing of the lowest energy singlet and triplet states at the perpendicular geometry.

2D Kac-Moody symmetry of 4D Yang-Mills theory

DOE PAGES

He, Temple; Mitra, Prahar; Strominger, Andrew

2016-10-25

Scattering amplitudes of any four-dimensional theory with nonabelian gauge group G may be recast as two-dimensional correlation functions on the asymptotic twosphere at null in nity. The soft gluon theorem is shown, for massless theories at the semiclassical level, to be the Ward identity of a holomorphic two-dimensional G-Kac-Moody symmetry acting on these correlation functions. Holomorphic Kac-Moody current insertions are positive helicity soft gluon insertions. Furthermore, the Kac-Moody transformations are a CPT invariant subgroup of gauge transformations which act nontrivially at null in nity and comprise the four-dimensional asymptotic symmetry group.

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.

CR extension from hypersurfaces of higher type

NASA Astrophysics Data System (ADS)

Baracco, Luca

2007-07-01

We prove extension of CR functions from a hypersurface M of in presence of the so-called sector property. If M has finite type in the Bloom-Graham sense, then our result is already contained in [C. Rea, Prolongement holomorphe des fonctions CR, conditions suffisantes, C. R. Acad. Sci. Paris 297 (1983) 163-166] by Rea. We think however, that the argument of our proof carries an expressive geometric meaning and deserves interest on its own right. Also, our method applies in some case to hypersurfaces of infinite type; note that for these, the classical methods fail. CR extension is treated by many authors mainly in two frames: extension in directions of iterated of commutators of CR vector fields (cf., for instance, [A. Boggess, J. Pitts, CR extension near a point of higher type, Duke Math. J. 52 (1) (1985) 67-102; A. Boggess, J.C. Polking, Holomorphic extension of CR functions, Duke Math. J. 49 (1982) 757-784. ; M.S. Baouendi, L. Rothschild, Normal forms for generic manifolds and holomorphic extension of CR functions, J. Differential Geom. 25 (1987) 431-467. ]); extension through minimality towards unprecised directions [A.E. Tumanov, Extension of CR-functions into a wedge, Mat. Sb. 181 (7) (1990) 951-964. ; A.E. Tumanov, Analytic discs and the extendibility of CR functions, in: Integral Geometry, Radon Transforms and Complex Analysis, Venice, 1996, in: Lecture Notes in Math., vol. 1684, Springer, Berlin, 1998, pp. 123-141].

Immortal solution of the Ricci flow

NASA Astrophysics Data System (ADS)

Ruan, Qihua; Chen, Zhihua

2005-12-01

For any complete noncompact K$\\ddot{a}$hler manifold with nonnegative and bounded holomorphic bisectional curvature,we provide the necessary and sufficient condition for non-ancient solution to the Ricci flow in this paper.

Quantum Hall states and conformal field theory on a singular surface

NASA Astrophysics Data System (ADS)

Can, T.; Wiegmann, P.

2017-12-01

In Can et al (2016 Phys. Rev. Lett. 117), quantum Hall states on singular surfaces were shown to possess an emergent conformal symmetry. In this paper, we develop this idea further and flesh out details on the emergent conformal symmetry in holomorphic adiabatic states, which we define in the paper. We highlight the connection between the universal features of geometric transport of quantum Hall states and holomorphic dimension of primary fields in conformal field theory. In parallel we compute the universal finite-size corrections to the free energy of a critical system on a hyperbolic sphere with conical and cusp singularities, thus extending the result of Cardy and Peschel for critical systems on a flat cone (Cardy and Peschel 1988 Nucl. Phys. B 300 377-92), and the known results for critical systems on polyhedra and flat branched Riemann surfaces.

On the Automorphisms of a Rank One Deligne-Hitchin Moduli Space

NASA Astrophysics Data System (ADS)

Biswas, Indranil; Heller, Sebastian

2017-09-01

Let X be a compact connected Riemann surface of genus g ≥ 2, and let M_{DH} be the rank one Deligne-Hitchin moduli space associated to X. It is known that M_{DH} is the twistor space for the hyper-Kähler structure on the moduli space of rank one holomorphic connections on X. We investigate the group \\operatorname{Aut}(M_{DH}) of all holomorphic automorphisms of M_{DH}. The connected component of \\operatorname{Aut}(M_{DH}) containing the identity automorphism is computed. There is a natural element of H^2(M_{DH}, Z). We also compute the subgroup of \\operatorname{Aut}(M_{DH}) that fixes this second cohomology class. Since M_{DH} admits an ample rational curve, the notion of algebraic dimension extends to it by a theorem of Verbitsky. We prove that M_{DH} is Moishezon.

Partition functions for heterotic WZW conformal field theories

NASA Astrophysics Data System (ADS)

Gannon, Terry

1993-08-01

Thus far in the search for, and classification of, "physical" modular invariant partition functions ΣN LRχ Lχ R∗ the attention has been focused on the symmetric case where the holomorphic and anti-holomorphic sectors, and hence the characters χLand χR, are associated with the same Kac-Moody algebras ĝL = ĝR and levels κ L = κ R. In this paper we consider the more general possibility where ( ĝL, κ L) may not equal ( ĝR, κ R). We discuss which choices of algebras and levels may correspond to well-defined conformal field theories, we find the "smallest" such heterotic (i.e. asymmetric) partition functions, and we give a method, generalizing the Roberts-Terao-Warner lattice method, for explicitly constructing many other modular invariants. We conclude the paper by proving that this new lattice method will succeed in generating all the heterotic partition functions, for all choices of algebras and levels.

Differential Models for B-Type Open-Closed Topological Landau-Ginzburg Theories

NASA Astrophysics Data System (ADS)

Babalic, Elena Mirela; Doryn, Dmitry; Lazaroiu, Calin Iuliu; Tavakol, Mehdi

2018-05-01

We propose a family of differential models for B-type open-closed topological Landau-Ginzburg theories defined by a pair (X,W), where X is any non-compact Calabi-Yau manifold and W is any holomorphic complex-valued function defined on X whose critical set is compact. The models are constructed at cochain level using smooth data, including the twisted Dolbeault algebra of polyvector-valued forms and a twisted Dolbeault category of holomorphic factorizations of W. We give explicit proposals for cochain level versions of the bulk and boundary traces and for the bulk-boundary and boundary-bulk maps of the Landau-Ginzburg theory. We prove that most of the axioms of an open-closed TFT (topological field theory) are satisfied on cohomology and conjecture that the remaining two axioms (namely non-degeneracy of bulk and boundary traces and the topological Cardy constraint) are also satisfied.

Deformations of super Riemann surfaces

NASA Astrophysics Data System (ADS)

Ninnemann, Holger

1992-11-01

Two different approaches to (Kostant-Leites-) super Riemann surfaces are investigated. In the local approach, i.e. glueing open superdomains by superconformal transition functions, deformations of the superconformal structure are discussed. On the other hand, the representation of compact super Riemann surfaces of genus greater than one as a fundamental domain in the Poincaré upper half-plane provides a simple description of super Laplace operators acting on automorphic p-forms. Considering purely odd deformations of super Riemann surfaces, the number of linear independent holomorphic sections of arbitrary holomorphic line bundles will be shown to be independent of the odd moduli, leading to a simple proof of the Riemann-Roch theorem for compact super Riemann surfaces. As a further consequence, the explicit connections between determinants of super Laplacians and Selberg's super zeta functions can be determined, allowing to calculate at least the 2-loop contribution to the fermionic string partition function.

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.

Complex Chern-Simons Theory at Level k via the 3d-3d Correspondence

NASA Astrophysics Data System (ADS)

Dimofte, Tudor

2015-10-01

We use the 3d-3d correspondence together with the DGG construction of theories T n [ M] labelled by 3-manifolds M to define a non-perturbative state-integral model for Chern-Simons theory at any level k, based on ideal triangulations. The resulting partition functions generalize a widely studied k = 1 state-integral, as well as the 3d index, which is k = 0. The Chern-Simons partition functions correspond to partition functions of T n [ M] on squashed lens spaces L( k, 1). At any k, they admit a holomorphic-antiholomorphic factorization, corresponding to the decomposition of L( k, 1) into two solid tori, and the associated holomorphic block decomposition of the partition functions of T n [ M]. A generalization to L( k, p) is also presented. Convergence of the state integrals, for any k, requires triangulations to admit a positive angle structure; we propose that this is also necessary for the DGG gauge theory T n [ M] to flow to a desired IR SCFT.

Shape-based diffeomorphic registration on hippocampal surfaces using Beltrami holomorphic flow.

PubMed

Lui, Lok Ming; Wong, Tsz Wai; Thompson, Paul; Chan, Tony; Gu, Xianfeng; Yau, Shing-Tung

2010-01-01

We develop a new algorithm to automatically register hippocampal (HP) surfaces with complete geometric matching, avoiding the need to manually label landmark features. A good registration depends on a reasonable choice of shape energy that measures the dissimilarity between surfaces. In our work, we first propose a complete shape index using the Beltrami coefficient and curvatures, which measures subtle local differences. The proposed shape energy is zero if and only if two shapes are identical up to a rigid motion. We then seek the best surface registration by minimizing the shape energy. We propose a simple representation of surface diffeomorphisms using Beltrami coefficients, which simplifies the optimization process. We then iteratively minimize the shape energy using the proposed Beltrami Holomorphic flow (BHF) method. Experimental results on 212 HP of normal and diseased (Alzheimer's disease) subjects show our proposed algorithm is effective in registering HP surfaces with complete geometric matching. The proposed shape energy can also capture local shape differences between HP for disease analysis.

Genome sequence and annotation of Trichoderma parareesei, the ancestor of the cellulase producer Trichoderma reesei

DOE PAGES

Yang, Dongqing; Pomraning, Kyle; Kopchinskiy, Alexey; ...

2015-08-13

The filamentous fungus Trichoderma parareesei is the asexually reproducing ancestor of Trichoderma reesei, the holomorphic industrial producer of cellulase and hemicellulase. Here, we present the genome sequence of the T. parareesei type strain CBS 125925, which contains genes for 9,318 proteins.

Lattices, vertex algebras, and modular categories

NASA Astrophysics Data System (ADS)

van Ekeren, Jethro

2018-03-01

In this note we give an account of recent progress on the construction of holomorphic vertex algebras as cyclic orbifolds as well as related topics in lattices and modular categories. We present a novel computation of the Schur indicator of a lattice involution orbifold using finite Heisenberg groups and discriminant forms.

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.

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.

Integrands for QCD rational terms and {N} = {4} SYM from massive CSW rules

NASA Astrophysics Data System (ADS)

Elvang, Henriette; Freedman, Daniel Z.; Kiermaier, Michael

2012-06-01

We use massive CSW rules to derive explicit compact expressions for integrands of rational terms in QCD with any number of external legs. Specifically, we present all- n integrands for the one-loop all-plus and one-minus gluon amplitudes in QCD. We extract the finite part of spurious external-bubble contributions systematically; this is crucial for the application of integrand-level CSW rules in theories without supersymmetry. Our approach yields integrands that are independent of the choice of CSW reference spinor even before integration. Furthermore, we present a recursive derivation of the recently proposed massive CSW-style vertex expansion for massive tree amplitudes and loop integrands on the Coulomb-branch of {N} = {4} SYM. The derivation requires a careful study of boundary terms in all-line shift recursion relations, and provides a rigorous (albeit indirect) proof of the recently proposed construction of massive amplitudes from soft-limits of massless on-shell amplitudes. We show that the massive vertex expansion manifestly preserves all holomorphic and half of the anti-holomorphic supercharges, diagram-by-diagram, even off-shell.

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

Conformal invariance of (0, 2) sigma models on Calabi-Yau manifolds

NASA Astrophysics Data System (ADS)

Jardine, Ian T.; Quigley, Callum

2018-03-01

Long ago, Nemeschansky and Sen demonstrated that the Ricci-flat metric on a Calabi-Yau manifold could be corrected, order by order in perturbation theory, to produce a conformally invariant (2, 2) nonlinear sigma model. Here we extend this result to (0, 2) sigma models for stable holomorphic vector bundles over Calabi-Yaus.

Computational approach to compact Riemann surfaces

NASA Astrophysics Data System (ADS)

Frauendiener, Jörg; Klein, Christian

2017-01-01

A purely numerical approach to compact Riemann surfaces starting from plane algebraic curves is presented. The critical points of the algebraic curve are computed via a two-dimensional Newton iteration. The starting values for this iteration are obtained from the resultants with respect to both coordinates of the algebraic curve and a suitable pairing of their zeros. A set of generators of the fundamental group for the complement of these critical points in the complex plane is constructed from circles around these points and connecting lines obtained from a minimal spanning tree. The monodromies are computed by solving the defining equation of the algebraic curve on collocation points along these contours and by analytically continuing the roots. The collocation points are chosen to correspond to Chebychev collocation points for an ensuing Clenshaw-Curtis integration of the holomorphic differentials which gives the periods of the Riemann surface with spectral accuracy. At the singularities of the algebraic curve, Puiseux expansions computed by contour integration on the circles around the singularities are used to identify the holomorphic differentials. The Abel map is also computed with the Clenshaw-Curtis algorithm and contour integrals. As an application of the code, solutions to the Kadomtsev-Petviashvili equation are computed on non-hyperelliptic Riemann surfaces.

Explicitly broken supersymmetry with exactly massless moduli

NASA Astrophysics Data System (ADS)

Dong, Xi; Freedman, Daniel Z.; Zhao, Yue

2016-06-01

The AdS/CFT correspondence is applied to an analogue of the little hierarchy problem in three-dimensional supersymmetric theories. The bulk is governed by a super-gravity theory in which a U(1) × U(1) R-symmetry is gauged by Chern-Simons fields. The bulk theory is deformed by a boundary term quadratic in the gauge fields. It breaks SUSY completely and sources an exactly marginal operator in the dual CFT. SUSY breaking is communicated by gauge interactions to bulk scalar fields and their spinor superpartners. The bulk-to-boundary propagator of the Chern-Simons fields is a total derivative with respect to the bulk coordinates. Integration by parts and the Ward identity permit evaluation of SUSY breaking effects to all orders in the strength of the deformation. The R-charges of scalars and spinors differ so large SUSY breaking mass shifts are generated. Masses of R-neutral particles such as scalar moduli are not shifted to any order in the deformation strength, despite the fact that they may couple to R-charged fields running in loops. We also obtain a universal deformation formula for correlation functions under an exactly marginal deformation by a product of holomorphic and anti-holomorphic U(1) currents.

On the dualization of scalars into ( d - 2)-forms in supergravity. Momentum maps, R-symmetry and gauged supergravity

NASA Astrophysics Data System (ADS)

Bandos, Igor A.; Ortín, Tomás

2016-08-01

We review and investigate different aspects of scalar fields in supergravity theories both when they parametrize symmetric spaces and when they parametrize spaces of special holonomy which are not necessarily symmetric (Kähler and Quaternionic-Kähler spaces): their rôle in the definition of derivatives of the fermions covariant under the R-symmetry group and (in gauged supergravities) under some gauge group, their dualization into ( d - 2)-forms, their role in the supersymmetry transformation rules (via fermion shifts, for instance) etc. We find a general definition of momentum map that applies to any manifold admitting a Killing vector and coincides with those of the holomorphic and tri-holomorphic momentum maps in Kähler and quaternionic-Kähler spaces and with an independent definition that can be given in symmetric spaces. We show how the momen-tum map occurs ubiquitously: in gauge-covariant derivatives of fermions, in fermion shifts, in the supersymmetry transformation rules of ( d - 2)-forms etc. We also give the general structure of the Noether-Gaillard-Zumino conserved currents in theories with fields of different ranks in any dimension.

Deformation quantization with separation of variables of an endomorphism bundle

NASA Astrophysics Data System (ADS)

Karabegov, Alexander

2014-01-01

Given a holomorphic Hermitian vector bundle E and a star-product with separation of variables on a pseudo-Kähler manifold, we construct a star product on the sections of the endomorphism bundle of the dual bundle E∗ which also has the appropriately generalized property of separation of variables. For this star product we prove a generalization of Gammelgaard's graph-theoretic formula.

On F-Algebras M p  (1 < p < ∞) of Holomorphic Functions

PubMed Central

Meštrović, Romeo

2014-01-01

We consider the classes M p (1 < p < ∞) of holomorphic functions on the open unit disk 𝔻 in the complex plane. These classes are in fact generalizations of the class M introduced by Kim (1986). The space M p equipped with the topology given by the metric ρ p defined by ρ p(f, g) = ||f − g||p = (∫ 0 2πlogp(1 + M(f − g)(θ))(dθ/2π))1/p, with f, g∈M p and Mf(θ) = sup0⩽r<1 ⁡|f(re iθ)|, becomes an F-space. By a result of Stoll (1977), the Privalov space N p (1 < p < ∞) with the topology given by the Stoll metric d p is an F-algebra. By using these two facts, we prove that the spaces M p and N p coincide and have the same topological structure. Consequently, we describe a general form of continuous linear functionals on M p (with respect to the metric ρ p). Furthermore, we give a characterization of bounded subsets of the spaces M p. Moreover, we give the examples of bounded subsets of M p that are not relatively compact. PMID:24672388

Graviton 1-loop partition function for 3-dimensional massive gravity

NASA Astrophysics Data System (ADS)

Gaberdiel, Matthias R.; Grumiller, Daniel; Vassilevich, Dmitri

2010-11-01

Thegraviton1-loop partition function in Euclidean topologically massivegravity (TMG) is calculated using heat kernel techniques. The partition function does not factorize holomorphically, and at the chiral point it has the structure expected from a logarithmic conformal field theory. This gives strong evidence for the proposal that the dual conformal field theory to TMG at the chiral point is indeed logarithmic. We also generalize our results to new massive gravity.

Symmetries and conservation laws of a nonlinear sigma model with gravitino

NASA Astrophysics Data System (ADS)

Jost, Jürgen; Keßler, Enno; Tolksdorf, Jürgen; Wu, Ruijun; Zhu, Miaomiao

2018-06-01

We study the symmetries and invariances of a version of the action functional of the nonlinear sigma model with gravitino, as considered in Jost et al. (2017). The action is invariant under rescaled conformal transformations, super Weyl transformations, and diffeomorphisms. In particular cases the functional possesses a degenerate supersymmetry. The corresponding conservation laws lead to a geometric interpretation of the energy-momentum tensor and supercurrent as holomorphic sections of appropriate bundles.

Occams Quantum Strop: Synchronizing and Compressing Classical Cryptic Processes via a Quantum Channel (Open Source)

DTIC Science & Technology

2016-02-15

do not quote them here. A sequel details a yet more efficient analytic technique based on holomorphic functions of the internal - state Markov chain...required, though, when synchronizing over a quantum channel? Recent work demonstrated that representing causal similarity as quantum state ...minimal, unifilar predictor4. The -machine’s causal states σ ∈ are defined by the equivalence relation that groups all histories = −∞ ←x x :0 that

Deformation quantizations with separation of variables on a Kähler manifold

NASA Astrophysics Data System (ADS)

Karabegov, Alexander V.

1996-10-01

We give a simple geometric description of all formal differentiable deformation quantizations on a Kähler manifold M such that for each open subset U⊂ M ⋆-multiplication from the left by a holomorphic function and from the right by an antiholomorphic function on U coincides with the pointwise multiplication by these functions. We show that these quantizations are in 1-1 correspondence with the formal deformations of the original Kähler metrics on M.

A Scale-Invariant ``Discrete-Time'' Balitsky--Kovchegov Equation

NASA Astrophysics Data System (ADS)

Bialas, A.; Peschanski, R.

2005-06-01

We consider a version of QCD dipole cascading corresponding to a finite number n of discrete Δ Y steps of branching in rapidity. Using the discretization scheme preserving the holomorphic factorizability and scale-invariance in position space of the dipole splitting function, we derive an exact recurrence formula from step to step which plays the rôle of a ``discrete-time'' Balitsky--Kovchegov equation. The BK solutions are recovered in the limit n=∞ and Δ Y=0.

General solutions of the supersymmetric ℂP{sup 2} sigma model and its generalisation to ℂP{sup N−1}

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

Delisle, L., E-mail: laurent.delisle@imj-prg.fr; Hussin, V., E-mail: hussin@dms.umontreal.ca; Centre de Recherches Mathématiques, Université de Montréal, C.P. 6128, Succ. Centre-ville, Montréal, Québec H3C 3J7

A new approach for the construction of finite action solutions of the supersymmetric ℂP{sup N−1} sigma model is presented. We show that this approach produces more non-holomorphic solutions than those obtained in previous approaches. We study the ℂP{sup 2} model in detail and present its solutions in an explicit form. We also show how to generalise this construction to N > 3.

Geometric structures of super-(Diff(S/sup 1/)/S/sup 1/)*

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

Schmidke, W.B.; Vokos, S.P.

Superconformal invariance is of central importance to a perturbative and non-perturbative formulation of stringy theory. The group that describes the invariances of the superstring is the super-Virasoro group, Super-Diff(S/sup 1/). The super-reparameterizations of the circle that leave a point fixed compose the quotient space Super-(Diff(S/sup 1/)/S/sup 1/). We investigate the holomorphic geometry of this infinite-dimensional Kaehler supermanifold and calculate its curvature. copyright 1989 Academic Press, Inc.

Zeta functions on tori using contour integration

NASA Astrophysics Data System (ADS)

Elizalde, Emilio; Kirsten, Klaus; Robles, Nicolas; Williams, Floyd

2015-12-01

A new, seemingly useful presentation of zeta functions on complex tori is derived by using contour integration. It is shown to agree with the one obtained by using the Chowla-Selberg series formula, for which an alternative proof is thereby given. In addition, a new proof of the functional determinant on the torus results, which does not use the Kronecker first limit formula nor the functional equation of the non-holomorphic Eisenstein series. As a bonus, several identities involving the Dedekind eta function are obtained as well.

Weinberg propagator of a massive particle with an arbitrary spin (in Ukrainian)

NASA Astrophysics Data System (ADS)

Zima, V. G.; Fedoruk, S. O.

The transition amplitude is obtained for a free massive particle of an arbitrary spin by calculating the path integral in the index--spinor formulation within the BFV--BRST approach. None renormalizations of the path integral measure were applied. The calculation has given the Weinberg propagator written in the index--free form with the use of an index spinor. The choice of boundary conditions on the index spinor determines holomorphic or antiholomorphic representation for the canonical description of particle/antiparticle spin.

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.

The Trichoderma harzianum demon: complex speciation history resulting in coexistence of hypothetical biological species, recent agamospecies and numerous relict lineages

PubMed Central

2010-01-01

Background The mitosporic fungus Trichoderma harzianum (Hypocrea, Ascomycota, Hypocreales, Hypocreaceae) is an ubiquitous species in the environment with some strains commercially exploited for the biological control of plant pathogenic fungi. Although T. harzianum is asexual (or anamorphic), its sexual stage (or teleomorph) has been described as Hypocrea lixii. Since recombination would be an important issue for the efficacy of an agent of the biological control in the field, we investigated the phylogenetic structure of the species. Results Using DNA sequence data from three unlinked loci for each of 93 strains collected worldwide, we detected a complex speciation process revealing overlapping reproductively isolated biological species, recent agamospecies and numerous relict lineages with unresolved phylogenetic positions. Genealogical concordance and recombination analyses confirm the existence of two genetically isolated agamospecies including T. harzianum sensu stricto and two hypothetical holomorphic species related to but different from H. lixii. The exact phylogenetic position of the majority of strains was not resolved and therefore attributed to a diverse network of recombining strains conventionally called 'pseudoharzianum matrix'. Since H. lixii and T. harzianum are evidently genetically isolated, the anamorph - teleomorph combination comprising H. lixii/T. harzianum in one holomorph must be rejected in favor of two separate species. Conclusions Our data illustrate a complex speciation within H. lixii - T. harzianum species group, which is based on coexistence and interaction of organisms with different evolutionary histories and on the absence of strict genetic borders between them. PMID:20359347

Non-vanishing superpotentials in heterotic string theory and discrete torsion

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

Buchbinder, Evgeny I.; Ovrut, Burt A.

Here, we study the non-perturbative superpotential in E8 E8 heterotic string theory on a non-simply connected Calabi-Yau manifold X, as well as on its simply connected covering space ~X . The superpotential is induced by the string wrapping holomorphic, isolated, genus 0 curves. According to the residue theorem of Beasley and Witten, the non-perturbative superpotential must vanish in a large class of heterotic vacua because the contributions from curves in the same homology class cancel each other. We point out, however, that in certain cases the curves treated in the residue theorem as lying in the same homology class, canmore » actually have different area with respect to the physical Kahler form and can be in different homology classes. In these cases, the residue theorem is not directly applicable and the structure of the superpotential is more subtle. We also show, in a specific example, that the superpotential is non-zero both on ~X and on X. On the non-simply connected manifold X, we explicitly compute the leading contribution to the superpotential from all holomorphic, isolated, genus 0 curves with minimal area. Furthermore, the reason for the non-vanishing of the superpotental on X is that the second homology class contains a finite part called discrete torsion. As a result, the curves with the same area are distributed among different torsion classes and, hence, do not cancel each other« less

Non-vanishing superpotentials in heterotic string theory and discrete torsion

DOE PAGES

Buchbinder, Evgeny I.; Ovrut, Burt A.

2017-01-10

Here, we study the non-perturbative superpotential in E8 E8 heterotic string theory on a non-simply connected Calabi-Yau manifold X, as well as on its simply connected covering space ~X . The superpotential is induced by the string wrapping holomorphic, isolated, genus 0 curves. According to the residue theorem of Beasley and Witten, the non-perturbative superpotential must vanish in a large class of heterotic vacua because the contributions from curves in the same homology class cancel each other. We point out, however, that in certain cases the curves treated in the residue theorem as lying in the same homology class, canmore » actually have different area with respect to the physical Kahler form and can be in different homology classes. In these cases, the residue theorem is not directly applicable and the structure of the superpotential is more subtle. We also show, in a specific example, that the superpotential is non-zero both on ~X and on X. On the non-simply connected manifold X, we explicitly compute the leading contribution to the superpotential from all holomorphic, isolated, genus 0 curves with minimal area. Furthermore, the reason for the non-vanishing of the superpotental on X is that the second homology class contains a finite part called discrete torsion. As a result, the curves with the same area are distributed among different torsion classes and, hence, do not cancel each other« less

Perturbative Power Counting, Lowest-Index Operators and Their Renormalization in Standard Model Effective Field Theory

NASA Astrophysics Data System (ADS)

Liao, Yi; Ma, Xiao-Dong

2018-03-01

We study two aspects of higher dimensional operators in standard model effective field theory. We first introduce a perturbative power counting rule for the entries in the anomalous dimension matrix of operators with equal mass dimension. The power counting is determined by the number of loops and the difference of the indices of the two operators involved, which in turn is defined by assuming that all terms in the standard model Lagrangian have an equal perturbative power. Then we show that the operators with the lowest index are unique at each mass dimension d, i.e., (H † H) d/2 for even d ≥ 4, and (LT∈ H)C(LT∈ H) T (H † H)(d-5)/2 for odd d ≥ 5. Here H, L are the Higgs and lepton doublet, and ∈, C the antisymmetric matrix of rank two and the charge conjugation matrix, respectively. The renormalization group running of these operators can be studied separately from other operators of equal mass dimension at the leading order in power counting. We compute their anomalous dimensions at one loop for general d and find that they are enhanced quadratically in d due to combinatorics. We also make connections with classification of operators in terms of their holomorphic and anti-holomorphic weights. Supported by the National Natural Science Foundation of China under Grant Nos. 11025525, 11575089, and by the CAS Center for Excellence in Particle Physics (CCEPP)

Weinberg propagator of a free massive particle with an arbitrary spin from the BFV-BRST path integral

NASA Astrophysics Data System (ADS)

Zima, V. G.; Fedoruk, S. O.

1999-11-01

The transition amplitude is obtained for a free massive particle of arbitrary spin by calculating the path integral in the index-spinor formulation within the BFV-BRST approach. No renormalizations of the path integral measure were applied. The calculation has given the Weinberg propagator written in the index-free form by the use of an index spinor. The choice of boundary conditions on the index spinor determines the holomorphic or antiholomorphic representation for the canonical description of particle/antiparticle spin.

Higher dimensional curved domain walls on Kähler surfaces

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

Akbar, Fiki T., E-mail: ftakbar@fi.itb.ac.id; Gunara, Bobby E., E-mail: bobby@fi.itb.ac.id; Radjabaycolle, Flinn C.

In this paper we study some aspects of curved BPS-like domain walls in higher dimensional gravity theory coupled to scalars where the scalars span a complex Kähler surface with scalar potential turned on. Assuming that a fake superpotential has a special form which depends on Kähler potential and a holomorphic function, we prove that BPS-like equations have a local unique solution. Then, we analyze the vacuum structure of the theory including their stability using dynamical system and their existence in ultraviolet-infrared regions using renormalization group flow.

Construction of all N=4 conformal supergravities.

PubMed

Butter, Daniel; Ciceri, Franz; de Wit, Bernard; Sahoo, Bindusar

2017-02-24

All N=4 conformal supergravities in four space-time dimensions are constructed. These are the only N=4 supergravity theories whose actions are invariant under off-shell supersymmetry. They are encoded in terms of a holomorphic function that is homogeneous of zeroth degree in scalar fields that parametrize an SU(1,1)/U(1) coset space. When this function equals a constant the Lagrangian is invariant under continuous SU(1,1) transformations. The construction of these higher-derivative invariants also opens the door to various applications for nonconformal theories.

d-Brane Instantons in Type II Orientifolds

NASA Astrophysics Data System (ADS)

Blumenhagen, Ralph; Cvetič, Mirjam; Kachru, Shamit; Weigand, Timo

2009-11-01

We review recent progress in determining the effects of d-brane instantons in [Formula: see text] supersymmetric compactifications of Type II string theory to four dimensions. We describe the abstract d-brane instanton calculus for holomorphic couplings such as the superpotential, the gauge kinetic function, and higher fermionic F-terms, and we briefly discuss the implications of background fluxes for the instanton sector. We then summarize the concrete consequences of stringy d-brane instantons for the construction of semirealistic models of particle physics or supersymmetry breaking in compact and noncompact geometries.

Nearly perturbative lattice-motivated QCD coupling with zero IR limit

NASA Astrophysics Data System (ADS)

Ayala, César; Cvetič, Gorazd; Kögerler, Reinhart; Kondrashuk, Igor

2018-03-01

The product of the gluon dressing function and the square of the ghost dressing function in the Landau gauge can be regarded to represent, apart from the inverse power corrections 1/{Q}2n, a nonperturbative generalization { \\mathcal A }({Q}2) of the perturbative QCD running coupling a({Q}2) (\\equiv {α }s({Q}2)/π ). Recent large volume lattice calculations for these dressing functions indicate that the coupling defined in such a way goes to zero as { \\mathcal A }({Q}2)∼ {Q}2 when the squared momenta Q 2 go to zero ({Q}2\\ll 1 {GeV}}2). In this work we construct such a QCD coupling { \\mathcal A }({Q}2) which fulfills also various other physically motivated conditions. At high momenta it becomes the underlying perturbative coupling a({Q}2) to a very high precision. And at intermediate low squared momenta {Q}2∼ 1 {GeV}}2 it gives results consistent with the data of the semihadronic τ lepton decays as measured by OPAL and ALEPH. The coupling is constructed in a dispersive way, resulting as a byproduct in the holomorphic behavior of { \\mathcal A }({Q}2) in the complex Q 2-plane which reflects the holomorphic behavior of the spacelike QCD observables. Application of the Borel sum rules to τ-decay V + A spectral functions allows us to obtain values for the gluon (dimension-4) condensate and the dimension-6 condensate, which reproduce the measured OPAL and ALEPH data to a significantly better precision than the perturbative \\overline{MS}} coupling approach.

Algebraic Structure of tt * Equations for Calabi-Yau Sigma Models

NASA Astrophysics Data System (ADS)

Alim, Murad

2017-08-01

The tt * equations define a flat connection on the moduli spaces of {2d, \\mathcal{N}=2} quantum field theories. For conformal theories with c = 3 d, which can be realized as nonlinear sigma models into Calabi-Yau d-folds, this flat connection is equivalent to special geometry for threefolds and to its analogs in other dimensions. We show that the non-holomorphic content of the tt * equations, restricted to the conformal directions, in the cases d = 1, 2, 3 is captured in terms of finitely many generators of special functions, which close under derivatives. The generators are understood as coordinates on a larger moduli space. This space parameterizes a freedom in choosing representatives of the chiral ring while preserving a constant topological metric. Geometrically, the freedom corresponds to a choice of forms on the target space respecting the Hodge filtration and having a constant pairing. Linear combinations of vector fields on that space are identified with the generators of a Lie algebra. This Lie algebra replaces the non-holomorphic derivatives of tt * and provides these with a finer and algebraic meaning. For sigma models into lattice polarized K3 manifolds, the differential ring of special functions on the moduli space is constructed, extending known structures for d = 1 and 3. The generators of the differential rings of special functions are given by quasi-modular forms for d = 1 and their generalizations in d = 2, 3. Some explicit examples are worked out including the case of the mirror of the quartic in {\\mathbbm{P}^3}, where due to further algebraic constraints, the differential ring coincides with quasi modular forms.

On parametric Gevrey asymptotics for some nonlinear initial value Cauchy problems

NASA Astrophysics Data System (ADS)

Lastra, A.; Malek, S.

2015-11-01

We study a nonlinear initial value Cauchy problem depending upon a complex perturbation parameter ɛ with vanishing initial data at complex time t = 0 and whose coefficients depend analytically on (ɛ, t) near the origin in C2 and are bounded holomorphic on some horizontal strip in C w.r.t. the space variable. This problem is assumed to be non-Kowalevskian in time t, therefore analytic solutions at t = 0 cannot be expected in general. Nevertheless, we are able to construct a family of actual holomorphic solutions defined on a common bounded open sector with vertex at 0 in time and on the given strip above in space, when the complex parameter ɛ belongs to a suitably chosen set of open bounded sectors whose union form a covering of some neighborhood Ω of 0 in C*. These solutions are achieved by means of Laplace and Fourier inverse transforms of some common ɛ-depending function on C × R, analytic near the origin and with exponential growth on some unbounded sectors with appropriate bisecting directions in the first variable and exponential decay in the second, when the perturbation parameter belongs to Ω. Moreover, these solutions satisfy the remarkable property that the difference between any two of them is exponentially flat for some integer order w.r.t. ɛ. With the help of the classical Ramis-Sibuya theorem, we obtain the existence of a formal series (generally divergent) in ɛ which is the common Gevrey asymptotic expansion of the built up actual solutions considered above.

Spectral transform and orthogonality relations for the Kadomtsev-Petviashvili I equation

NASA Astrophysics Data System (ADS)

Boiti, M.; Leon, J. J.-P.; Pempinelli, F.

1989-10-01

We define a new spectral transform r(k, l) of the potential u in the time dependent Schrödinger equation (associated to the KPI equation). Orthogonality relations for the sectionally holomorphic eigenfunctions of the Schrödinger equation are used to express the spectral transform f( k, l) previously introduced by Manakov and Fokas and Ablowitz in terms of r( k, l). The main advantage of the new spectral transform r( k, l) is that its definition does not require to introduce an additional nonanalytic eigenfunction N. Characterization equations for r( k, l) are also obtained.

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.

Unification of the complex Langevin method and the Lefschetzthimble method

NASA Astrophysics Data System (ADS)

Nishimura, Jun; Shimasaki, Shinji

2018-03-01

Recently there has been remarkable progress in solving the sign problem, which occurs in investigating statistical systems with a complex weight. The two promising methods, the complex Langevin method and the Lefschetz thimble method, share the idea of complexifying the dynamical variables, but their relationship has not been clear. Here we propose a unified formulation, in which the sign problem is taken care of by both the Langevin dynamics and the holomorphic gradient flow. We apply our formulation to a simple model in three different ways and show that one of them interpolates the two methods by changing the flow time.

Exploring non-holomorphic soft terms in the framework of gauge mediated supersymmetry breaking

NASA Astrophysics Data System (ADS)

Chattopadhyay, Utpal; Das, Debottam; Mukherjee, Samadrita

2018-01-01

It is known that in the absence of a gauge singlet field, a specific class of supersymmetry (SUSY) breaking non-holomorphic (NH) terms can be soft breaking in nature so that they may be considered along with the Minimal Supersymmetric Standard Model (MSSM) and beyond. There have been studies related to these terms in minimal supergravity based models. Consideration of an F-type SUSY breaking scenario in the hidden sector with two chiral superfields however showed Planck scale suppression of such terms. In an unbiased point of view for the sources of SUSY breaking, the NH terms in a phenomenological MSSM (pMSSM) type of analysis showed a possibility of a large SUSY contribution to muon g - 2, a reasonable amount of corrections to the Higgs boson mass and a drastic reduction of the electroweak fine-tuning for a higgsino dominated {\\tilde{χ}}_1^0 in some regions of parameter space. We first investigate here the effects of the NH terms in a low scale SUSY breaking scenario. In our analysis with minimal gauge mediated supersymmetry breaking (mGMSB) we probe how far the results can be compared with the previous pMSSM plus NH terms based study. We particularly analyze the Higgs, stop and the electroweakino sectors focusing on a higgsino dominated {\\tilde{χ}}_1^0 and {\\tilde{χ}}_1^{± } , a feature typically different from what appears in mGMSB. The effect of a limited degree of RG evolutions and vanishing of the trilinear coupling terms at the messenger scale can be overcome by choosing a non-minimal GMSB scenario, such as one with a matter-messenger interaction.

The Frölicher-type inequalities of foliations

NASA Astrophysics Data System (ADS)

Raźny, Paweł

2017-04-01

The purpose of this article is to adapt the Frölicher-type inequality, stated and proven for complex and symplectic manifolds in Angella and Tomassini (2015), to the case of transversely holomorphic and symplectic foliations. These inequalities provide a criterion for checking whether a foliation transversely satisfies the ∂ ∂ ¯ -lemma and the ddΛ-lemma (i.e. whether the basic forms of a given foliation satisfy them). These lemmas are linked to such properties as the formality of the basic de Rham complex of a foliation and the transverse hard Lefschetz property. In particular they provide an obstruction to the existence of a transverse Kähler structure for a given foliation. In the second section we will provide some information concerning the d‧d″-lemma for a given double complex (K • , • ,d‧ ,d″) and state the main results from Angella and Tomassini (2015). We will also recall some basic facts and definitions concerning foliations. In the third section we treat the case of transversely holomorphic foliations. We also give a brief review of some properties of the basic Bott-Chern and Aeppli cohomology theories. In Section 4 we prove the symplectic version of the Frölicher-type inequality. The final 3 sections of this paper are devoted to the applications of our main theorems. In them we verify the aforementioned lemmas for some simple examples, give the orbifold versions of the Frölicher-type inequalities and show that transversely Kähler foliations satisfy both the ∂ ∂ ¯ -lemma and the ddΛ-lemma (or in other words that our main theorems provide an obstruction to the existence of a transversely Kähler structure).

Self-dual geometry of generalized Hermitian surfaces

NASA Astrophysics Data System (ADS)

Arsen'eva, O. E.; Kirichenko, V. F.

1998-02-01

Several results on the geometry of conformally semiflat Hermitian surfaces of both classical and hyperbolic types (generalized Hermitian surfaces) are obtained. Some of these results are generalizations and clarifications of already known results in this direction due to Koda, Itoh, and other authors. They reveal some unexpected beautiful connections between such classical characteristics of conformally semiflat (generalized) Hermitian surfaces as the Einstein property, the constancy of the holomorphic sectional curvature, and so on. A complete classification of compact self-dual Hermitian RK-surfaces that are at the same time generalized Hopf manifolds is obtained. This provides a complete solution of the Chen problem in this class of Hermitian surfaces.

S-duality constraint on higher-derivative couplings

NASA Astrophysics Data System (ADS)

Garousi, Mohammad R.

2014-05-01

The Riemann curvature correction to the type II supergravity at eightderivative level in string frame is given as . For constant dilaton, it has been extended in the literature to the S-duality invariant form by extending the dilaton factor in the Einstein frame to the non-holomorphic Eisenstein series. For non-constant dilaton, however, there are various couplings in the Einstein frame which are not consistent with the S-duality. By constructing the tensors t 2 n from Born-Infeld action, we include the appropriate Ricci and scalar curvatures as well as the dilaton couplings to make the above action to be consistent with the S-duality.

The Clifford Deformation of the Hermite Semigroup

NASA Astrophysics Data System (ADS)

De Bie, Hendrik; Örsted, Bent; Somberg, Petr; Souček, Vladimir

2013-02-01

This paper is a continuation of the paper [De Bie H., Örsted B., Somberg P., Souček V., Trans. Amer. Math. Soc. 364 (2012), 3875-3902], investigating a natural radial deformation of the Fourier transform in the setting of Clifford analysis. At the same time, it gives extensions of many results obtained in [Ben Saïd S., Kobayashi T., Örsted B., Compos. Math. 148 (2012), 1265-1336]. We establish the analogues of Bochner's formula and the Heisenberg uncertainty relation in the framework of the (holomorphic) Hermite semigroup, and also give a detailed analytic treatment of the series expansion of the associated integral transform.

Invariant resolutions for several Fueter operators

NASA Astrophysics Data System (ADS)

Colombo, Fabrizio; Souček, Vladimir; Struppa, Daniele C.

2006-07-01

A proper generalization of complex function theory to higher dimension is Clifford analysis and an analogue of holomorphic functions of several complex variables were recently described as the space of solutions of several Dirac equations. The four-dimensional case has special features and is closely connected to functions of quaternionic variables. In this paper we present an approach to the Dolbeault sequence for several quaternionic variables based on symmetries and representation theory. In particular we prove that the resolution of the Cauchy-Fueter system obtained algebraically, via Gröbner bases techniques, is equivalent to the one obtained by R.J. Baston (J. Geom. Phys. 1992).

LCK rank of locally conformally Kähler manifolds with potential

NASA Astrophysics Data System (ADS)

Ornea, Liviu; Verbitsky, Misha

2016-09-01

An LCK manifold with potential is a quotient of a Kähler manifold X equipped with a positive Kähler potential f, such that the monodromy group acts on X by holomorphic homotheties and multiplies f by a character. The LCK rank is the rank of the image of this character, considered as a function from the monodromy group to real numbers. We prove that an LCK manifold with potential can have any rank between 1 and b1(M) . Moreover, LCK manifolds with proper potential (ones with rank 1) are dense. Two errata to our previous work are given in the last section.

On twisting type [N] ⊗ [N] Ricci flat complex spacetimes with two homothetic symmetries

NASA Astrophysics Data System (ADS)

Chudecki, Adam; Przanowski, Maciej

2018-04-01

In this article, H H spaces of type [N] ⊗ [N] with twisting congruence of null geodesics defined by the 4-fold undotted and dotted Penrose spinors are investigated. It is assumed that these spaces admit two homothetic symmetries. The general form of the homothetic vector fields is found. New coordinates are introduced, which enable us to reduce the H H system of partial differential equations to one ordinary differential equation (ODE) on one holomorphic function. In a special case, this is a second-order ODE and its general solution is explicitly given. In the generic case, one gets rather involved fifth-order ODE.

Impulsive spherical gravitational waves

NASA Astrophysics Data System (ADS)

Aliev, A. N.; Nutku, Y.

2001-03-01

Penrose's identification with warp provides the general framework for constructing the continuous form of impulsive gravitational wave metrics. We present the two-component spinor formalism for the derivation of the full family of impulsive spherical gravitational wave metrics which brings out the power in identification with warp and leads to the simplest derivation of exact solutions. These solutions of the Einstein vacuum field equations are obtained by cutting Minkowski space into two pieces along a null cone and re-identifying them with warp which is given by an arbitrary nonlinear holomorphic transformation. Using two-component spinor techniques we construct a new metric describing an impulsive spherical gravitational wave where the vertex of the null cone lies on a worldline with constant acceleration.

Self-dual geometry of generalized Hermitian surfaces

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

Arsen'eva, O E; Kirichenko, V F

Several results on the geometry of conformally semiflat Hermitian surfaces of both classical and hyperbolic types (generalized Hermitian surfaces) are obtained. Some of these results are generalizations and clarifications of already known results in this direction due to Koda, Itoh, and other authors. They reveal some unexpected beautiful connections between such classical characteristics of conformally semiflat (generalized) Hermitian surfaces as the Einstein property, the constancy of the holomorphic sectional curvature, and so on. A complete classification of compact self-dual Hermitian RK-surfaces that are at the same time generalized Hopf manifolds is obtained. This provides a complete solution of the Chenmore » problem in this class of Hermitian surfaces.« less

Deep learning beyond Lefschetz thimbles

NASA Astrophysics Data System (ADS)

Alexandru, Andrei; Bedaque, Paulo F.; Lamm, Henry; Lawrence, Scott

2017-11-01

The generalized thimble method to treat field theories with sign problems requires repeatedly solving the computationally expensive holomorphic flow equations. We present a machine learning technique to bypass this problem. The central idea is to obtain a few field configurations via the flow equations to train a feed-forward neural network. The trained network defines a new manifold of integration which reduces the sign problem and can be rapidly sampled. We present results for the 1 +1 dimensional Thirring model with Wilson fermions on sizable lattices. In addition to the gain in speed, the parametrization of the integration manifold we use avoids the "trapping" of Monte Carlo chains which plagues large-flow calculations, a considerable shortcoming of the previous attempts.

R 4 couplings in M- and type II theories on Calabi-Yau spaces

NASA Astrophysics Data System (ADS)

Antoniadis, I.; Feffara, S.; Minasian, R.; Narain, K. S.

1997-02-01

We discuss several implications of R 4 couplings in M-theory when compactified on Calabi-Yau (CY) manifolds. In particular, these couplings can be predicted by supersymmetry from the mixed gauge-gravitational Chem-Simons couplings in five dimensions and are related to the one-loop holomorphic anomaly in four-dimensional N = 2 theories. We find a new contribution to the Einstein term in five dimensions proportional to the Euler number of the internal CY threefold, which corresponds to a one-loop correction of the hypermultiplet geometry. This correction is reproduced by a direct computation in type 11 string theories. Finally, we discuss a universal non-perturbative correction to the type IIB hyper-metric.

Induced vacuum energy-momentum tensor in the background of a cosmic string

NASA Astrophysics Data System (ADS)

Sitenko, Yu A.; Vlasii, N. D.

2012-05-01

A massive scalar field is quantized in the background of a cosmic string which is generalized to a static flux-carrying codimension-2 brane in the locally flat multidimensional spacetime. We find that the finite energy-momentum tensor is induced in the vacuum. The dependence of the tensor components on the brane flux and tension, as well as on the coupling to the spacetime curvature scalar, is comprehensively analyzed. The tensor components are holomorphic functions of space dimension, decreasing exponentially with the distance from the brane. The case of the massless quantized scalar field is also considered, and the relevance of Bernoulli’s polynomials of even order for this case is discussed.

Pluripotential theory and convex bodies

NASA Astrophysics Data System (ADS)

Bayraktar, T.; Bloom, T.; Levenberg, N.

2018-03-01

A seminal paper by Berman and Boucksom exploited ideas from complex geometry to analyze the asymptotics of spaces of holomorphic sections of tensor powers of certain line bundles L over compact, complex manifolds as the power grows. This yielded results on weighted polynomial spaces in weighted pluripotential theory in {C}^d. Here, motivated by a recent paper by the first author on random sparse polynomials, we work in the setting of weighted pluripotential theory arising from polynomials associated to a convex body in ({R}^+)^d. These classes of polynomials need not occur as sections of tensor powers of a line bundle L over a compact, complex manifold. We follow the approach of Berman and Boucksom to obtain analogous results. Bibliography: 16 titles.

Covariant symplectic structure of the complex Monge-Ampère equation

NASA Astrophysics Data System (ADS)

Nutku, Y.

2000-04-01

The complex Monge-Ampère equation is invariant under arbitrary holomorphic changes of the independent variables with unit Jacobian. We present its variational formulation where the action remains invariant under this infinite group. The new Lagrangian enables us to obtain the first symplectic 2-form for the complex Monge-Ampère equation in the framework of the covariant Witten-Zuckerman approach to symplectic structure. We base our considerations on a reformulation of the Witten-Zuckerman theory in terms of holomorphic differential forms. The first closed and conserved Witten-Zuckerman symplectic 2-form for the complex Monge-Ampère equation is obtained in arbitrary dimension and for all cases elliptic, hyperbolic and homogeneous. The connection of the complex Monge-Ampère equation with Ricci-flat Kähler geometry suggests the use of the Hilbert action principle as an alternative variational formulation. However, we point out that Hilbert's Lagrangian is a divergence for Kähler metrics and serves as a topological invariant rather than yielding the Euclideanized Einstein field equations. Nevertheless, since the Witten-Zuckerman theory employs only the boundary terms in the first variation of the action, Hilbert's Lagrangian can be used to obtain the second Witten-Zuckerman symplectic 2-form. This symplectic 2-form vanishes on shell, thus defining a Lagrangian submanifold. In its derivation the connection of the second symplectic 2-form with the complex Monge-Ampère equation is indirect but we show that it satisfies all the properties required of a symplectic 2-form for the complex elliptic, or hyperbolic Monge-Ampère equation when the dimension of the complex manifold is 3 or higher. The complex Monge-Ampère equation admits covariant bisymplectic structure for complex dimension 3, or higher. However, in the physically interesting case of n=2 we have only one symplectic 2-form. The extension of these results to the case of complex Monge-Ampère-Liouville equation is also presented.

SURFACE FLUID REGISTRATION OF CONFORMAL REPRESENTATION: APPLICATION TO DETECT DISEASE BURDEN AND GENETIC INFLUENCE ON HIPPOCAMPUS

PubMed Central

Shi, Jie; Thompson, Paul M.; Gutman, Boris; Wang, Yalin

2013-01-01

In this paper, we develop a new automated surface registration system based on surface conformal parameterization by holomorphic 1-forms, inverse consistentsurface fluid registration, and multivariate tensor-based morphometry (mTBM). First, we conformally map a surface onto a planar rectangle space with holomorphic 1-forms. Second, we compute surface conformal representation by combining its local conformal factor and mean curvature and linearly scale the dynamic range of the conformal representation to form the feature image of the surface. Third, we align the feature image with a chosen template image via the fluid image registration algorithm, which has been extended into the curvilinear coordinates to adjust for the distortion introduced by surface parameterization. The inverse consistent image registration algorithm is also incorporated in the system to jointly estimate the forward and inverse transformations between the study and template images. This alignment induces a corresponding deformation on the surface. We tested the system on Alzheimer's Disease Neuroimaging Initiative (ADNI) baseline dataset to study AD symptoms on hippocampus. In our system, by modeling a hippocampus as a 3D parametric surface, we nonlinearly registered each surface with a selected template surface. Then we used mTBM to analyze the morphometrydifference between diagnostic groups. Experimental results show that the new system has better performance than two publically available subcortical surface registration tools: FIRST and SPHARM. We also analyzed the genetic influence of the Apolipoprotein E ε4 allele (ApoE4),which is considered as the most prevalent risk factor for AD.Our work successfully detected statistically significant difference between ApoE4 carriers and non-carriers in both patients of mild cognitive impairment (MCI) and healthy control subjects. The results show evidence that the ApoE genotype may be associated with accelerated brain atrophy so that our workprovides a new MRI analysis tool that may help presymptomatic AD research. PMID:23587689

Complex Langevin dynamics and zeroes of the fermion determinant

NASA Astrophysics Data System (ADS)

Aarts, Gert; Seiler, Erhard; Sexty, Dénes; Stamatescu, Ion-Olimpiu

2017-05-01

QCD at nonzero baryon chemical potential suffers from the sign problem, due to the complex quark determinant. Complex Langevin dynamics can provide a solution, provided certain conditions are met. One of these conditions, holomorphicity of the Langevin drift, is absent in QCD since zeroes of the determinant result in a meromorphic drift. We first derive how poles in the drift affect the formal justification of the approach and then explore the various possibilities in simple models. The lessons from these are subsequently applied to both heavy dense QCD and full QCD, and we find that the results obtained show a consistent picture. We conclude that with careful monitoring, the method can be justified a posteriori, even in the presence of meromorphicity.

Twistor Geometry of Null Foliations in Complex Euclidean Space

NASA Astrophysics Data System (ADS)

Taghavi-Chabert, Arman

2017-01-01

We give a detailed account of the geometric correspondence between a smooth complex projective quadric hypersurface Q^n of dimension n ≥ 3, and its twistor space PT, defined to be the space of all linear subspaces of maximal dimension of Q^n. Viewing complex Euclidean space CE^n as a dense open subset of Q^n, we show how local foliations tangent to certain integrable holomorphic totally null distributions of maximal rank on CE^n can be constructed in terms of complex submanifolds of PT. The construction is illustrated by means of two examples, one involving conformal Killing spinors, the other, conformal Killing-Yano 2-forms. We focus on the odd-dimensional case, and we treat the even-dimensional case only tangentially for comparison.

A tableau approach of the KSS nest

NASA Astrophysics Data System (ADS)

Peng, Wenjuan; Qiu, Weiyuan; Roesch, Pascale; Tan, Lei; Yin, Yongcheng

The KSS nest is a sophisticated choice of puzzle pieces given in [Ann. of Math. 165 (2007), 749-841]. This nest, once combined with the KL-Lemma, has proven to be a powerful machinery, leading to several important advancements in the field of holomorphic dynamics. We give here a presentation of the KSS nest in terms of tableau. This is an effective language invented by Branner and Hubbard to deal with the complexity of the dynamics of puzzle pieces. We show, in a typical situation, how to make the combination between the KSS nest and the KL-Lemma. One consequence of this is the recently proved Branner-Hubbard conjecture. Our estimates here can be used to give an alternative proof of the rigidity property.

The moduli space of vacua of $$ \\mathcal{N}=2 $$ class $$ \\mathcal{S} $$ theories

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

Xie, Dan; Yonekura, Kazuya

We develop a systematic method to describe the moduli space of vacua of four dimensional N=2 class S theories including Coulomb branch, Higgs branch and mixed branches. In particular, we determine the Higgs and mixed branch roots, and the dimensions of the Coulomb and Higgs components of mixed branches. They are derived by using generalized Hitchin’s equations obtained from twisted compactification of 5d maximal Super-Yang-Mills, with local degrees of freedom at punctures given by (nilpotent) orbits. The crucial thing is the holomorphic factorization of the Seiberg-Witten curve and reduction of singularity at punctures. We illustrate our method by many examplesmore » including N=2 SQCD, T N theory and Argyres-Douglas theories.« less

Exponential Thurston maps and limits of quadratic differentials

NASA Astrophysics Data System (ADS)

Hubbard, John; Schleicher, Dierk; Shishikura, Mitsuhiro

2009-01-01

We give a topological characterization of postsingularly finite topological exponential maps, i.e., universal covers g\\colon{C}to{C}setminus\\{0\\} such that 0 has a finite orbit. Such a map either is Thurston equivalent to a unique holomorphic exponential map λ e^z or it has a topological obstruction called a degenerate Levy cycle. This is the first analog of Thurston's topological characterization theorem of rational maps, as published by Douady and Hubbard, for the case of infinite degree. One main tool is a theorem about the distribution of mass of an integrable quadratic differential with a given number of poles, providing an almost compact space of models for the entire mass of quadratic differentials. This theorem is given for arbitrary Riemann surfaces of finite type in a uniform way.

Conformal higher spin theory and twistor space actions

NASA Astrophysics Data System (ADS)

Hähnel, Philipp; McLoughlin, Tristan

2017-12-01

We consider the twistor description of conformal higher spin theories and give twistor space actions for the self-dual sector of theories with spin greater than two that produce the correct flat space-time spectrum. We identify a ghost-free subsector, analogous to the embedding of Einstein gravity with cosmological constant in Weyl gravity, which generates the unique spin-s three-point anti-MHV amplitude consistent with Poincaré invariance and helicity constraints. By including interactions between the infinite tower of higher-spin fields we give a geometric interpretation to the twistor equations of motion as the integrability condition for a holomorphic structure on an infinite jet bundle. Finally, we conjecture anti-self-dual interaction terms which give an implicit definition of a twistor action for the full conformal higher spin theory.

Discrete transparent boundary conditions for the mixed KDV-BBM equation

NASA Astrophysics Data System (ADS)

Besse, Christophe; Noble, Pascal; Sanchez, David

2017-09-01

In this paper, we consider artificial boundary conditions for the linearized mixed Korteweg-de Vries (KDV) and Benjamin-Bona-Mahoney (BBM) equation which models water waves in the small amplitude, large wavelength regime. Continuous (respectively discrete) artificial boundary conditions involve non local operators in time which in turn requires to compute time convolutions and invert the Laplace transform of an analytic function (respectively the Z-transform of an holomorphic function). In this paper, we propose a new, stable and fairly general strategy to carry out this crucial step in the design of transparent boundary conditions. For large time simulations, we also introduce a methodology based on the asymptotic expansion of coefficients involved in exact direct transparent boundary conditions. We illustrate the accuracy of our methods for Gaussian and wave packets initial data.

A classical Perron method for existence of smooth solutions to boundary value and obstacle problems for degenerate-elliptic operators via holomorphic maps

NASA Astrophysics Data System (ADS)

Feehan, Paul M. N.

2017-09-01

We prove existence of solutions to boundary value problems and obstacle problems for degenerate-elliptic, linear, second-order partial differential operators with partial Dirichlet boundary conditions using a new version of the Perron method. The elliptic operators considered have a degeneracy along a portion of the domain boundary which is similar to the degeneracy of a model linear operator identified by Daskalopoulos and Hamilton [9] in their study of the porous medium equation or the degeneracy of the Heston operator [21] in mathematical finance. Existence of a solution to the partial Dirichlet problem on a half-ball, where the operator becomes degenerate on the flat boundary and a Dirichlet condition is only imposed on the spherical boundary, provides the key additional ingredient required for our Perron method. Surprisingly, proving existence of a solution to this partial Dirichlet problem with ;mixed; boundary conditions on a half-ball is more challenging than one might expect. Due to the difficulty in developing a global Schauder estimate and due to compatibility conditions arising where the ;degenerate; and ;non-degenerate boundaries; touch, one cannot directly apply the continuity or approximate solution methods. However, in dimension two, there is a holomorphic map from the half-disk onto the infinite strip in the complex plane and one can extend this definition to higher dimensions to give a diffeomorphism from the half-ball onto the infinite ;slab;. The solution to the partial Dirichlet problem on the half-ball can thus be converted to a partial Dirichlet problem on the slab, albeit for an operator which now has exponentially growing coefficients. The required Schauder regularity theory and existence of a solution to the partial Dirichlet problem on the slab can nevertheless be obtained using previous work of the author and C. Pop [16]. Our Perron method relies on weak and strong maximum principles for degenerate-elliptic operators, concepts of continuous subsolutions and supersolutions for boundary value and obstacle problems for degenerate-elliptic operators, and maximum and comparison principle estimates previously developed by the author [13].

On the effective field theory of heterotic vacua.

PubMed

McOrist, Jock

2018-01-01

The effective field theory of heterotic vacua that realise [Formula: see text] preserving [Formula: see text] supersymmetry is studied. The vacua in question admit large radius limits taking the form [Formula: see text], with [Formula: see text] a smooth threefold with vanishing first Chern class and a stable holomorphic gauge bundle [Formula: see text]. In a previous paper we calculated the kinetic terms for moduli, deducing the moduli metric and Kähler potential. In this paper, we compute the remaining couplings in the effective field theory, correct to first order in [Formula: see text]. In particular, we compute the contribution of the matter sector to the Kähler potential and derive the Yukawa couplings and other quadratic fermionic couplings. From this we write down a Kähler potential [Formula: see text] and superpotential [Formula: see text].

Higher symmetries of the Schrödinger operator in Newton-Cartan geometry

NASA Astrophysics Data System (ADS)

Gundry, James

2017-03-01

We establish several relationships between the non-relativistic conformal symmetries of Newton-Cartan geometry and the Schrödinger equation. In particular we discuss the algebra sch(d) of vector fields conformally-preserving a flat Newton-Cartan spacetime, and we prove that its curved generalisation generates the symmetry group of the covariant Schrödinger equation coupled to a Newtonian potential and generalised Coriolis force. We provide intrinsic Newton-Cartan definitions of Killing tensors and conformal Schrödinger-Killing tensors, and we discuss their respective links to conserved quantities and to the higher symmetries of the Schrödinger equation. Finally we consider the role of conformal symmetries in Newtonian twistor theory, where the infinite-dimensional algebra of holomorphic vector fields on twistor space corresponds to the symmetry algebra cnc(3) on the Newton-Cartan spacetime.

Universal RCFT correlators from the holomorphic bootstrap

NASA Astrophysics Data System (ADS)

Mukhi, Sunil; Muralidhara, Girish

2018-02-01

We elaborate and extend the method of Wronskian differential equations for conformal blocks to compute four-point correlation functions on the plane for classes of primary fields in rational (and possibly more general) conformal field theories. This approach leads to universal differential equations for families of CFT's and provides a very simple re-derivation of the BPZ results for the degenerate fields ϕ 1,2 and ϕ 2,1 in the c < 1 minimal models. We apply this technique to compute correlators for the WZW models corresponding to the Deligne-Cvitanović exceptional series of Lie algebras. The application turns out to be subtle in certain cases where there are multiple decoupled primaries. The power of this approach is demonstrated by applying it to compute four-point functions for the Baby Monster CFT, which does not belong to any minimal series.

An exact elliptic superpotential for N=1 ∗ deformations of finite N=2 gauge theories

NASA Astrophysics Data System (ADS)

Dorey, Nick; Hollowood, Timothy J.; Kumar, S. Prem

2002-03-01

We study relevant deformations of the N=2 superconformal theory on the world-volume of N D3-branes at an Ak-1 singularity. In particular, we determine the vacuum structure of the mass-deformed theory with N=1 supersymmetry and show how the different vacua are permuted by an extended duality symmetry. We then obtain exact, modular covariant formulae (for all k, N and arbitrary gauge couplings) for the holomorphic observables in the massive vacua in two different ways: by lifting to M-theory, and by compactification to three dimensions and subsequent use of mirror symmetry. In the latter case, we find an exact superpotential for the model which coincides with a certain combination of the quadratic Hamiltonians of the spin generalization of the elliptic Calogero-Moser integrable system.

The Coulomb Branch of 3d N= 4 Theories

NASA Astrophysics Data System (ADS)

Bullimore, Mathew; Dimofte, Tudor; Gaiotto, Davide

2017-09-01

We propose a construction for the quantum-corrected Coulomb branch of a general 3d gauge theory with N=4 supersymmetry, in terms of local coordinates associated with an abelianized theory. In a fixed complex structure, the holomorphic functions on the Coulomb branch are given by expectation values of chiral monopole operators. We construct the chiral ring of such operators, using equivariant integration over BPS moduli spaces. We also quantize the chiral ring, which corresponds to placing the 3d theory in a 2d Omega background. Then, by unifying all complex structures in a twistor space, we encode the full hyperkähler metric on the Coulomb branch. We verify our proposals in a multitude of examples, including SQCD and linear quiver gauge theories, whose Coulomb branches have alternative descriptions as solutions to Bogomolnyi and/or Nahm equations.

A simple model of low-scale direct gauge mediation

NASA Astrophysics Data System (ADS)

Csáki, Csaba; Shirman, Yuri; Terning, John

2007-05-01

We construct a calculable model of low-energy direct gauge mediation making use of the metastable supersymmetry breaking vacua recently discovered by Intriligator, Seiberg and Shih. The standard model gauge group is a subgroup of the global symmetries of the SUSY breaking sector and messengers play an essential role in dynamical SUSY breaking: they are composites of a confining gauge theory, and the holomorphic scalar messenger mass appears as a consequence of the confining dynamics. The SUSY breaking scale is around 100 TeV nevertheless the model is calculable. The minimal non-renormalizable coupling of the Higgs to the DSB sector leads in a simple way to a μ-term, while the B-term arises at two-loop order resulting in a moderately large tan β. A novel feature of this class of models is that some particles from the dynamical SUSY breaking sector may be accessible at the LHC.

Geometric and Topological Methods for Quantum Field Theory

NASA Astrophysics Data System (ADS)

Cardona, Alexander; Contreras, Iván.; Reyes-Lega, Andrés. F.

2013-05-01

Introduction; 1. A brief introduction to Dirac manifolds Henrique Bursztyn; 2. Differential geometry of holomorphic vector bundles on a curve Florent Schaffhauser; 3. Paths towards an extension of Chern-Weil calculus to a class of infinite dimensional vector bundles Sylvie Paycha; 4. Introduction to Feynman integrals Stefan Weinzierl; 5. Iterated integrals in quantum field theory Francis Brown; 6. Geometric issues in quantum field theory and string theory Luis J. Boya; 7. Geometric aspects of the standard model and the mysteries of matter Florian Scheck; 8. Absence of singular continuous spectrum for some geometric Laplacians Leonardo A. Cano García; 9. Models for formal groupoids Iván Contreras; 10. Elliptic PDEs and smoothness of weakly Einstein metrics of Hölder regularity Andrés Vargas; 11. Regularized traces and the index formula for manifolds with boundary Alexander Cardona and César Del Corral; Index.

Dirac gauginos, R symmetry and the 125 GeV Higgs

DOE PAGES

Bertuzzo, Enrico; Frugiuele, Claudia; Gregoire, Thomas; ...

2015-04-20

We study a supersymmetric scenario with a quasi exact R-symmetry in light of the discovery of a Higgs resonance with a mass of 125 GeV. In such a framework, the additional adjoint superfields, needed to give Dirac masses to the gauginos, contribute both to the Higgs mass and to electroweak precision observables. We then analyze the interplay between the two aspects, finding regions in parameter space in which the contributions to the precision observables are under control and a 125 GeV Higgs boson can be accommodated. Furthermore, we estimate the fine-tuning of the model finding regions of the parameter spacemore » still unexplored by the LHC with a fine-tuning considerably improved with respect to the minimal supersymmetric scenario. In particular, sizable non-holomorphic (non-supersoft) adjoints masses are required to reduce the fine-tuning.« 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.

Donaldson-Witten theory and indefinite theta functions

NASA Astrophysics Data System (ADS)

Korpas, Georgios; Manschot, Jan

2017-11-01

We consider partition functions with insertions of surface operators of topologically twisted N=2 , SU(2) supersymmetric Yang-Mills theory, or Donaldson-Witten theory for short, on a four-manifold. If the metric of the compact four-manifold has positive scalar curvature, Moore and Witten have shown that the partition function is completely determined by the integral over the Coulomb branch parameter a, while more generally the Coulomb branch integral captures the wall-crossing behavior of both Donaldson polynomials and Seiberg-Witten invariants. We show that after addition of a \\overlineQ -exact surface operator to the Moore-Witten integrand, the integrand can be written as a total derivative to the anti-holomorphic coordinate ā using Zwegers' indefinite theta functions. In this way, we reproduce Göttsche's expressions for Donaldson invariants of rational surfaces in terms of indefinite theta functions for any choice of metric.

Poisson equation for the three-loop ladder diagram in string theory at genus one

NASA Astrophysics Data System (ADS)

Basu, Anirban

2016-11-01

The three-loop ladder diagram is a graph with six links and four cubic vertices that contributes to the D12ℛ4 amplitude at genus one in type II string theory. The vertices represent the insertion points of vertex operators on the toroidal worldsheet and the links represent scalar Green functions connecting them. By using the properties of the Green function and manipulating the various expressions, we obtain a modular invariant Poisson equation satisfied by this diagram, with source terms involving one-, two- and three-loop diagrams. Unlike the source terms in the Poisson equations for diagrams at lower orders in the momentum expansion or the Mercedes diagram, a particular source term involves a five-point function containing a holomorphic and a antiholomorphic worldsheet derivative acting on different Green functions. We also obtain simple equalities between topologically distinct diagrams, and consider some elementary examples.

On the effective field theory of heterotic vacua

NASA Astrophysics Data System (ADS)

McOrist, Jock

2018-04-01

The effective field theory of heterotic vacua that realise [InlineEquation not available: see fulltext.] preserving N{=}1 supersymmetry is studied. The vacua in question admit large radius limits taking the form [InlineEquation not available: see fulltext.], with [InlineEquation not available: see fulltext.] a smooth threefold with vanishing first Chern class and a stable holomorphic gauge bundle [InlineEquation not available: see fulltext.]. In a previous paper we calculated the kinetic terms for moduli, deducing the moduli metric and Kähler potential. In this paper, we compute the remaining couplings in the effective field theory, correct to first order in {α ^{\\backprime } }. In particular, we compute the contribution of the matter sector to the Kähler potential and derive the Yukawa couplings and other quadratic fermionic couplings. From this we write down a Kähler potential [InlineEquation not available: see fulltext.] and superpotential [InlineEquation not available: see fulltext.].

The Coulomb Branch of 3d $${\\mathcal{N}= 4}$$ N = 4 Theories

DOE PAGES

Bullimore, Mathew; Dimofte, Tudor; Gaiotto, Davide

2017-06-03

We propose a construction for the quantum-corrected Coulomb branch of a general 3d gauge theory with N=4 supersymmetry, in terms of local coordinates associated with an abelianized theory. In a fixed complex structure, the holomorphic functions on the Coulomb branch are given by expectation values of chiral monopole operators. We construct the chiral ring of such operators, using equivariant integration over BPS moduli spaces. We also quantize the chiral ring, which corresponds to placing the 3d theory in a 2d Omega background. Then, by unifying all complex structures in a twistor space, we encode the full hyperkähler metric on themore » Coulomb branch. We verify our proposals in a multitude of examples, including SQCD and linear quiver gauge theories, whose Coulomb branches have alternative descriptions as solutions to Bogomolnyi and/or Nahm equations.« less

Molecular identification of Aspergillus and Eurotium species isolated from rice and their toxin-producing ability.

PubMed

Yazdani, D; Zainal Abidin, M A; Tan, Y H; Kamaruzaman, S

2011-01-01

Thirty milled rice samples were collected from retailers in 4 provinces of Malaysia. These samples were evaluated for Aspergillus spp. infection by direct plating on malt extract salt agar (MESA). All Aspergillus holomorphs were isolated and identified using nucleotide sequences of ITS 1 and ITS 2 of rDNA. Five anamorphs (Aspergillus flavus, A. oryzae, A. tamarii, A. fumigatus and A. niger) and 5 teleomorphs (Eurotium rubrum, E. amstelodami, E. chevalieri, E. cristatum and E. tonophilum) were identified. The PCR-sequencing based technique for sequences of ITS 1 and ITS 2 is a fast technique for identification of Aspergillus and Eurotium species, although it doesn't work flawlessly for differentiation of Eurotium species. All Aspergillus and Eurotium isolates were screened for their ability to produce aflatoxin and ochratoxin A (OTA) by HPLC and TLC techniques. Only A. flavus isolate UPM 89 was able to produce aflatoxins B1 and B2.

"Analytic continuation" of = 2 minimal model

NASA Astrophysics Data System (ADS)

Sugawara, Yuji

2014-04-01

In this paper we discuss what theory should be identified as the "analytic continuation" with N rArr -N of the {mathcal N}=2 minimal model with the central charge hat {c} = 1 - frac {2}{N}. We clarify how the elliptic genus of the expected model is written in terms of holomorphic linear combinations of the "modular completions" introduced in [T. Eguchi and Y. Sugawara, JHEP 1103, 107 (2011)] in the SL(2)_{N+2}/U(1) supercoset theory. We further discuss how this model could be interpreted as a kind of model of the SL(2)_{N+2}/U(1) supercoset in the (widetilde {{R}},widetilde {R}) sector, in which only the discrete spectrum appears in the torus partition function and the potential IR divergence due to the non-compactness of the target space is removed. We also briefly discuss possible definitions of the sectors with other spin structures.

Topological semimetals with Riemann surface states

NASA Astrophysics Data System (ADS)

Fang, Chen; Lu, Ling; Liu, Junwei; Fu, Liang

Topological semimetals have robust bulk band crossings between the conduction and the valence bands. Among them, Weyl semimetals are so far the only class having topologically protected signatures on the surface known as the ``Fermi arcs''. Here we theoretically find new classes of topological semimetals protected by nonsymmorphic glide reflection symmetries. On a symmetric surface, there are multiple Fermi arcs protected by nontrivial Z2 spectral flows between two high-symmetry lines (or two segments of one line) in the surface Brillouin zone. We observe that so far topological semimetals with protected Fermi arcs have surface dispersions that can be mapped to noncompact Riemann surfaces representing simple holomorphic functions. We propose perovskite superlattice [(SrIrO3)2m, (CaIrO3)2n] as a nonsymmorphic Dirac semimetal. C.F. and L.F. were supported by the S3TEC Solid State Solar Thermal Energy Conversion Center, an Energy Frontier Research Center funded by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under Award No. DE-SC0001299/DE.

On the modular structure of the genus-one Type II superstring low energy expansion

NASA Astrophysics Data System (ADS)

D'Hoker, Eric; Green, Michael B.; Vanhove, Pierre

2015-08-01

The analytic contribution to the low energy expansion of Type II string amplitudes at genus-one is a power series in space-time derivatives with coefficients that are determined by integrals of modular functions over the complex structure modulus of the world-sheet torus. These modular functions are associated with world-sheet vacuum Feynman diagrams and given by multiple sums over the discrete momenta on the torus. In this paper we exhibit exact differential and algebraic relations for a certain infinite class of such modular functions by showing that they satisfy Laplace eigenvalue equations with inhomogeneous terms that are polynomial in non-holomorphic Eisenstein series. Furthermore, we argue that the set of modular functions that contribute to the coefficients of interactions up to order are linear sums of functions in this class and quadratic polynomials in Eisenstein series and odd Riemann zeta values. Integration over the complex structure results in coefficients of the low energy expansion that are rational numbers multiplying monomials in odd Riemann zeta values.

Squashed Toric Sigma Models and Mock Modular Forms

NASA Astrophysics Data System (ADS)

Gupta, Rajesh Kumar; Murthy, Sameer

2018-05-01

We study a class of two-dimensional N}=(2,2)} sigma models called squashed toric sigma models, using their Gauged Linear Sigma Models (GLSM) description. These models are obtained by gauging the global {U(1)} symmetries of toric GLSMs and introducing a set of corresponding compensator superfields. The geometry of the resulting vacuum manifold is a deformation of the corresponding toric manifold in which the torus fibration maintains a constant size in the interior of the manifold, thus producing a neck-like region. We compute the elliptic genus of these models, using localization, in the case when the unsquashed vacuum manifolds obey the Calabi-Yau condition. The elliptic genera have a non-holomorphic dependence on the modular parameter {τ} coming from the continuum produced by the neck. In the simplest case corresponding to squashed {C / Z_{2 the elliptic genus is a mixed mock Jacobi form which coincides with the elliptic genus of the {N=(2,2)} {SL(2,R) / U(1)} cigar coset.

Conformal anomaly of generalized form factors and finite loop integrals

NASA Astrophysics Data System (ADS)

Chicherin, Dmitry; Sokatchev, Emery

2018-04-01

We reveal a new mechanism of conformal symmetry breaking at Born level. It occurs in generalized form factors with several local operators and an on-shell state of massless particles. The effect is due to hidden singularities on collinear configurations of the momenta. This conformal anomaly is different from the holomorphic anomaly of amplitudes. We present a number of examples in four and six dimensions. We find an application of the new conformal anomaly to finite loop momentum integrals with one or more massless legs. The collinear region around a massless leg creates a contact anomaly, made visible by the loop integration. The anomalous conformal Ward identity for an ℓ-loop integral is a 2nd-order differential equation whose right-hand side is an (ℓ - 1)-loop integral. It could serve as a new useful tool to find/test analytic expressions for conformal integrals. We illustrate this point with several examples of known integrals. We propose a new differential equation for the four-dimensional scalar double box.

Projective limits of state spaces II. Quantum formalism

NASA Astrophysics Data System (ADS)

Lanéry, Suzanne; Thiemann, Thomas

2017-06-01

In this series of papers, we investigate the projective framework initiated by Kijowski (1977) and Okołów (2009, 2014, 2013), which describes the states of a quantum theory as projective families of density matrices. A short reading guide to the series can be found in Lanéry (2016). After discussing the formalism at the classical level in a first paper (Lanéry, 2017), the present second paper is devoted to the quantum theory. In particular, we inspect in detail how such quantum projective state spaces relate to inductive limit Hilbert spaces and to infinite tensor product constructions (Lanéry, 2016, subsection 3.1) [1]. Regarding the quantization of classical projective structures into quantum ones, we extend the results by Okołów (2013), that were set up in the context of linear configuration spaces, to configuration spaces given by simply-connected Lie groups, and to holomorphic quantization of complex phase spaces (Lanéry, 2016, subsection 2.2) [1].

Chern-Simons-Rozansky-Witten topological field theory

NASA Astrophysics Data System (ADS)

Kapustin, Anton; Saulina, Natalia

2009-12-01

We construct and study a new topological field theory in three dimensions. It is a hybrid between Chern-Simons and Rozansky-Witten theory and can be regarded as a topologically-twisted version of the N=4d=3 supersymmetric gauge theory recently discovered by Gaiotto and Witten. The model depends on a gauge group G and a hyper-Kähler manifold X with a tri-holomorphic action of G. In the case when X is an affine space, we show that the model is equivalent to Chern-Simons theory whose gauge group is a supergroup. This explains the role of Lie superalgebras in the construction of Gaiotto and Witten. For general X, our model appears to be new. We describe some of its properties, focusing on the case when G is simple and X is the cotangent bundle of the flag variety of G. In particular, we show that Wilson loops are labeled by objects of a certain category which is a quantum deformation of the equivariant derived category of coherent sheaves on X.

Constructions and classifications of projective Poisson varieties.

PubMed

Pym, Brent

2018-01-01

This paper is intended both as an introduction to the algebraic geometry of holomorphic Poisson brackets, and as a survey of results on the classification of projective Poisson manifolds that have been obtained in the past 20 years. It is based on the lecture series delivered by the author at the Poisson 2016 Summer School in Geneva. The paper begins with a detailed treatment of Poisson surfaces, including adjunction, ruled surfaces and blowups, and leading to a statement of the full birational classification. We then describe several constructions of Poisson threefolds, outlining the classification in the regular case, and the case of rank-one Fano threefolds (such as projective space). Following a brief introduction to the notion of Poisson subspaces, we discuss Bondal's conjecture on the dimensions of degeneracy loci on Poisson Fano manifolds. We close with a discussion of log symplectic manifolds with simple normal crossings degeneracy divisor, including a new proof of the classification in the case of rank-one Fano manifolds.

Constructions and classifications of projective Poisson varieties

NASA Astrophysics Data System (ADS)

Pym, Brent

2018-03-01

This paper is intended both as an introduction to the algebraic geometry of holomorphic Poisson brackets, and as a survey of results on the classification of projective Poisson manifolds that have been obtained in the past 20 years. It is based on the lecture series delivered by the author at the Poisson 2016 Summer School in Geneva. The paper begins with a detailed treatment of Poisson surfaces, including adjunction, ruled surfaces and blowups, and leading to a statement of the full birational classification. We then describe several constructions of Poisson threefolds, outlining the classification in the regular case, and the case of rank-one Fano threefolds (such as projective space). Following a brief introduction to the notion of Poisson subspaces, we discuss Bondal's conjecture on the dimensions of degeneracy loci on Poisson Fano manifolds. We close with a discussion of log symplectic manifolds with simple normal crossings degeneracy divisor, including a new proof of the classification in the case of rank-one Fano manifolds.

Eisenstein Series and String Thresholds

NASA Astrophysics Data System (ADS)

Obers, N. A.; Pioline, B.

We investigate the relevance of Eisenstein series for representing certain G()-invariant string theory amplitudes which receive corrections from BPS states only. G() may stand for any of the mapping class, T-duality and U-duality groups Sl(d,(), SO(d,d,() or Ed+1(d+1)(() respectively. Using G()-invariant mass formulae, we construct invariant modular functions on the symmetric space K\\G() of non-compact type, with K the maximal compact subgroup of G(), that generalize the standard non-holomorphic Eisenstein series arising in harmonic analysis on the fundamental domain of the Poincaré upper half-plane. Comparing the asymptotics and eigenvalues of the Eisenstein series under second order differential operators with quantities arising in one- and g-loop string amplitudes, we obtain a manifestly T-duality invariant representation of the latter, conjecture their non-perturbative U-duality invariant extension, and analyze the resulting non-perturbative effects. This includes the R4 and R4H4g-4 couplings in toroidal compactifications of M-theory to any dimension D>= 4 and D>= 6 respectively.

Forbidden territories in the string landscape

NASA Astrophysics Data System (ADS)

Kumar, Alok; Mukhopadhyay, Subir; Ray, Koushik

2007-12-01

Problems of stabilizing moduli of the type-IIB string theory on toroidal orientifolds T6/Z2, in presence of worldvolume fluxes on various D-branes, are considered. For Z2 actions, introducing either O9 or O3 planes, we rule out the possibility of moduli stabilization in a wide class of models with Script N = 1 supersymmetry, characterized by the type of fluxes turned on along D-brane worldvolume. Our results, in particular, imply that Abelian worldvolume fluxes can not by themselves stabilize closed string moduli, in a consistent supersymmtric model, for above orientifold compactifications. We also discuss other Z2 orientifolds of T6 and show that certain other brane wrappings are also ruled out by similar consistency requirements. In specific setups we consider examples with D9-branes wrapping on a complex three-torus with its world-volume fluxes taken to be semi-homogeneous bundles and D7-branes wrapping holomorphic four-cycles of the complex three-torus carrying world-volume fluxes.

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.

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.

Quantum corrections to Bekenstein-Hawking black hole entropy and gravity partition functions

NASA Astrophysics Data System (ADS)

Bytsenko, A. A.; Tureanu, A.

2013-08-01

Algebraic aspects of the computation of partition functions for quantum gravity and black holes in AdS3 are discussed. We compute the sub-leading quantum corrections to the Bekenstein-Hawking entropy. It is shown that the quantum corrections to the classical result can be included systematically by making use of the comparison with conformal field theory partition functions, via the AdS3/CFT2 correspondence. This leads to a better understanding of the role of modular and spectral functions, from the point of view of the representation theory of infinite-dimensional Lie algebras. Besides, the sum of known quantum contributions to the partition function can be presented in a closed form, involving the Patterson-Selberg spectral function. These contributions can be reproduced in a holomorphically factorized theory whose partition functions are associated with the formal characters of the Virasoro modules. We propose a spectral function formulation for quantum corrections to the elliptic genus from supergravity states.

Teichmüller TQFT vs. Chern-Simons theory

NASA Astrophysics Data System (ADS)

Mikhaylov, Victor

2018-04-01

Teichmüller TQFT is a unitary 3d topological theory whose Hilbert spaces are spanned by Liouville conformal blocks. It is related but not identical to PSL(2, ℝ) Chern-Simons theory. To physicists, it is known in particular in the context of 3d-3d correspondence and also in the holographic description of Virasoro conformal blocks. We propose that this theory can be defined by an analytically-continued Chern-Simons path-integral with an unusual integration cycle. On hyperbolic three-manifolds, this cycle is singled out by the requirement of invertible vielbein. Mathematically, our proposal translates a known conjecture by Andersen and Kashaev into a conjecture about the Kapustin-Witten equations. We further explain that Teichmüller TQFT is dual to complex SL(2, ℂ) Chern-Simons theory at integer level k = 1, clarifying some puzzles previously encountered in the 3d-3d correspondence literature. We also present a new simple derivation of complex Chern-Simons theories from the 6d (2,0) theory on a lens space with a transversely-holomorphic foliation.

AdS/CFT in string theory and M-theory

NASA Astrophysics Data System (ADS)

Gulotta, Daniel R.

The AdS/CFT correspondence is a powerful tool that can help shed light on the relationship between geometry and field theory. The first part of this thesis will focus on the construction of theories dual to Type IIB string theory on AdS5 × Y5, where Y5 is a toric Sasaki-Einstein manifold. This thesis will introduce a consistency condition called ``proper ordering'' and demonstrate that it is equivalent to several other previously known consistency conditions. It will then give an efficient algorithm that produces a consistent field theory for any toric Sasaki-Einstein Y5. The second part of this thesis will examine the large-N limit of the Kapustin-Willett-Yaakov matrix model. This model computes the S3 partition function for a CFT dual to M-theory on AdS4 × Y7. One of the main results will be a formula that relates the distribution of eigenvalues in the matrix model to the distribution of holomorphic operators on the cone over Y7. A variety of examples are given to support this formula.

Husimi function and phase-space analysis of bilayer quantum Hall systems at ν = 2/λ

NASA Astrophysics Data System (ADS)

Calixto, M.; Peón-Nieto, C.

2018-05-01

We propose localization measures in phase space of the ground state of bilayer quantum Hall systems at fractional filling factors , to characterize the three quantum phases (shortly denoted by spin, canted and ppin) for arbitrary -isospin λ. We use a coherent state (Bargmann) representation of quantum states, as holomorphic functions in the 8-dimensional Grassmannian phase-space (a higher-dimensional generalization of the Haldane’s 2-dimensional sphere ). We quantify the localization (inverse volume) of the ground state wave function in phase-space throughout the phase diagram (i.e. as a function of Zeeman, tunneling, layer distance, etc, control parameters) with the Husimi function second moment, a kind of inverse participation ratio that behaves as an order parameter. Then we visualize the different ground state structure in phase space of the three quantum phases, the canted phase displaying a much higher delocalization (a Schrödinger cat structure) than the spin and ppin phases, where the ground state is highly coherent. We find a good agreement between analytic (variational) and numeric diagonalization results.

Observables and microscopic entropy of higher spin black holes

NASA Astrophysics Data System (ADS)

Compère, Geoffrey; Jottar, Juan I.; Song, Wei

2013-11-01

In the context of recently proposed holographic dualities between higher spin theories in AdS3 and (1 + 1)-dimensional CFTs with symmetry algebras, we revisit the definition of higher spin black hole thermodynamics and the dictionary between bulk fields and dual CFT operators. We build a canonical formalism based on three ingredients: a gauge-invariant definition of conserved charges and chemical potentials in the presence of higher spin black holes, a canonical definition of entropy in the bulk, and a bulk-to-boundary dictionary aligned with the asymptotic symmetry algebra. We show that our canonical formalism shares the same formal structure as the so-called holomorphic formalism, but differs in the definition of charges and chemical potentials and in the bulk-to-boundary dictionary. Most importantly, we show that it admits a consistent CFT interpretation. We discuss the spin-2 and spin-3 cases in detail and generalize our construction to theories based on the hs[ λ] algebra, and on the sl( N,[InlineMediaObject not available: see fulltext.]) algebra for any choice of sl(2 ,[InlineMediaObject not available: see fulltext.]) embedding.

Topological Nodal Cooper Pairing in Doped Weyl Metals

NASA Astrophysics Data System (ADS)

Li, Yi; Haldane, F. D. M.

2018-02-01

We generalize the concept of Berry connection of the single-electron band structure to that of a two-particle Cooper pairing state between two Fermi surfaces with opposite Chern numbers. Because of underlying Fermi surface topology, the pairing Berry phase acquires nontrivial monopole structure. Consequently, pairing gap functions have topologically protected nodal structure as vortices in the momentum space with the total vorticity solely determined by the pair monopole charge qp. The nodes of gap function behave as the Weyl-Majorana points of the Bogoliubov-de Gennes pairing Hamiltonian. Their relation with the connection patterns of the surface modes from the Weyl band structure and the Majorana surface modes inside the pairing gap is also discussed. Under the approximation of spherical Fermi surfaces, the pairing symmetry are represented by monopole harmonic functions. The lowest possible pairing channel carries angular momentum number j =|qp|, and the corresponding gap functions are holomorphic or antiholomorphic functions on Fermi surfaces. After projected on the Fermi surfaces with nontrivial topology, all the partial-wave channels of pairing interactions acquire the monopole charge qp independent of concrete pairing mechanism.

Beyond the spectral theorem: Spectrally decomposing arbitrary functions of nondiagonalizable operators

NASA Astrophysics Data System (ADS)

Riechers, Paul M.; Crutchfield, James P.

2018-06-01

Nonlinearities in finite dimensions can be linearized by projecting them into infinite dimensions. Unfortunately, the familiar linear operator techniques that one would then hope to use often fail since the operators cannot be diagonalized. The curse of nondiagonalizability also plays an important role even in finite-dimensional linear operators, leading to analytical impediments that occur across many scientific domains. We show how to circumvent it via two tracks. First, using the well-known holomorphic functional calculus, we develop new practical results about spectral projection operators and the relationship between left and right generalized eigenvectors. Second, we generalize the holomorphic calculus to a meromorphic functional calculus that can decompose arbitrary functions of nondiagonalizable linear operators in terms of their eigenvalues and projection operators. This simultaneously simplifies and generalizes functional calculus so that it is readily applicable to analyzing complex physical systems. Together, these results extend the spectral theorem of normal operators to a much wider class, including circumstances in which poles and zeros of the function coincide with the operator spectrum. By allowing the direct manipulation of individual eigenspaces of nonnormal and nondiagonalizable operators, the new theory avoids spurious divergences. As such, it yields novel insights and closed-form expressions across several areas of physics in which nondiagonalizable dynamics arise, including memoryful stochastic processes, open nonunitary quantum systems, and far-from-equilibrium thermodynamics. The technical contributions include the first full treatment of arbitrary powers of an operator, highlighting the special role of the zero eigenvalue. Furthermore, we show that the Drazin inverse, previously only defined axiomatically, can be derived as the negative-one power of singular operators within the meromorphic functional calculus and we give a new general method to construct it. We provide new formulae for constructing spectral projection operators and delineate the relations among projection operators, eigenvectors, and left and right generalized eigenvectors. By way of illustrating its application, we explore several, rather distinct examples. First, we analyze stochastic transition operators in discrete and continuous time. Second, we show that nondiagonalizability can be a robust feature of a stochastic process, induced even by simple counting. As a result, we directly derive distributions of the time-dependent Poisson process and point out that nondiagonalizability is intrinsic to it and the broad class of hidden semi-Markov processes. Third, we show that the Drazin inverse arises naturally in stochastic thermodynamics and that applying the meromorphic functional calculus provides closed-form solutions for the dynamics of key thermodynamic observables. Finally, we draw connections to the Ruelle-Frobenius-Perron and Koopman operators for chaotic dynamical systems and propose how to extract eigenvalues from a time-series.

Dimers in Piecewise Temperleyan Domains

NASA Astrophysics Data System (ADS)

Russkikh, Marianna

2018-03-01

We study the large-scale behavior of the height function in the dimer model on the square lattice. Richard Kenyon has shown that the fluctuations of the height function on Temperleyan discretizations of a planar domain converge in the scaling limit (as the mesh size tends to zero) to the Gaussian Free Field with Dirichlet boundary conditions. We extend Kenyon's result to a more general class of discretizations. Moreover, we introduce a new factorization of the coupling function of the double-dimer model into two discrete holomorphic functions, which are similar to discrete fermions defined in Smirnov (Proceedings of the international congress of mathematicians (ICM), Madrid, Spain, 2006; Ann Math (2) 172:1435-1467, 2010). For Temperleyan discretizations with appropriate boundary modifications, the results of Kenyon imply that the expectation of the double-dimer height function converges to a harmonic function in the scaling limit. We use the above factorization to extend this result to the class of all polygonal discretizations, that are not necessarily Temperleyan. Furthermore, we show that, quite surprisingly, the expectation of the double-dimer height function in the Temperleyan case is exactly discrete harmonic (for an appropriate choice of Laplacian) even before taking the scaling limit.

Invariant functionals in higher-spin theory

NASA Astrophysics Data System (ADS)

Vasiliev, M. A.

2017-03-01

A new construction for gauge invariant functionals in the nonlinear higher-spin theory is proposed. Being supported by differential forms closed by virtue of the higher-spin equations, invariant functionals are associated with central elements of the higher-spin algebra. In the on-shell AdS4 higher-spin theory we identify a four-form conjectured to represent the generating functional for 3d boundary correlators and a two-form argued to support charges for black hole solutions. Two actions for 3d boundary conformal higher-spin theory are associated with the two parity-invariant higher-spin models in AdS4. The peculiarity of the spinorial formulation of the on-shell AdS3 higher-spin theory, where the invariant functional is supported by a two-form, is conjectured to be related to the holomorphic factorization at the boundary. The nonlinear part of the star-product function F* (B (x)) in the higher-spin equations is argued to lead to divergencies in the boundary limit representing singularities at coinciding boundary space-time points of the factors of B (x), which can be regularized by the point splitting. An interpretation of the RG flow in terms of proposed construction is briefly discussed.

Modular amplitudes and flux-superpotentials on elliptic Calabi-Yau fourfolds

NASA Astrophysics Data System (ADS)

Cota, Cesar Fierro; Klemm, Albrecht; Schimannek, Thorsten

2018-01-01

We discuss the period geometry and the topological string amplitudes on elliptically fibered Calabi-Yau fourfolds in toric ambient spaces. In particular, we describe a general procedure to fix integral periods. Using some elementary facts from homological mirror symmetry we then obtain Bridgelands involution and its monodromy action on the integral basis for non-singular elliptically fibered fourfolds. The full monodromy group contains a subgroup that acts as PSL(2,Z) on the Kähler modulus of the fiber and we analyze the consequences of this modularity for the genus zero and genus one amplitudes as well as the associated geometric invariants. We find holomorphic anomaly equations for the amplitudes, reflecting precisely the failure of exact PSL(2,Z) invariance that relates them to quasi-modular forms. Finally we use the integral basis of periods to study the horizontal flux superpotential and the leading order Kähler potential for the moduli fields in F-theory compactifications globally on the complex structure moduli space. For a particular example we verify attractor behaviour at the generic conifold given an aligned choice of flux which we expect to be universal. Furthermore we analyze the superpotential at the orbifold points but find no stable vacua.

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.

Baker-Akhiezer Spinor Kernel and Tau-functions on Moduli Spaces of Meromorphic Differentials

NASA Astrophysics Data System (ADS)

Kalla, C.; Korotkin, D.

2014-11-01

In this paper we study the Baker-Akhiezer spinor kernel on moduli spaces of meromorphic differentials on Riemann surfaces. We introduce the Baker-Akhiezer tau-function which is related to both the Bergman tau-function (which was studied before in the context of Hurwitz spaces and spaces of holomorphic Abelian and quadratic differentials) and the KP tau-function on such spaces. In particular, we derive variational formulas of Rauch-Ahlfors type on moduli spaces of meromorphic differentials with prescribed singularities: we use the system of homological coordinates, consisting of absolute and relative periods of the meromorphic differential, and show how to vary the fundamental objects associated to a Riemann surface (the matrix of b-periods, normalized Abelian differentials, the Bergman bidifferential, the Szegö kernel and the Baker-Akhiezer spinor kernel) with respect to these coordinates. The variational formulas encode dependence both on the moduli of the Riemann surface and on the choice of meromorphic differential (variation of the meromorphic differential while keeping the Riemann surface fixed corresponds to flows of KP type). Analyzing the global properties of the Bergman and Baker-Akhiezer tau-functions, we establish relationships between various divisor classes on the moduli spaces.

Vorticity dipoles and a theoretical model of a finite force at the moving contact line singularity

NASA Astrophysics Data System (ADS)

Zhang, Peter; Devoria, Adam; Mohseni, Kamran

2017-11-01

In the well known works of Moffatt (1964) and Huh & Scriven (1971), an infinite force was reported at the moving contact line (MCL) and attributed to a non-integrable stress along the fluid-solid boundary. In our recent investigation of the boundary driven wedge, a model of the MCL, we find that the classical solution theoretically predicts a finite force at the contact line if the forces applied by the two boundaries that make up the corner are taken into consideration. Mathematically, this force can be obtained by the complex contour integral of the holomorphic vorticity-pressure function given by G = μω + ip . Alternatively, this force can also be found using a carefully defined real integral that incorporates the two boundaries. Motivated by this discovery, we have found that the rate of change in circulation, viscous energy dissipation, and viscous energy flux is also finite per unit contact line length. The analysis presented demonstrates that despite a singular stress and a relatively simple geometry, the no-slip semi-infinite wedge is capable of capturing some physical quantities of interest. Furthermore, this result provides a foundation for other challenging topics such as dynamic contact angle.

Entropy and temperature from black-hole/near-horizon-CFT duality

NASA Astrophysics Data System (ADS)

Rodriguez, Leo; Yildirim, Tuna

2010-08-01

We construct a two-dimensional CFT, in the form of a Liouville theory, in the near-horizon limit of four- and three-dimensional black holes. The near-horizon CFT assumes two-dimensional black hole solutions first introduced by Christensen and Fulling (1977 Phys. Rev. D 15 2088-104) and expanded to a greater class of black holes via Robinson and Wilczek (2005 Phys. Rev. Lett. 95 011303). The two-dimensional black holes admit a Diff(S1) subalgebra, which upon quantization in the horizon limit becomes Virasoro with calculable central charge. This charge and the lowest Virasoro eigen-mode reproduce the correct Bekenstein-Hawking entropy of the four- and three-dimensional black holes via the known Cardy formula (Blöte et al 1986 Phys. Rev. Lett. 56 742; Cardy 1986 Nucl. Phys. B 270 186). Furthermore, the two-dimensional CFT's energy-momentum tensor is anomalous. However, in the horizon limit the energy-momentum tensor becomes holomorphic equaling the Hawking flux of the four- and three-dimensional black holes. This encoding of both entropy and temperature provides a uniformity in the calculation of black hole thermodynamic and statistical quantities for the non-local effective action approach.

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.

High energy scattering in QCD and in quantum gravity

NASA Astrophysics Data System (ADS)

Lipatov, L. N.

2014-06-01

The theory of the high energy scattering in QCD is based on the BFKL equation for the Pomeron wave function and on its generalization for composite multi-gluon states in the crossing channel. At a large number of colors the equations for the gluon composite states have remarkable mathematical properties including their Möbius invariance, holomorphic separability, duality symmetry and integrability. High energy QCD interactions local in the particle rapidities are formulated in the form of the gauge invariant effective action. In the maximally extended N = 4 super-symmetry the Pomeron turns out to be dual to the reggeized graviton in the 10-dimensional anti-de-Sitter space. As a result, the Gribov calculus for the Pomeron interactions should be reformulated here as a generally covariant effective field theory for the reggeized gravitons. We construct the corresponding effective action, which gives a possibility to calculate their trajectory and couplings. The graviton trajectory in the leading order contains an ultraviolet divergency meaning the presence of the double-logarithmic (DL) terms. We sum the DL contributions in all orders of the perturbation theory in the Einstein-Hilbert gravity and in its super-symmetric generalizations. In the N = 8 super gravity the ratio of the scattering amplitude in the DL approximation to the Born expression tends to zero at large energies.

On N = 1 partition functions without R-symmetry

DOE PAGES

Knodel, Gino; Liu, James T.; Zayas, Leopoldo A. Pando

2015-03-25

Here, we examine the dependence of four-dimensional Euclidean N = 1 partition functions on coupling constants. In particular, we focus on backgrounds without R-symmetry, which arise in the rigid limit of old minimal supergravity. Backgrounds preserving a single supercharge may be classified as having either trivial or SU(2) structure, with the former including S 4. We show that, in the absence of additional symmetries, the partition function depends non-trivially on all couplings in the trivial structure case, and (anti)-holomorphically on couplings in the SU(2) structure case. In both cases, this allows for ambiguities in the form of finite counterterms, whichmore » in principle render the partition function unphysical. However, we argue that on dimensional grounds, ambiguities are restricted to finite powers in relevant couplings, and can therefore be kept under control. On the other hand, for backgrounds preserving supercharges of opposite chiralities, the partition function is completely independent of all couplings. In this case, the background admits an R-symmetry, and the partition function is physical, in agreement with the results obtained in the rigid limit of new minimal supergravity. Based on a systematic analysis of supersymmetric invariants, we also demonstrate that N = 1 localization is not possible for backgrounds without R-symmetry.« less

On exact correlation functions of chiral ring operators in 2 d N=(2, 2) SCFTs via localization

NASA Astrophysics Data System (ADS)

Chen, Jin

2018-03-01

We study the extremal correlation functions of (twisted) chiral ring operators via superlocalization in N=(2, 2) superconformal field theories (SCFTs) with central charge c ≥ 3, especially for SCFTs with Calabi-Yau geometric phases. We extend the method in arXiv: 1602.05971 with mild modifications, so that it is applicable to disentangle operators mixing on S 2 in nilpotent (twisted) chiral rings of 2 d SCFTs. With the extended algorithm and technique of localization, we compute exactly the extremal correlators in 2 d N=(2, 2) (twisted) chiral rings as non-holomorphic functions of marginal parameters of the theories. Especially in the context of Calabi-Yau geometries, we give an explicit geometric interpretation to our algorithm as the Griffiths transversality with projection on the Hodge bundle over Calabi-Yau complex moduli. We also apply the method to compute extremal correlators in Kähler moduli, or say twisted chiral rings, of several interesting Calabi-Yau manifolds. In the case of complete intersections in toric varieties, we provide an alternative formalism for extremal correlators via localization onto Higgs branch. In addition, as a spinoff we find that, from the extremal correlators of the top element in twisted chiral rings, one can extract chiral correlators in A-twisted topological theories.

Early universe cosmology, effective supergravity, and invariants of algebraic forms

NASA Astrophysics Data System (ADS)

Sinha, Kuver

2015-09-01

The presence of light scalars can have profound effects on early universe cosmology, influencing its thermal history as well as paradigms like inflation and baryogenesis. Effective supergravity provides a framework to make quantifiable, model-independent studies of these effects. The Riemannian curvature of the Kähler manifold spanned by scalars belonging to chiral superfields, evaluated along supersymmetry breaking directions, provides an order parameter (in the sense that it must necessarily take certain values) for phenomena as diverse as slow roll modular inflation, nonthermal cosmological histories, and the viability of Affleck-Dine baryogenesis. Within certain classes of UV completions, the order parameter for theories with n scalar moduli is conjectured to be related to invariants of n -ary cubic forms (for example, for models with three moduli, the order parameter is given by a function on the ring of invariants spanned by the Aronhold invariants). Within these completions, and under the caveats spelled out, this may provide an avenue to obtain necessary conditions for the above phenomena that are in principle calculable given nothing but the intersection numbers of a Calabi-Yau compactification geometry. As an additional result, abstract relations between holomorphic sectional and bisectional curvatures are utilized to constrain Affleck-Dine baryogenesis on a wide class of Kähler geometries.

Topological strings on singular elliptic Calabi-Yau 3-folds and minimal 6d SCFTs

NASA Astrophysics Data System (ADS)

Del Zotto, Michele; Gu, Jie; Huang, Min-xin; Kashani-Poor, Amir-Kian; Klemm, Albrecht; Lockhart, Guglielmo

2018-03-01

We apply the modular approach to computing the topological string partition function on non-compact elliptically fibered Calabi-Yau 3-folds with higher Kodaira singularities in the fiber. The approach consists in making an ansatz for the partition function at given base degree, exact in all fiber classes to arbitrary order and to all genus, in terms of a rational function of weak Jacobi forms. Our results yield, at given base degree, the elliptic genus of the corresponding non-critical 6d string, and thus the associated BPS invariants of the 6d theory. The required elliptic indices are determined from the chiral anomaly 4-form of the 2d worldsheet theories, or the 8-form of the corresponding 6d theories, and completely fix the holomorphic anomaly equation constraining the partition function. We introduce subrings of the known rings of Weyl invariant Jacobi forms which are adapted to the additional symmetries of the partition function, making its computation feasible to low base wrapping number. In contradistinction to the case of simpler singularities, generic vanishing conditions on BPS numbers are no longer sufficient to fix the modular ansatz at arbitrary base wrapping degree. We show that to low degree, imposing exact vanishing conditions does suffice, and conjecture this to be the case generally.

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.

Lectures on Kähler Geometry - Series: London Mathematical Society Student Texts (No. 69)

NASA Astrophysics Data System (ADS)

Moroianu, Andrei

2004-03-01

Kähler geometry is a beautiful and intriguing area of mathematics, of substantial research interest to both mathematicians and physicists. This self-contained graduate text provides a concise and accessible introduction to the topic. The book begins with a review of basic differential geometry, before moving on to a description of complex manifolds and holomorphic vector bundles. Kähler manifolds are discussed from the point of view of Riemannian geometry, and Hodge and Dolbeault theories are outlined, together with a simple proof of the famous Kähler identities. The final part of the text studies several aspects of compact Kähler manifolds: the Calabi conjecture, Weitzenböck techniques, Calabi Yau manifolds, and divisors. All sections of the book end with a series of exercises and students and researchers working in the fields of algebraic and differential geometry and theoretical physics will find that the book provides them with a sound understanding of this theory. The first graduate-level text on Kähler geometry, providing a concise introduction for both mathematicians and physicists with a basic knowledge of calculus in several variables and linear algebra Over 130 exercises and worked examples Self-contained and presents varying viewpoints including Riemannian, complex and algebraic

Quantum Field Theory in Two Dimensions: Light-front Versus Space-like Solutions

NASA Astrophysics Data System (ADS)

Martinovic̆, L'ubomír

2017-07-01

A few non-perturbative topics of quantum field theory in D=1+1 are studied in both the conventional (SL) and light-front (LF) versions. First, we give a concise review of the recently proposed quantization of the two-dimensional massless LF fields. The LF version of bosonization follows in a simple and natural way including the bosonized form of the Thirring model. As a further application, we demonstrate the closeness of the 2D massless LF quantum fields to conformal field theory (CFT). We calculate several correlation functions including those between the components of the LF energy-momentum tensor and derive the LF version of the Virasoro algebra. Using the Euclidean time variable, we can immediately transform calculated quantities to the (anti)holomorphic form. The results found are in agreement with those from CFT. Finally, we show that the proposed framework provides us with the elements needed for an independent LF study of exactly solvable models. We compute the non-perturbative correlation functions from the exact operator solution of the LF Thirring model and compare it to the analogous results in the SL theory. While the vacuum effects are automatically taken into account in the LF case, the non-trivial vacuum structure has to be incorported by an explicit diagonalization of the SL Hamiltonians, to obtain the equivalently complete solution.

One-dimensional super Calabi-Yau manifolds and their mirrors

NASA Astrophysics Data System (ADS)

Noja, S.; Cacciatori, S. L.; Piazza, F. Dalla; Marrani, A.; Re, R.

2017-04-01

We apply a definition of generalised super Calabi-Yau variety (SCY) to supermanifolds of complex dimension one. One of our results is that there are two SCY's having reduced manifold equal to P^1, namely the projective super space P^{.1|2} and the weighted projective super space W{P}_{(2)}^{.1|1} . Then we compute the corresponding sheaf cohomology of superforms, showing that the cohomology with picture number one is infinite dimensional, while the de Rham cohomology, which is what matters from a physical point of view, remains finite dimensional. Moreover, we provide the complete real and holomorphic de Rham cohomology for generic projective super spaces {P}^{.n|m} . We also determine the automorphism groups: these always match the dimension of the projective super group with the only exception of {P}^{.1|2} , whose automorphism group turns out to be larger than the projective super group. By considering the cohomology of the super tangent sheaf, we compute the deformations of {P}^{.1|m} , discovering that the presence of a fermionic structure allows for deformations even if the reduced manifold is rigid. Finally, we show that {P}^{.1|2} is self-mirror, whereas W{P}_{(2)}^{.1|1} has a zero dimensional mirror. Also, the mirror map for {P}^{.1|2} naturally endows it with a structure of N = 2 super Riemann surface.

Holographic hierarchy in the Gaussian matrix model via the fuzzy sphere

NASA Astrophysics Data System (ADS)

Garner, David; Ramgoolam, Sanjaye

2013-10-01

The Gaussian Hermitian matrix model was recently proposed to have a dual string description with worldsheets mapping to a sphere target space. The correlators were written as sums over holomorphic (Belyi) maps from worldsheets to the two-dimensional sphere, branched over three points. We express the matrix model correlators by using the fuzzy sphere construction of matrix algebras, which can be interpreted as a string field theory description of the Belyi strings. This gives the correlators in terms of trivalent ribbon graphs that represent the couplings of irreducible representations of su(2), which can be evaluated in terms of 3j and 6j symbols. The Gaussian model perturbed by a cubic potential is then recognised as a generating function for Ponzano-Regge partition functions for 3-manifolds having the worldsheet as boundary, and equipped with boundary data determined by the ribbon graphs. This can be viewed as a holographic extension of the Belyi string worldsheets to membrane worldvolumes, forming part of a holographic hierarchy linking, via the large N expansion, the zero-dimensional QFT of the Matrix model to 2D strings and 3D membranes. Note that if, after removing the white vertices, the graph contains a blue edge connecting to the same black vertex at both ends, then the triangulation generated from the black edges will contain faces that resemble cut discs. These faces are triangles with two of the edges identified.

Multivariate Tensor-based Morphometry on Surfaces: Application to Mapping Ventricular Abnormalities in HIV/AIDS

PubMed Central

Wang, Yalin; Zhang, Jie; Gutman, Boris; Chan, Tony F.; Becker, James T.; Aizenstein, Howard J.; Lopez, Oscar L.; Tamburo, Robert J.; Toga, Arthur W.; Thompson, Paul M.

2010-01-01

Here we developed a new method, called multivariate tensor-based surface morphometry (TBM), and applied it to study lateral ventricular surface differences associated with HIV/AIDS. Using concepts from differential geometry and the theory of differential forms, we created mathematical structures known as holomorphic one-forms, to obtain an efficient and accurate conformal parameterization of the lateral ventricular surfaces in the brain. The new meshing approach also provides a natural way to register anatomical surfaces across subjects, and improves on prior methods as it handles surfaces that branch and join at complex 3D junctions. To analyze anatomical differences, we computed new statistics from the Riemannian surface metrics - these retain multivariate information on local surface geometry. We applied this framework to analyze lateral ventricular surface morphometry in 3D MRI data from 11 subjects with HIV/AIDS and 8 healthy controls. Our method detected a 3D profile of surface abnormalities even in this small sample. Multivariate statistics on the local tensors gave better effect sizes for detecting group differences, relative to other TBM-based methods including analysis of the Jacobian determinant, the largest and smallest eigenvalues of the surface metric, and the pair of eigenvalues of the Jacobian matrix. The resulting analysis pipeline may improve the power of surface-based morphometry studies of the brain. PMID:19900560

Decorated Heegaard Diagrams and Combinatorial Heegaard Floer Homology

NASA Astrophysics Data System (ADS)

Hammarsten, Carl

Heegaard Floer homology is a collection of invariants for closed oriented three-manifolds, introduced by Ozsvath and Szabo in 2001. The simplest version is defined as the homology of a chain complex coming from a Heegaard diagram of the three manifold. In the original definition, the differentials count the number of points in certain moduli spaces of holomorphic disks, which are hard to compute in general. More recently, Sarkar and Wang (2006) and Ozsvath, Stipsicz and Szabo, (2009) have determined combinatorial methods for computing this homology with Z2 coefficients. Both methods rely on the construction of very specific Heegaard diagrams for the manifold, which are generally very complicated. Given a decorated Heegaard diagram H for a closed oriented 3-manifold Y, that is a Heegaard diagram together with a collection of embedded paths satisfying certain criteria, we describe a combinatorial recipe for a chain complex CF'[special character omitted]( H). If H satisfies some technical constraints we show that this chain complex is homotopically equivalent to the Heegaard Floer chain complex CF[special character omitted](H) and hence has the Heegaard Floer homology HF[special character omitted](Y) as its homology groups. Using branched spines we give an algorithm to construct a decorated Heegaard diagram which satisfies the necessary technical constraints for every closed oriented Y. We present this diagram graphically in the form of a strip diagram.

Entomopathogens of Amazonian stick insects and locusts are members of the Beauveria species complex (Cordyceps sensu stricto).

PubMed

Sanjuan, Tatiana; Tabima, Javier; Restrepo, Silvia; Læssøe, Thomas; Spatafora, Joseph W; Franco-Molano, Ana Esperanza

2014-01-01

In the Amazon the only described species of Cordyceps sensu stricto (Hypocreales, Cordycipitaceae) that parasitize insects of Orthopterida (orders Orthoptera and Phasmida) are Cordyceps locustiphila and C. uleana. However, the type specimens for both taxa have been lost and the concepts of these species are uncertain. To achieve a more comprehensive understanding of the systematics of these species, collections of Cordyceps from the Amazon regions of Colombia, Ecuador and Guyana were subjected to morphological, ecological and molecular phylogenetic studies. Phylogenetic analyses were conducted on partial sequences of SSU, LSU, TEF, RPB1 and RPB2 nuclear loci. Two new species are proposed including C. diapheromeriphila, a parasite of Phasmida, and C. acridophila, a parasite of the superfamily Acridomorpha (Orthoptera), which is broadly distributed across the Amazon. For C. locustiphila a lectotypification and an epitypification are made. Cordyceps locustiphila is host specific with Colpolopha (Acridomorpha: Romaleidae), and its distribution coincides with that of its host. The phylogenetic placement of these three species was resolved with strong support in the Beauveria clade of Cordyceps s. str. (Cordycipitaceae). This relationship and the morphological similarity of their yellow stromata with known teleomorphs of the clade, suggest that the holomorphs of these species may include Beauveria or Beauveria-like anamorphs. The varying host specificity of the beauverioid Cordyceps species suggest the potential importance of identifying the natural host taxon before future consideration of strains for use in biological control of pest locusts.

Direct Images, Fields of Hilbert Spaces, and Geometric Quantization

NASA Astrophysics Data System (ADS)

Lempert, László; Szőke, Róbert

2014-04-01

Geometric quantization often produces not one Hilbert space to represent the quantum states of a classical system but a whole family H s of Hilbert spaces, and the question arises if the spaces H s are canonically isomorphic. Axelrod et al. (J. Diff. Geo. 33:787-902, 1991) and Hitchin (Commun. Math. Phys. 131:347-380, 1990) suggest viewing H s as fibers of a Hilbert bundle H, introduce a connection on H, and use parallel transport to identify different fibers. Here we explore to what extent this can be done. First we introduce the notion of smooth and analytic fields of Hilbert spaces, and prove that if an analytic field over a simply connected base is flat, then it corresponds to a Hermitian Hilbert bundle with a flat connection and path independent parallel transport. Second we address a general direct image problem in complex geometry: pushing forward a Hermitian holomorphic vector bundle along a non-proper map . We give criteria for the direct image to be a smooth field of Hilbert spaces. Third we consider quantizing an analytic Riemannian manifold M by endowing TM with the family of adapted Kähler structures from Lempert and Szőke (Bull. Lond. Math. Soc. 44:367-374, 2012). This leads to a direct image problem. When M is homogeneous, we prove the direct image is an analytic field of Hilbert spaces. For certain such M—but not all—the direct image is even flat; which means that in those cases quantization is unique.

ITS2 sequence-structure phylogeny reveals diverse endophytic Pseudocercospora fungi on poplars.

PubMed

Yan, Dong-Hui; Gao, Qian; Sun, Xiaoming; Song, Xiaoyu; Li, Hongchang

2018-04-01

For matching the new fungal nomenclature to abolish pleomorphic names for a fungus, a genus Pseudocercospora s. str. was suggested to host holomorphic Pseudocercosproa fungi. But the Pseudocercosproa fungi need extra phylogenetic loci to clarify their taxonomy and diversity for their existing and coming species. Internal transcribed spacer 2 (ITS2) secondary structures have been promising in charactering species phylogeny in plants, animals and fungi. In present study, a conserved model of ITS2 secondary structures was confirmed on fungi in Pseudocercospora s. str. genus using RNAshape program. The model has a typical eukaryotic four-helix ITS2 secondary structure. But a single U base occurred in conserved motif of U-U mismatch in Helix 2, and a UG emerged in UGGU motif in Helix 3 to Pseudocercospora fungi. The phylogeny analyses based on the ITS2 sequence-secondary structures with compensatory base change characterizations are able to delimit more species for Pseudocercospora s. str. than phylogenic inferences of traditional multi-loci alignments do. The model was employed to explore the diversity of endophytic Pseudocercospora fungi in poplar trees. The analysis results also showed that endophytic Pseudocercospora fungi were diverse in species and evolved a specific lineage in poplar trees. This work suggested that ITS2 sequence-structures could become as additionally significant loci for species phylogenetic and taxonomic studies on Pseudocerospora fungi, and that Pseudocercospora endophytes could be important roles to Pseudocercospora fungi's evolution and function in ecology.

Arithmetic and Hyperbolic Structures in String Theory

NASA Astrophysics Data System (ADS)

Persson, Daniel

2010-01-01

This monograph is an updated and extended version of the author's PhD thesis. It consists of an introductory text followed by two separate parts which are loosely related but may be read independently of each other. In Part I we analyze certain hyperbolic structures arising when studying gravity in the vicinity of a spacelike singularity (the "BKL-limit"). In this limit, spatial points decouple and the dynamics exhibits ultralocal behaviour which may be described in terms of a (possibly chaotic) hyperbolic billiard. In all supergravities arising as low-energy limits of string theory or M-theory, the billiard dynamics takes place within the fundamental Weyl chambers of certain hyperbolic Kac-Moody algebras, suggesting that these algebras generate hidden infinite-dimensional symmetries of the theory. Part II of the thesis is devoted to a study of how (U-)dualities in string theory provide powerful constraints on perturbative and non-perturbative quantum corrections. These dualities are described by certain arithmetic groups G(Z) which are conjectured to be preserved in the effective action. The exact couplings are given by automorphic forms on the double quotient G(Z)G/K. We discuss in detail various methods of constructing automorphic forms, with particular emphasis on non-holomorphic Eisenstein series. We provide detailed examples for the physically relevant cases of SL(2,Z) and SL(3,Z), for which we construct their respective Eisenstein series and compute their (non-abelian) Fourier expansions. We also show how these techniques can be applied to hypermultiplet moduli spaces in type II Calabi-Yau compactifications, and we provide a detailed analysis for the universal hypermultiplet.

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.

Renormalization in Quantum Field Theory and the Riemann-Hilbert Problem I: The Hopf Algebra Structure of Graphs and the Main Theorem

NASA Astrophysics Data System (ADS)

Connes, Alain; Kreimer, Dirk

This paper gives a complete selfcontained proof of our result announced in [6] showing that renormalization in quantum field theory is a special instance of a general mathematical procedure of extraction of finite values based on the Riemann-Hilbert problem. We shall first show that for any quantum field theory, the combinatorics of Feynman graphs gives rise to a Hopf algebra which is commutative as an algebra. It is the dual Hopf algebra of the enveloping algebra of a Lie algebra whose basis is labelled by the one particle irreducible Feynman graphs. The Lie bracket of two such graphs is computed from insertions of one graph in the other and vice versa. The corresponding Lie group G is the group of characters of . We shall then show that, using dimensional regularization, the bare (unrenormalized) theory gives rise to a loop where C is a small circle of complex dimensions around the integer dimension D of space-time. Our main result is that the renormalized theory is just the evaluation at z=D of the holomorphic part γ+ of the Birkhoff decomposition of γ. We begin to analyse the group G and show that it is a semi-direct product of an easily understood abelian group by a highly non-trivial group closely tied up with groups of diffeomorphisms. The analysis of this latter group as well as the interpretation of the renormalization group and of anomalous dimensions are the content of our second paper with the same overall title.

Dispersion analysis of leaky guided waves in fluid-loaded waveguides of generic shape.

PubMed

Mazzotti, M; Marzani, A; Bartoli, I

2014-01-01

A fully coupled 2.5D formulation is proposed to compute the dispersive parameters of waveguides with arbitrary cross-section immersed in infinite inviscid fluids. The discretization of the waveguide is performed by means of a Semi-Analytical Finite Element (SAFE) approach, whereas a 2.5D BEM formulation is used to model the impedance of the surrounding infinite fluid. The kernels of the boundary integrals contain the fundamental solutions of the space Fourier-transformed Helmholtz equation, which governs the wave propagation process in the fluid domain. Numerical difficulties related to the evaluation of singular integrals are avoided by using a regularization procedure. To improve the numerical stability of the discretized boundary integral equations for the external Helmholtz problem, the so called CHIEF method is used. The discrete wave equation results in a nonlinear eigenvalue problem in the complex axial wavenumbers that is solved at the frequencies of interest by means of a contour integral algorithm. In order to separate physical from non-physical solutions and to fulfill the requirement of holomorphicity of the dynamic stiffness matrix inside the complex wavenumber contour, the phase of the radial bulk wavenumber is uniquely defined by enforcing the Snell-Descartes law at the fluid-waveguide interface. Three numerical applications are presented. The computed dispersion curves for a circular bar immersed in oil are in agreement with those extracted using the Global Matrix Method. Novel results are presented for viscoelastic steel bars of square and L-shaped cross-section immersed in water. Copyright © 2013 Elsevier B.V. All rights reserved.

Shape Analysis of Planar Multiply-Connected Objects Using Conformal Welding.

PubMed

Lok Ming Lui; Wei Zeng; Shing-Tung Yau; Xianfeng Gu

2014-07-01

Shape analysis is a central problem in the field of computer vision. In 2D shape analysis, classification and recognition of objects from their observed silhouettes are extremely crucial but difficult. It usually involves an efficient representation of 2D shape space with a metric, so that its mathematical structure can be used for further analysis. Although the study of 2D simply-connected shapes has been subject to a corpus of literatures, the analysis of multiply-connected shapes is comparatively less studied. In this work, we propose a representation for general 2D multiply-connected domains with arbitrary topologies using conformal welding. A metric can be defined on the proposed representation space, which gives a metric to measure dissimilarities between objects. The main idea is to map the exterior and interior of the domain conformally to unit disks and circle domains (unit disk with several inner disks removed), using holomorphic 1-forms. A set of diffeomorphisms of the unit circle S(1) can be obtained, which together with the conformal modules are used to define the shape signature. A shape distance between shape signatures can be defined to measure dissimilarities between shapes. We prove theoretically that the proposed shape signature uniquely determines the multiply-connected objects under suitable normalization. We also introduce a reconstruction algorithm to obtain shapes from their signatures. This completes our framework and allows us to move back and forth between shapes and signatures. With that, a morphing algorithm between shapes can be developed through the interpolation of the Beltrami coefficients associated with the signatures. Experiments have been carried out on shapes extracted from real images. Results demonstrate the efficacy of our proposed algorithm as a stable shape representation scheme.

Investigation of possible observable e ects in a proposed theory of physics

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

Freidan, Daniel

2015-03-31

The work supported by this grant produced rigorous mathematical results on what is possible in quantum field theory. Quantum field theory is the well-established mathematical language for fundamental particle physics, for critical phenomena in condensed matter physics, and for Physical Mathematics (the numerous branches of Mathematics that have benefitted from ideas, constructions, and conjectures imported from Theoretical Physics). Proving rigorous constraints on what is possible in quantum field theories thus guides the field, puts actual constraints on what is physically possible in physical or mathematical systems described by quantum field theories, and saves the community the effort of trying tomore » do what is proved impossible. Results were obtained in two dimensional qft (describing, e.g., quantum circuits) and in higher dimensional qft. Rigorous bounds were derived on basic quantities in 2d conformal field theories, i.e., in 2d critical phenomena. Conformal field theories are the basic objects in quantum field theory, the scale invariant theories describing renormalization group fixed points from which all qfts flow. The first known lower bounds on the 2d boundary entropy were found. This is the entropy- information content- in junctions in critical quantum circuits. For dimensions d > 2, a no-go theorem was proved on the possibilities of Cauchy fields, which are the analogs of the holomorphic fields in d = 2 dimensions, which have had enormously useful applications in Physics and Mathematics over the last four decades. This closed o the possibility of finding analogously rich theories in dimensions above 2. The work of two postdoctoral research fellows was partially supported by this grant. Both have gone on to tenure track positions.« less

(N)LSP decays and gravitino dark matter relic abundance in big divisor (nearly) SLagy D3/D7μ-split SUSY

NASA Astrophysics Data System (ADS)

Dhuria, Mansi; Misra, Aalok

2013-02-01

Using the (nearly) Ricci-flat Swiss-Cheese metric of Misra (2012) [1], in the context of a mobile space-time filling D3-brane restricted to a nearly special Lagrangian sub-manifold (in the large volume limit, the pull-back of the Kähler form close to zero and the real part of the pull-back of e, θ=π/2 times the nowhere-vanishing holomorphic three-form providing the volume form on the three-cycle) of the "big" divisor with (fluxed stacks of) space-time filling D7-branes also wrapping the "big" divisor (corresponding to a local minimum), we provide an explicit identification of the electron and the u-quark, as well as their SU (2-singlet cousins, with fermionic superpartners of four Wilson line moduli; their superpartners turn out to be very heavy, the Higgsino-mass parameter turns out to be large, one obtains one light (with a mass of 125 GeV) and one heavy Higgs and the gluino is long lived (from a collider point of view) providing a possible realization of "μ-Split Supersymmetry". By explicitly calculating the lifetimes of decays of the co-NLSPs - the first generation squark/slepton and a neutralino - to the LSP - the gravitino - as well as gravitino decays, we verify that BBN constraints relevant to the former as well as the requirement of the latter to be (more than) the age of the universe, are satisfied. For the purpose of calculation of the gravitino relic density in terms of the neutralino/slepton relic density, we evaluate the latter by evaluating the neutralino/slepton (co-)annihilation cross sections and hence show that the former satisfies the requirement for a dark matter candidate.

Parametrization of local CR automorphisms by finite jets and applications

NASA Astrophysics Data System (ADS)

Lamel, Bernhard; Mir, Nordine

2007-04-01

For any real-analytic hypersurface Msubset {C}^N , which does not contain any complex-analytic subvariety of positive dimension, we show that for every point pin M the local real-analytic CR automorphisms of M fixing p can be parametrized real-analytically by their ell_p jets at p . As a direct application, we derive a Lie group structure for the topological group operatorname{Aut}(M,p) . Furthermore, we also show that the order ell_p of the jet space in which the group operatorname{Aut}(M,p) embeds can be chosen to depend upper-semicontinuously on p . As a first consequence, it follows that given any compact real-analytic hypersurface M in {C}^N , there exists an integer k depending only on M such that for every point pin M germs at p of CR diffeomorphisms mapping M into another real-analytic hypersurface in {C}^N are uniquely determined by their k -jet at that point. Another consequence is the following boundary version of H. Cartan's uniqueness theorem: given any bounded domain Ω with smooth real-analytic boundary, there exists an integer k depending only on partial Ω such that if H\\colon Ωto Ω is a proper holomorphic mapping extending smoothly up to partial Ω near some point pin partial Ω with the same k -jet at p with that of the identity mapping, then necessarily H=Id . Our parametrization theorem also holds for the stability group of any essentially finite minimal real-analytic CR manifold of arbitrary codimension. One of the new main tools developed in the paper, which may be of independent interest, is a parametrization theorem for invertible solutions of a certain kind of singular analytic equations, which roughly speaking consists of inverting certain families of parametrized maps with singularities.

Cercosporoid fungi (Mycosphaerellaceae) 2. Species on monocots (Acoraceae to Xyridaceae, excluding Poaceae).

PubMed

Braun, Uwe; Crous, Pedro W; Nakashima, Chiharu

2014-12-01

Cercosporoid fungi (formerly Cercospora s. lat.) represent one of the largest groups of hyphomycetes belonging to the Mycosphaerellaceae (Ascomycota). They include asexual morphs, asexual holomorphs, or species with mycosphaerella-like sexual morphs. Most of them are leaf-spotting plant pathogens with special phytopathological relevance. In the first part of a new monographic work, cercosporoid hyphomycetes occurring on other fungi (fungicolous species), on ferns (pteridophytes) and gymnosperms were treated. This second part deals with cercosporoid fungi on monocots (Liliopsida; Equisetopsida, Magnoliidae, Lilianae), which covers species occurring on host plants belonging to families arranged in alphabetical order from Acoraceae to Xyridaceae, excluding Poaceae (cereals and grasses) which requires a separate treatment. The species are described and illustrated in alphabetical order under the particular cercosporoid genera, supplemented by keys to the species concerned. A detailed introduction, a survey of currently recognised cercosporoid genera, a key to the genera concerned, and a discussion of taxonomically relevant characters were published in the first part of this series. Neopseudocercospora, an additional recently introduced cercosporoid genus, is briefly discussed. The following taxonomic novelties are introduced: Cercospora alpiniigena sp. nov., C. neomaricae sp. nov., Corynespora palmicola comb. nov., Exosporium miyakei comb. nov., E. petersii comb. nov., Neopseudocercospora zambiensis comb. nov., Passalora caladiicola comb. nov., P. streptopi comb. nov., P. togashiana comb. nov., P. tranzschelii var. chinensis var. nov., Pseudocercospora beaucarneae comb. nov., P. constrictoflexuosa comb. et stat. nov., P. curcumicola sp. nov., P. dispori comb. nov., P. smilacicola sp. nov., P. urariigena nom. nov., Zasmidium agavicola comb. nov., Z. cercestidis-afzelii comb. nov., Z. citri-griseum comb. nov., Z. cyrtopodii comb. nov., Z. gahnae comb. nov., Z. indicum comb. nov., Z. liriopes comb. nov., Z. mycovellosielloides sp. nov., Z. scleriae comb. nov., Z. smilacicola comb. nov., and Z. thaliae comb. nov.

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

Calixto, M., E-mail: calixto@ugr.es; Pérez-Romero, E.

We revise the unireps. of U(2, 2) describing conformal particles with continuous mass spectrum from a many-body perspective, which shows massive conformal particles as compounds of two correlated massless particles. The statistics of the compound (boson/fermion) depends on the helicity h of the massless components (integer/half-integer). Coherent states (CS) of particle-hole pairs (“excitons”) are also explicitly constructed as the exponential action of exciton (non-canonical) creation operators on the ground state of unpaired particles. These CS are labeled by points Z (2×2 complex matrices) on the Cartan-Bergman domain D₄=U(2,2)/U(2)², and constitute a generalized (matrix) version of Perelomov U(1, 1) coherent statesmore » labeled by points z on the unit disk D₁=U(1,1)/U(1)². First, we follow a geometric approach to the construction of CS, orthonormal basis, U(2, 2) generators and their matrix elements and symbols in the reproducing kernel Hilbert space H{sub λ}(D₄) of analytic square-integrable holomorphic functions on D₄, which carries a unitary irreducible representation of U(2, 2) with index λϵN (the conformal or scale dimension). Then we introduce a many-body representation of the previous construction through an oscillator realization of the U(2, 2) Lie algebra generators in terms of eight boson operators with constraints. This particle picture allows us for a physical interpretation of our abstract mathematical construction in the many-body jargon. In particular, the index λ is related to the number 2(λ – 2) of unpaired quanta and to the helicity h = (λ – 2)/2 of each massless particle forming the massive compound.« less

Hypotrochoids in conformal restriction systems and Virasoro descendants

NASA Astrophysics Data System (ADS)

Doyon, Benjamin

2013-09-01

A conformal restriction system is a commutative, associative, unital algebra equipped with a representation of the groupoid of univalent conformal maps on connected open sets of the Riemann sphere, along with a family of linear functionals on subalgebras, satisfying a set of properties including conformal invariance and a type of restriction. This embodies some expected properties of expectation values in conformal loop ensembles CLEκ (at least for 8/3 < κ ≤ 4). In the context of conformal restriction systems, we study certain algebra elements associated with hypotrochoid simple curves (a family of curves including the ellipse). These have the CLE interpretation of being ‘renormalized random variables’ that are nonzero only if there is at least one loop of hypotrochoid shape. Each curve has a center w, a scale ɛ and a rotation angle θ, and we analyze the renormalized random variable as a function of u = ɛeiθ and w. We find that it has an expansion in positive powers of u and \\bar {u}, and that the coefficients of pure u (\\bar {u}) powers are holomorphic in w (\\bar {w}). We identify these coefficients (the ‘hypotrochoid fields’) with certain Virasoro descendants of the identity field in conformal field theory, thereby showing that they form part of a vertex operator algebraic structure. This largely generalizes works by the author (in CLE), and the author with his collaborators Riva and Cardy (in SLE8/3 and other restriction measures), where the case of the ellipse, at the order u2, led to the stress-energy tensor of CFT. The derivation uses in an essential way the Virasoro vertex operator algebra structure of conformal derivatives established recently by the author. The results suggest in particular the exact evaluation of CLE expectations of products of hypotrochoid fields as well as nontrivial relations amongst them through the vertex operator algebra, and further shed light onto the relationship between CLE and CFT.

Maass Forms and Quantum Modular Forms

NASA Astrophysics Data System (ADS)

Rolen, Larry

This thesis describes several new results in the theory of harmonic Maass forms and related objects. Maass forms have recently led to a flood of applications throughout number theory and combinatorics in recent years, especially following their development by the work of Bruinier and Funke the modern understanding Ramanujan's mock theta functions due to Zwegers. The first of three main theorems discussed in this thesis concerns the integrality properties of singular moduli. These are well-known to be algebraic integers, and they play a beautiful role in complex multiplication and explicit class field theory for imaginary quadratic fields. One can also study "singular moduli" for special non-holomorphic functions, which are algebraic but are not necessarily algebraic integers. Here we will explain the phenomenon of integrality properties and provide a sharp bound on denominators of symmetric functions in singular moduli. The second main theme of the thesis concerns Zagier's recent definition of a quantum modular form. Since their definition in 2010 by Zagier, quantum modular forms have been connected to numerous different topics such as strongly unimodal sequences, ranks, cranks, and asymptotics for mock theta functions. Motivated by Zagier's example of the quantum modularity of Kontsevich's "strange" function F(q), we revisit work of Andrews, Jimenez-Urroz, and Ono to construct a natural vector-valued quantum modular form whose components. The final chapter of this thesis is devoted to a study of asymptotics of mock theta functions near roots of unity. In his famous deathbed letter, Ramanujan introduced the notion of a mock theta function, and he offered some alleged examples. The theory of mock theta functions has been brought to fruition using the framework of harmonic Maass forms, thanks to Zwegers. Despite this understanding, little attention has been given to Ramanujan's original definition. Here we prove that Ramanujan's examples do indeed satisfy his original definition.

Black-hole/near-horizon-CFT duality and 4 dimensional classical spacetimes

NASA Astrophysics Data System (ADS)

Rodriguez, Leo L.

2011-09-01

In this thesis we accomplish two goals: We construct a two dimensional conformal field theory (CFT), in the form of a Liouville theory, in the near horizon limit for three and four dimensions black holes. The near horizon CFT assumes the two dimensional black hole solutions that were first introduced by Christensen and Fulling (1977 Phys. Rev. D 15 2088-104) and later expanded to a greater class of black holes via Robinson and Wilczek (2005 Phys. Rev. Lett. 95 011303). The two dimensions black holes admit a Diff( S1) or Witt subalgebra, which upon quantization in the horizon limit becomes Virasoro with calculable central charge. These charges and lowest Virasoro eigen-modes reproduce the correct Bekenstein-Hawking entropy of the four and three dimensions black holes via the Cardy formula (Blote et al 1986 Phys. Rev. Lett. 56 742; Cardy 1986 Nucl. Phys. B 270 186). Furthermore, the two dimensions CFT's energy momentum tensor is anomalous, i.e. its trace is nonzero. However, In the horizon limit the energy momentum tensor becomes holomorphic equaling the Hawking flux of the four and three dimensions black holes. This encoding of both entropy and temperature provides a uniformity in the calculation of black hole thermodynamics and statistical quantities for the non local effective action approach. We also show that the near horizon regime of a Kerr-Newman-AdS (KNAdS) black hole, given by its two dimensional analogue a la Robinson and Wilczek, is asymptotically AdS 2 and dual to a one dimensional quantum conformal field theory (CFT). The s-wave contribution of the resulting CFT's energy-momentum-tensor together with the asymptotic symmetries, generate a centrally extended Virasoro algebra, whose central charge reproduces the Bekenstein-Hawking entropy via Cardy's Formula. Our derived central charge also agrees with the near extremal Kerr/CFT Correspondence in the appropriate limits. We also compute the Hawking temperature of the KNAdS black hole by coupling its Robinson and Wilczek two dimensional analogue (RW2DA) to conformal matter.

Gauge/Gravity correspondence and black hole attractors in various dimensions

NASA Astrophysics Data System (ADS)

Li, Wei

This thesis investigates several topics on Gauge/Gravity correspondence and black hole attractors in various dimensions. The first chapter contains a brief review and summary of main results. Chapters 2 and 3 aim at a microscopic description of black objects in five dimensions. Chapter 2 studies higher-derivative corrections for 5D black rings and spinning black holes. It shows that certain R 2 terms found in Calabi-Yau compactifications of M-theory yield macroscopic corrections to the entropies that match the microscopic corrections. Chapter 3 constructs probe brane configurations that preserve half of the enhanced near-horizon supersymmetry of 5D spinning black holes, whose near-horizon geometry is squashed AdS2 x S 3. There are supersymmetric zero-brane probes stabilized by orbital angular momentum on S3 and one-brane probes with momentum and winding around a U(1)L x U(1)R torus in S3. Chapter 4 constructs and analyzes generic single-centered and multi-centered black hole attractor solutions in various four-dimensional models which, after Kaluza-Klein reduction, admit a description in terms of 3D gravity coupled to a sigma model whose target space is symmetric coset space. The solutions correspond to certain nilpotent generators of the coset algebra. The non-BPS black hole attractors are found to be drastically different from their BPS counterparts. Chapter 5 examines three-dimensional topologically massive gravity with negative cosmological constant in asymptotically AdS 3 spacetimes. It proves that the theory is unitary and stable only at a special value of Chern-Simons coupling, where the theory becomes chiral. This suggests the existence of a stable, consistent quantum gravity theory at the chiral point which is dual to a holomorphic boundary CFT 2. Finally, Chapter 6 studies the two-dimensional N = 1 critical string theory with a linear dilaton background. It constructs time-dependent boundary state solutions that correspond to D0-branes falling toward the Liouville wall. It also shows that there exist four types of stable, falling D0-branes (two branes and two anti-branes) in Type 0A projection and two unstable ones in Type 0B projection.

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).

Special issue on coherent states: mathematical and physical aspects Special issue on coherent states: mathematical and physical aspects

NASA Astrophysics Data System (ADS)

Twareque Ali, Syed; Antoine, Jean-Pierre; Bagarello, Fabio; Gazeau, Jean-Pierre

2011-07-01

This is a call for contributions to a special issue of Journal of Physics A: Mathematical and Theoretical dedicated to coherent states. The motivation behind this special issue is to gather in a single comprehensive volume the main aspects (past and present), latest developments, different viewpoints and directions being followed in this multidisciplinary field. Given the impressive development of the field in the past two decades, the topicality of such a volume can hardly be overemphasized. We strongly believe that such a special issue could become a particularly valuable reference for the broad scientific community working in mathematical and theoretical physics, as well as in signal processing and mathematics. Editorial policy The Guest Editors for this issue will be Syed Twareque Ali, Jean-Pierre Antoine, Fabio Bagarello and Jean-Pierre Gazeau. Potential topics include, but are not limited to, developments in the theory and applications of coherent states in: quantum optics, optomechanics, Bose-Einstein condensates quantum information, quantum measurement signal processing quantum gravity pseudo-Hermitian quantum mechanics supersymmetric quantum mechanics non-commutative quantum mechanics quantization theory harmonic and functional analysis operator theory Berezin-Toeplitz operators, PT-symmetric operators holomorphic representation theory, reproducing kernel spaces generalization of coherent states All contributions will be refereed and processed according to the usual procedure of the journal. Papers should report original and significant research that has not already been published. Guidelines for preparation of contributions The deadline for contributed papers will be 31 October 2011. This deadline will allow the special issue to appear before the end of May 2012 There is a nominal page limit of 15 printed pages per contribution (invited review papers can be longer). For papers exceeding this limit, the Guest Editors reserve the right to request a reduction in length. Further advice on publishing your work in Journal of Physics A: Mathematical and Theoretical may be found at iopscience.iop.org/jphysa. Contributions to the special issue should be submitted by web upload via authors.iop.org/, or by email to jphysa@iop.org, quoting `JPhysA Special issue on coherent states: mathematical and physical aspects'. Submissions should ideally be in standard LaTeX form. Please see the website for further information on electronic submissions. All contributions should be accompanied by a read-me file or covering letter giving the postal and e-mail addresses for correspondence. The Publishing Office should be notified of any subsequent change of address. The special issue will be published in the print and online versions of the journal.

Special issue on coherent states: mathematical and physical aspects Special issue on coherent states: mathematical and physical aspects

NASA Astrophysics Data System (ADS)

Twareque Ali, Syed; Antoine, Jean-Pierre; Bagarello, Fabio; Gazeau, Jean-Pierre

2011-06-01

This is a call for contributions to a special issue of Journal of Physics A: Mathematical and Theoretical dedicated to coherent states. The motivation behind this special issue is to gather in a single comprehensive volume the main aspects (past and present), latest developments, different viewpoints and directions being followed in this multidisciplinary field. Given the impressive development of the field in the past two decades, the topicality of such a volume can hardly be overemphasized. We strongly believe that such a special issue could become a particularly valuable reference for the broad scientific community working in mathematical and theoretical physics, as well as in signal processing and mathematics. Editorial policy The Guest Editors for this issue will be Syed Twareque Ali, Jean-Pierre Antoine, Fabio Bagarello and Jean-Pierre Gazeau. Potential topics include, but are not limited to, developments in the theory and applications of coherent states in: quantum optics, optomechanics, Bose-Einstein condensates quantum information, quantum measurement signal processing quantum gravity pseudo-Hermitian quantum mechanics supersymmetric quantum mechanics non-commutative quantum mechanics quantization theory harmonic and functional analysis operator theory Berezin-Toeplitz operators, PT-symmetric operators holomorphic representation theory, reproducing kernel spaces generalization of coherent states All contributions will be refereed and processed according to the usual procedure of the journal. Papers should report original and significant research that has not already been published. Guidelines for preparation of contributions The deadline for contributed papers will be 31 October 2011. This deadline will allow the special issue to appear before the end of May 2012 There is a nominal page limit of 15 printed pages per contribution (invited review papers can be longer). For papers exceeding this limit, the Guest Editors reserve the right to request a reduction in length. Further advice on publishing your work in Journal of Physics A: Mathematical and Theoretical may be found at iopscience.iop.org/jphysa. Contributions to the special issue should be submitted by web upload via authors.iop.org/, or by email to jphysa@iop.org, quoting `JPhysA Special issue on coherent states: mathematical and physical aspects'. Submissions should ideally be in standard LaTeX form. Please see the website for further information on electronic submissions. All contributions should be accompanied by a read-me file or covering letter giving the postal and e-mail addresses for correspondence. The Publishing Office should be notified of any subsequent change of address. The special issue will be published in the print and online versions of the journal.

Topological BF Theories

NASA Astrophysics Data System (ADS)

Sǎraru, Silviu-Constantin

Topological field theories originate in the papers of Schwarz and Witten. Initially, Schwarz shown that one of the topological invariants, namely the Ray-Singer torsion, can be represented as the partition function of a certain quantum field theory. Subsequently, Witten constructed a framework for understanding Morse theory in terms of supersymmetric quantum mechanics. These two constructions represent the prototypes of all topological field theories. The model used by Witten has been applied to classical index theorems and, moreover, suggested some generalizations that led to new mathematical results on holomorphic Morse inequalities. Starting with these results, further developments in the domain of topological field theories have been achieved. The Becchi-Rouet-Stora-Tyutin (BRST) symmetry allowed for a new definition of topological ...eld theories as theories whose BRST-invariant Hamiltonian is also BRST-exact. An important class of topological theories of Schwarz type is the class of BF models. This type of models describes three-dimensional quantum gravity and is useful at the study of four-dimensional quantum gravity in Ashtekar-Rovelli-Smolin formulation. Two-dimensional BF models are correlated to Poisson sigma models from various two-dimensional gravities. The analysis of Poisson sigma models, including their relationship to two-dimensional gravity and the study of classical solutions, has been intensively studied in the literature. In this thesis we approach the problem of construction of some classes of interacting BF models in the context of the BRST formalism. In view of this, we use the method of the deformation of the BRST charge and BRST-invariant Hamiltonian. Both methods rely on specific techniques of local BRST cohomology. The main hypotheses in which we construct the above mentioned interactions are: space-time locality, Poincare invariance, smoothness of deformations in the coupling constant and the preservation of the number of derivatives on each field. The first two hypotheses implies that the resulting interacting theory must be local in space-time and Poincare invariant. The smoothness of deformations means that the deformed objects that contribute to the construction of interactions must be smooth in the coupling constant and reduce to the objects corresponding to the free theory in the zero limit of the coupling constant. The preservation of the number of derivatives on each field imp! lies two aspects that must be simultaneously fulfilled: (i) the differential order of each free field equation must coincide with that of the corresponding interacting field equation; (ii) the maximum number of space-time derivatives from the interacting vertices cannot exceed the maximum number of derivatives from the free Lagrangian. The main results obtained can be synthesized into: obtaining self-interactions for certain classes of BF models; generation of couplings between some classes of BF theories and matter theories; construction of interactions between a class of BF models and a system of massless vector fields.

Phylogeny and nomenclature of the genus Talaromyces and taxa accommodated in Penicillium subgenus Biverticillium

PubMed Central

Samson, R.A.; Yilmaz, N.; Houbraken, J.; Spierenburg, H.; Seifert, K.A.; Peterson, S.W.; Varga, J.; Frisvad, J.C.

2011-01-01

The taxonomic history of anamorphic species attributed to Penicillium subgenus Biverticillium is reviewed, along with evidence supporting their relationship with teleomorphic species classified in Talaromyces. To supplement previous conclusions based on ITS, SSU and/or LSU sequencing that Talaromyces and subgenus Biverticillium comprise a monophyletic group that is distinct from Penicillium at the generic level, the phylogenetic relationships of these two groups with other genera of Trichocomaceae was further studied by sequencing a part of the RPB1 (RNA polymerase II largest subunit) gene. Talaromyces species and most species of Penicillium subgenus Biverticillium sensu Pitt reside in a monophyletic clade distant from species of other subgenera of Penicillium. For detailed phylogenetic analysis of species relationships, the ITS region (incl. 5.8S nrDNA) was sequenced for the available type strains and/or representative isolates of Talaromyces and related biverticillate anamorphic species. Extrolite profiles were compiled for all type strains and many supplementary cultures. All evidence supports our conclusions that Penicillium subgenus Biverticillium is distinct from other subgenera in Penicillium and should be taxonomically unified with the Talaromyces species that reside in the same clade. Following the concepts of nomenclatural priority and single name nomenclature, we transfer all accepted species of Penicillium subgenus Biverticillium to Talaromyces. A holomorphic generic diagnosis for the expanded concept of Talaromyces, including teleomorph and anamorph characters, is provided. A list of accepted Talaromyces names and newly combined Penicillium names is given. Species of biotechnological and medical importance, such as P. funiculosum and P. marneffei, are now combined in Talaromyces. Excluded species and taxa that need further taxonomic study are discussed. An appendix lists other generic names, usually considered synonyms of Penicillium sensu lato that were considered prior to our adoption of the name Talaromyces. Taxonomic novelties: Taxonomic novelties: New species – Talaromyces apiculatus Samson, Yilmaz & Frisvad, sp. nov. New combinations and names – Talaromyces aculeatus (Raper & Fennell) Samson, Yilmaz, Frisvad & Seifert, T. albobiverticillius (H.-M. Hsieh, Y.-M. Ju & S.-Y. Hsieh) Samson, Yilmaz, Frisvad & Seifert, T. allahabadensis (B.S. Mehrotra & D. Kumar) Samson, Yilmaz & Frisvad, T. aurantiacus (J.H. Mill., Giddens & A.A. Foster) Samson, Yilmaz, & Frisvad, T. boninensis (Yaguchi & Udagawa) Samson, Yilmaz, & Frisvad, T. brunneus (Udagawa) Samson, Yilmaz & Frisvad, T. calidicanius (J.L. Chen) Samson, Yilmaz & Frisvad, T. cecidicola (Seifert, Hoekstra & Frisvad) Samson, Yilmaz, Frisvad & Seifert, T. coalescens (Quintan.) Samson, Yilmaz & Frisvad, T. dendriticus (Pitt) Samson, Yilmaz, Frisvad & Seifert, T. diversus (Raper & Fennell) Samson, Yilmaz & Frisvad, T. duclauxii (Delacr.) Samson, Yilmaz, Frisvad & Seifert, T. echinosporus (Nehira) Samson, Yilmaz & Frisvad, comb. nov. T. erythromellis (A.D. Hocking) Samson, Yilmaz, Frisvad & Seifert, T. funiculosus (Thom) Samson, Yilmaz, Frisvad & Seifert, T. islandicus (Sopp) Samson, Yilmaz, Frisvad & Seifert, T. loliensis (Pitt) Samson, Yilmaz & Frisvad, T. marneffei (Segretain, Capponi & Sureau) Samson, Yilmaz, Frisvad & Seifert, T. minioluteus (Dierckx) Samson, Yilmaz, Frisvad & Seifert, T. palmae (Samson, Stolk & Frisvad) Samson, Yilmaz, Frisvad & Seifert, T. panamensis (Samson, Stolk & Frisvad) Samson, Yilmaz, Frisvad & Seifert, T. paucisporus (Yaguchi, Someya & Udagawa) Samson & Houbraken T. phialosporus (Udagawa) Samson, Yilmaz & Frisvad, T. piceus (Raper & Fennell) Samson, Yilmaz, Frisvad & Seifert, T. pinophilus (Hedgcock) Samson, Yilmaz, Frisvad & Seifert, T. pittii (Quintan.) Samson, Yilmaz, Frisvad & Seifert, T. primulinus (Pitt) Samson, Yilmaz & Frisvad, T. proteolyticus (Kamyschko) Samson, Yilmaz & Frisvad, T. pseudostromaticus (Hodges, G.M. Warner, Rogerson) Samson, Yilmaz, Frisvad & Seifert, T. purpurogenus (Stoll) Samson, Yilmaz, Frisvad & Seifert, T. rademirici (Quintan.) Samson, Yilmaz & Frisvad, T. radicus (A.D. Hocking & Whitelaw) Samson, Yilmaz, Frisvad & Seifert, T. ramulosus (Visagie & K. Jacobs) Samson, Yilmaz, Frisvad & Seifert, T. rubicundus (J.H. Mill., Giddens & A.A. Foster) Samson, Yilmaz, Frisvad & Seifert, T. rugulosus (Thom) Samson, Yilmaz, Frisvad & Seifert, T. sabulosus (Pitt & A.D. Hocking) Samson, Yilmaz & Frisvad, T. siamensis (Manoch & C. Ramírez) Samson, Yilmaz & Frisvad, T. sublevisporus (Yaguchi & Udagawa) Samson, Yilmaz & Frisvad, T. variabilis (Sopp) Samson, Yilmaz, Frisvad & Seifert, T. varians (G. Sm.) Samson, Yilmaz & Frisvad, T. verruculosus (Peyronel) Samson, Yilmaz, Frisvad & Seifert, T. viridulus Samson, Yilmaz & Frisvad. PMID:22308048

Coherent states: a contemporary panorama Coherent states: a contemporary panorama

NASA Astrophysics Data System (ADS)

Twareque Ali, S.; Antoine, Jean-Pierre; Bagarello, Fabio; Gazeau, Jean-Pierre

2012-06-01

Coherent states (CS) of the harmonic oscillator (also called canonical CS) were introduced in 1926 by Schrödinger in answer to a remark by Lorentz on the classical interpretation of the wave function. They were rediscovered in the early 1960s, first (somewhat implicitly) by Klauder in the context of a novel representation of quantum states, then by Glauber and Sudarshan for the description of coherence in lasers. Since then, CS have grown into an extremely rich domain that pervades almost every corner of physics and have also led to the development of several flourishing topics in mathematics. Along the way, a number of review articles have appeared in the literature, devoted to CS, notably the 1985 reprint volume of Klauder and Skagerstam [1], the 1990 review paper by Zhang et al [2], the 1993 Oak Ridge Conference [3] and the 1995 review paper by Ali et al [4]. Textbooks also have been published, among which one might mention the ground breaking text of Perelomov [5] focusing on the group-theoretical aspects, that of Ali et al [6]1 analyzing systematically the mathematical structure beyond the group-theoretical approach and also the relation to wavelet analysis, that of Dodonov and Man'ko [7] mostly devoted to quantum optics, that of Gazeau [8] more oriented towards the physical, probabilistic and quantization aspects, and finally the very recent one by Combescure and Robert [9]. In retrospect, one can see that the development of CS has gone through a two-phase transition. First, the (simultaneous) discovery in 1972 by Gilmore and Perelomov that CS were rooted in group theory, then the realization that CS can be defined in a purely algebraic way, as an eigenvalue problem or by a series expansion (Malkin and Man'ko 1969, Barut and Girardello 1971, Gazeau and Klauder 1999; references to the original articles may be found in the textbooks quoted above). Both facts resulted in an explosive expansion of the CS literature. We thought, therefore, that the time was ripe to devote a special issue of Journal of Physics A: Mathematical and Theoretical to CS. However, because of limitations of space and time, it would have been impossible to get a fully representative cross-section of papers, covering all the different facets of the subject. Consequently, we have selected 37 articles, including some by a few of the originators of the field. We thank all the authors for submitting their up-to-date thoughts on this fascinating subject. The contents of this special issue are subdivided into five categories: (1) review papers; (2) physics-oriented CS; (3) physics and quantum information; (4) mathematics, general topics; and (5) mathematics, particular problems. (1) Review papers We start with five review papers. The first paper, by Klauder, surveys the many possible applications of affine variables, both in classical and quantum physics. The second, by Sanders, proposes a grand tour of entangled CS, which are present in many fields, such as quantum optics, quantum information processing, etc. The next paper, by Rowe, surveys the field of vector CS and the attendant group representation problems (including induced representations). Then Oriti et al describe a particular class of CS relevant to (loop) quantum gravity. Finally, Combescure and Robert present a comprehensive review of fermionic CS, including all mathematical details. (2) Physics-oriented CS The six contributions in this section deal with specific physical problems: (i) Dajka-Luczka study Gazeau-Klauder cat states associated with a nonlinear Kerr oscillator, instead of the usual canonical CS leading to Schrödinger cat states; (ii) Angelova et al discuss squeezed CS associated with a 1D Morse potential, used in molecular physics; (iii) Bagrov et al study CS in a magnetic solenoid field and prove their completeness; (iv) Blasone-Jizba treat Nambu-Goldstone dynamics in spontaneously broken symmetries, using CS functional integrals; (v) Calixto et al describe accelerated relativistic particles in the context of spontaneous breakdown of conformal SU(2,2) symmetry, using SU(2,2) CS; and (vi) Mortazavi-Tavassoly study f-deformed charge CS and their physical properties (nonclassical features, sub-Poissonian statistical behavior, etc). (3) Physics and quantum information The second group of physically related CS contains four contributions with a distinct quantum information theoretic flavor. First, Thilagam describes the dynamical behavior of entanglement of a pair of qubits (excitons), using a CS basis. Next, Lavoie-de Guise study SU(3) intelligent states (i.e., minimal uncertainty states), of interest in the quantum information community. Then Muñoz constructs discrete CS for n qubits. Finally, Wagner-Kendon explore the continuous variable Deutsch-Jozsa algorithm known in quantum computing in a discrete formulation. (4) Mathematics, general topics In this subgroup, there are eight papers dealing with general properties of CS, independently of any particular system or application. A whole series discusses the interaction between CS and various mathematical objects: pseudodifferential operators and Weyl calculus (Unterberger); induced representations of the affine group and intertwining operators (Elmabrok-Hutnik) measure-free CS and reproducing kernels (Horzela-Szafraniec) extremal POV measures (Heinosaari-Pellonpää) Hilbert W*-modules (Bhattacharyya-Roy) Toeplitz operators (Hutníková-Hutník) and operator localization and homogeneous structure of nilpotent Lie groups (Kisil). In addition, Balazs et al consider multipliers for continuous frames, including CS or wavelet frames. (5) Mathematics, particular problems The second group of mathematically oriented papers contains 14 contributions, devoted to CS in particular systems. We start with a paper by Gilmore, which explores the (sometimes chaotic) evolution of atomic CS under a time-periodic driving field, using sphere maps S2 → S2. Next, we include a paper on CS on the 2-sphere in a magnetic field (Hall-Mitchell) a paper on CS for a quantum particle on a Möbius strip (Cirilo-Lombardo) a discussion of quantization on the circle (Chadzitaskos et al); SUSY CS for Pöschl-Teller potentials (Bergeron et al); generalized Bargmann functions and von Neumann lattices (Vourdas et al); partial reconstruction for a finite CS system, using the Fock-Bargmann representation (Calixto et al); phase operators for SU(3) irreps, thus for finite quantum systems (de Guise); semiclassical CS in periodic potentials (Carles-Sparber) complexified CS with non-Hermitian Hamiltonians (Graefe-Schubert) minimal uncertainty states in the context of (semisimple) group representation theory (Oszmaniec); localization operators in the time-frequency domain, i.e., in Gabor analysis (Muzhikyan-Avanesyan) and, finally, two papers about fermionic CS (Daoud-Kibler and Trifonov). This brief description illustrates perfectly the extreme versatility of the CS concept. As already stressed, coherent states constitute nowadays a flourishing research topic, with applications to a wide spectrum of domains. Indeed, CS are everywhere in physics: condensed matter physics, atomic physics, nuclear and particle physics, quantum optics, dynamics—both quantum and classical potentials—quantum gravity, quantization and quantum information theory. On the other hand, CS have grown into a fully-fledged domain in mathematics, incorporating many tools such as group representations, POV measures, frames, holomorphic functions, orthogonal polynomials and so on. Interestingly enough, the majority of contributions to this special issue (22 out of 37) are mathematically minded, demonstrating the widespread interest CS have generated in various areas of mathematics. A third field related to CS (but almost not represented in the present collection) is signal processing. Indeed both Gabor analysis and wavelet analysis derive in the first place from CS theory, namely, CS associated to the Weyl-Heisenberg and the ax + b group, respectively. Here too, a tremendous development has taken place in recent years, another testimony to the richness of the notion of CS. We leave it to the jury of public opinion to judge whether the call for a special issue of the journal, devoted to coherent states, has been justified. References [1] Klauder J R and Skagerstam B S 1985 Coherent States—Applications in Physics and Mathematical Physics (Singapore: World Scientific) [2] Zhang W-M, Feng D H and Gilmore R 1990 Coherent states: theory and some applications Rev. Mod. Phys. 62 867-927 [3] Feng D H, Klauder J R and Strayer M (ed) 1994 Coherent States: Past, Present and Future (Singapore: World Scientific) [4] Ali S T, Antoine J-P, Gazeau J-P and Mueller U A 1995 Coherent states and their generalizations: a mathematical overview Rev. Math. Phys. 7 1013-104 [5] Perelomov A M 1986 Generalized Coherent States and Their Applications (New York: Springer) [6] Ali S T, Antoine J-P and Gazeau J-P 2000 Coherent States, Wavelets and Their Generalizations (New York: Springer) [7] Dodonov V V and Man'ko V I (ed) 2003 Theory of Nonclassical States of Light (London: Taylor & Francis) [8] Gazeau J-P 2009 Coherent States in Quantum Physics (Berlin: Wiley) [9] Combescure M and Robert D 2012 Coherent States and Applications in Mathematical Physics (New York: Springer) 1 A second edition of that volume is in preparation.

Lattice models and integrability: a special issue in honour of F Y Wu

NASA Astrophysics Data System (ADS)

Guttmann, A. J.; Jacobsen, J. L.

2012-12-01

Fa Yueh (Fred) Wu was born on 5 January 1932 in Nanking (now known as Nanjing), China, the capital of the Nationalist government. Wu began kindergarten in 1937 in a comfortable setting, as his father held a relatively high government position. But the Sino-Japanese war broke out in July 1937, and Nanking fell to Japanese hands in November. Fleeing the Japanese, his parents brought Wu to their hometown in Hunan, and then to the war capital Chungking (now Chongqing) in 1938, where they lived for eight years until the end of the war. Around that time the Japanese began bombing Chungking, and Wu's childhood memories were dominated by air raids, bombings and burning not dissimilar to those experienced by Londoners during the war. At times the air raids lasted for days disrupting everyday lives in Chungking, including Wu's schooling. One day during a fierce bombing raid, a bomb fell in their garden reducing a pavilion and the surrounding pond to a huge crater; another bomb fell just a few metres from the tunnel where his family took shelter, almost sealing the only entrance. The family moved the very next day to the countryside. As a result of the war, Wu attended seven schools before finishing his primary education. Fortunately, by the time he entered junior high school in 1943, the Japanese forces were on the wane and Wu entered the elite middle school, Nankai. His early academic performance in Nankai seemed to him mediocre, but he nevertheless impressed his geometry teacher by showing bursts of talent. With hindsight, this early interest in geometry may have led to his later insights in graphical analyses of statistical systems. The family returned to Nanking in 1946 after the Victory over Japan Day. By this time his father had become elected to the Legislative Yuan, the equivalent of the US Senate. Wu entered high school in Nanking in 1946. Since he came from an elite school in Chungking, he excelled in most of his classes, especially mathematics. Notwithstanding his academic success, Wu probably spent more time playing Chinese chess, a board game similar to international chess. He ranked high in a city-wide tournament and often played blind-folded games. He also spent time playing bridge, a game he learned in Nankai and kept up throughout his years in the US. He also loved puzzles and riddles. But the good days did not last long, as the civil war drew closer to Nanking with the Communists winning. The family fled Nanking once again, following a zigzag path and traveling by boat, train, car and then by boat again, eventually reaching Taiwan in June 1949. By this time, the Nationalists had lost most of China, and there was no hope of returning to the mainland. Wu entered the Naval College of Technology to study electrical engineering, giving up an opportunity to study mathematics in the National Taiwan University, although his real interest was in mathematics. In 1954, Wu graduated from the Naval College with a BS degree and the commission of Ensign. Recognizing his outstanding academic record in the College, the Chinese Navy sent him to the US in 1955 to study radar and sonar and to receive training as an instructor. He stayed at the Naval School of Electronics in San Francisco and at the Instructor's School in San Diego. Wu felt that he benefited from the instructor's training much more than from the electronics school, as the training helped him to develop teaching and presentation skills that served him well throughout his career. The Navy assigned him to teach electronics in the Naval Academy when he returned to Taiwan in 1956. Wu was interested in attending a graduate school. The only institution that offered a graduate degree in Taiwan at the time was Taiwan's newly re-established Tsing Hua University. In its hurried retreat to Taiwan, the Nationalist government left the original Tsing Hua University, one of China's best-known institutions of higher learning with a history dating back to the 19th century, behind in Beijing. In 1956, after gaining footing in Taiwan, the Nationalist government revived Tsing Hua, and began offering a two-year Master's degree in nuclear science. Wu decided to apply for admission but faced considerable obstacles since he was in the Navy. After one year's effort, mostly on his father's part, Wu finally entered Tsing Hua in 1957. He completed the two-year program with an experimental thesis in 1959. By this time, the US was pushing for a scientific renaissance after the launch of the Soviet satellite Sputnik. Wu received offers of teaching assistantships from several physics departments in the US, and chose to continue his graduate education at Washington University in St. Louis in 1959. At Washington University he studied many-body theory under the late Eugene Feenberg and produced several influential papers [1, 2] on ground state properties of liquid helium-3 and liquid helium-4. In 1963, he published a paper on formulating cluster expansions in an N-body problem [3], extending the Mayer expansion to systems with indexed many-body interactions, which appeared to have escaped the attention of the community of statistical physics that it deserved. The expansion made extensive use of graphical terms, demonstrating his prowess in graphical analysis at an early stage of his career. Wu's interest in many-body theory continued over the years, with subsequent works on the electron gas, adsorbed systems, and the long-perplexing problem of density correlations in Fermi and Bose systems. After obtaining his PhD from Washington University in 1963, Wu went on to teach at Virginia Polytechnic Institute (VPI) as an assistant professor. In February 1967, Wu met Elliott Lieb who was visiting VPI to give a talk on the Bethe ansatz evaluation of the entropy of two-dimensional ice, a 6-vertex model. Wu soon realized the underlying graphical aspects of two-dimensional vertex models and solved the thermodynamics of a related 5-vertex model using the Pfaffian approach. The result was published in the April issue of Physical Review Letters (PRL) of the same year [4], and in September 1967, Wu moved to Northeastern University to join Lieb's group. Wu taught at Northeastern for 39 years until his retirement in 2006 as the Matthews Distinguished University Professor of Physics. Over the years, Wu has published more than 230 papers and monographs, and he continues to publish after retirement. Most of his research since 1967 is in exact and rigorous analyses of lattice models and integrable systems, which is the theme of this special issue. In 1968, after Wu's arrival at Northeastern, Lieb and Wu obtained the exact solution of the ground state of the one-dimensional Hubbard model and published the result in PRL [5], a work which has since become highly important after the advent of high-temperature superconductivity. This Lieb-Wu paper and Wu's 1982 review of the Potts model in Reviews of Modern Physics [37] are among the most cited papers in condensed matter physics. Later in 1968 Lieb departed Northeastern for MIT. As a result, the full version of the solution was not published until 34 years later [38] when Lieb and Wu collaborated to work on the manuscript on the occasion of Wu's 70th birthday. Wu spent the summer of 1968 at Stony Brook as the guest of C N Yang. Working with Yang's student, C Fan, he extended the Pfaffian solution of the Ising model to general lattices and termed such models 'free-fermion', a term now in common use [6]. In 1972, Wu visited R J Baxter, whom he had met earlier in 1968 at MIT, in Canberra, Australia, with the support of a Fulbright grant. They solved the triangular-lattice Ising model with 3-spin interactions [7], a model now known as the Baxter-Wu model. It was an ideal collaboration. While Baxter derived the solution algebraically, Wu used graphical methods to reduce the problem to an Ashkin-Teller model, which greatly simplifies the presentation. While in Canberra, Wu also studied the 8-vertex model on the honeycomb lattice [8], a model which proved to be useful in his later research. In 1973, Wu returned to Tsing Hua as a visiting professor and worked with colleague K Y Lin. They published two important papers introducing staggered vertex models for the first time [10, 11]. In other important work they clarified the nature of the phase diagram of the Ashkin-Teller model, and found it to have two phase transitions [9]. In the 1970s Wu traveled to Taiwan, Australia, Europe and to China when it re-opened. He met H N V Temperley in Aberdeen, Scotland in 1976, and collaborated with H J Brascamp and H Kunz in Lausanne to establish a number of rigorous results on vertex models, including a proof of the equivalence of boundary conditions for the 6-vertex model [13, 14]. From 1979 to 1980, Wu resided in the Netherlands and Germany, where he was the guest of Piet Kasteleyn at Leiden, Hans van Leeuwen at Delft and Kurt Binder in Juelich. It was in Juelich that Wu completed the 1982 review paper on the Potts model [37], a paper that has been cited 70 or more times every year since its publication. Another important work in that period is a 1976 graphical analysis of the Potts model on the triangular lattice in collaboration with Baxter and Kelland [15]. This paper provided an elegant and conceptually easy description of the duality relation of the model, complementary to the algebraic analysis of Temperley and Lieb [16]. Four years later, Wu and Lin further refined the graphical aspects to reduce the model to a 5-vertex model, under which the duality relation appears as a simple spatial symmetry [18]. The Wu-Lin formulation of the Potts model is used by Jacobsen and Sculland in an analysis of the kagome-lattice Potts model in their first paper in this issue [39]. In other pioneering work in 1976, Wu and Y K Wang introduced a spin model with chiral interactions and its duality relation in Fourier space [19]. Prior to that time, studies of spin models had invariably been confined to models with symmetric interactions. In 1977 Wu published an influential paper on spanning trees [20]. In it, he derived the spanning tree constants of the regular two-dimensional lattices. Since then, he has been the co-author of several papers extending this work to a variety of other two-dimensional Archimedean lattices [21-23]. In this issue Guttmann1 and Rogers solve the three-dimensional version of this problem, which has resisted attack for more than 30 years [40]. The connection between spanning trees and dimers was previously highlighted by Neville Temperley in 1974 [17]. The ideas from number theory needed to obtain the spanning tree constant of three-dimensional lattices, notably logarithmic Mahler measures, are further discussed in the article by Glasser2 in this issue [41]. Wu has had a long and productive collaboration with Maillard, particularly on aspects of the Ising model. Maillard also wrote the definitive description of Wu's many scientific contributions at the time of Wu's 70th birthday [24]. The paper was later included among the biographies of great names such as Newton and Feynman in the History of Physics: Individual Biographies section in the MIT Net Advance of Physics website [59]. Further developments in the Ising model are highlighted in the article by Boukraa, Hassani and Maillard3 in this issue [42]. Maillard's article also appears as the introduction to a wonderful collection of Wu's works that appeared in 2009 [25], entitled Exactly Solved Models: A Journey in Statistical Mechanics. The relation between bond percolation and the random-cluster formulation of the Potts model was pioneered by Kasteleyn and Fortuin in 1969 [26]. Later, in a 1977 paper, Wu showed how to rederive this relation in a different setting and used it to obtain various quantities of interest in the bond percolation problem, including critical exponents, from the exact solution of the Potts model [27]. A few months later, in collaboration with Kunz, he showed that site percolation can also be related to the Potts model [28]. Problems in bond percolation are treated in this issue by several works. The paper by Hu, Blöte4 and Deng5 investigates how the imposition of a 'canonical' constraint, that there be an equal number of open and closed edges, affects the universal properties [43]. The paper by Ziff6, Scullard, Wierman and Sedlock exactly solves inhomogeneous percolation on lattices of the bow-tie and checkerboard types [44]. In a 1979 paper on Potts model critical points, Wu proposed a conjecture, now known as the homogeneity hypothesis, on the location of the critical point of the kagome lattice [29]. Since then, numerous studies have been carried out to test the validity of that conjecture [12]. However, many of these tests proved to be inconclusive since they produced results extremely close to the conjectured value. The puzzle is finally solved by Jacobsen and Scullard in their two papers in this issue [39, 45]. Using a graphical analysis based on the Wu-Lin 5-vertex formulation, they recover the Wu conjecture of the kagome-lattice critical point as the first-order approximation in a well-defined graphical analysis. This establishes once and for all the approximate nature of the Wu conjecture. These investigations, and the exact solutions found by Wu, raised the question as to the conditions under which a lattice model is exactly solvable. Quite recently, such questions have been addressed through the technique of discrete holomorphicity (DH). This direction is represented in this issue by the contributions of Alam and Batchelor7, where the connection between DH and Yang-Baxter integrability is investigated [46]. DH is also a key ingredient in recent rigorous proofs that certain lattice models converge, in the continuum limit, to conformally invariant probabilistic processes known as Schramm-Loewner evolution (SLE). The theme of SLE appears within this issue in the article by Alberts, Kozdron and Lawler [47]. Finally, DH observables are used in this issue by Duminil-Copin to prove the divergence of the correlation length for the Potts model (in its formulation in terms of Fortuin-Kasteleyn clusters) when 1 <= q <= 4 [48]. Establishing the phase diagrams of lattice models is a recurrent theme in Wu's works. In an interesting but little-known work from 2000 with Guo and Blöte [30], he has shown that, contrary to common belief, the O(n) model on the honeycomb lattice has a second-order phase transition for n > 2. The question of phase diagrams for O(n)-type models is taken up in this issue by Blöte, Wang and Guo8 [49]. In 1983-84, Wu joined the National Science Foundation as the Director of the Condensed Matter Theory Program for 18 months. His duty was managing funding to individual researchers in condensed matter theory in the US. The 18-month tour in Washington offered Wu a bird's-eye view of condensed matter physics research in US universities, an understanding that proved useful to his later researches. Throughout his career, Wu has insisted on the general applicability of graphical analysis to a variety of lattices. This aspect was highlighted in his 1988 paper on the Potts model and graph theory [31], in which he derived a number of equivalences with (di)chromatic and flow polynomials on arbitrary planar graphs, both for the partition function and correlation functions. An earlier result in the same vein is the equivalence of the Potts model on a planar graph with a loop model on the corresponding medial graph, found in 1976 in collaboration with Baxter and Kelland [15]. Building on these results, and on recent progress in the combinatorial approach to planar maps, Borot, Bouttier and Guitter systematically investigate properties of percolation and Potts models on random planar maps in their contribution to this issue [50]. Wu has published extensively on dimer enumerations. His work includes exact enumerations on non-orientable surfaces and surfaces with a single boundary defect. In this issue, Lu and Zhang consider dimer enumerations on the Klein bottle, which is an example of a non-orientable surface [51]. Another contribution is the paper by Ciucu and Fischer, considering dimer coverings of a domain with a defect (hole) in the interior [52]. Wu has also worked extensively in knot theory. He has constructed new knot invariants based on statistical mechanical models [61, 62], and published a well-received review of knot invariants for physicists [32], which elucidates the connection of knot invariants with statistical mechanics. In 2004, Wu presented a new formulation of resistance networks [33], which permits the derivation of the exact expression of the resistance between two arbitrary nodes in any network. He later extended the formulation to impedance networks [34], a work which has since attracted interest in applications in petroleum research. These works can perhaps be seen as a distant echo of Wu's Navy training in electronics, more than 50 years earlier. In recent years Wu has developed this topic in joint work with Essam9, who together with Brak has related work on lattice paths in this issue [53]. A cognate paper by Arrowsmith, Bhatti and Essam also appears [54]. Wu has made other contributions to asymptotic analysis, for example in relation to dimers in his recent papers, where he also uses results from conformal invariance [60]. This thread is taken up by the article of Izmailian10 in this issue [55]. In 1997, Wu reported, in a short paper, a new formulation of duality relations of Potts correlation functions for n spins residing on the boundary of a lattice [35]. He gave the examples of n = 2 and 3, and remarked that the formulation can be extended to higher values of n 'in a straightforward fashion'. But the extension is by no means straightforward11 and its solution was eventually found by Wu and his student H Y Huang [36]. They found that the correlation functions are not all independent when n = 4 and higher. They also deduced the connecting relations expressing crossing correlations in terms of non-crossing correlations, thus resolving the discrepancy. Nowadays the interest in integrable systems largely transcends the realm of equilibrium statistical physics. Important and fundamental applications have appeared in out-of-equilibrium physics, in combinatorics, and in the study of certain dualities between string theories and gauge theories known under the common epithet of AdS/CFT duality. This last trend is represented in this issue by the contribution of Kostov [56]. Other interests of Wu in both quantum and classical systems are reflected in the article by Barry12, Muttalib and Tanaka [57], and in the paper by Bauer, Bernard and Benoist on iterated stochastic measurements [58]. This latter paper appears very timely, since it is inspired by the experiments carried out in the group of Serge Haroche who earned the 2012 Nobel Prize in Physics. Wu met his wife Ching Tse (Jane) in Taipei. They married in 1963 in St. Louis, Missouri. They have three daughters; Yvonne, a Professor of Child Neurology at the University of California San Francisco, Yolanda, a women's rights lawyer and a teacher of Suzuki violin, and Yelena, a postdoc in Child Clinical Psychology at Cincinnati Children's Hospital. Fred and Jane have five grandchildren. Wu left four siblings behind when he left China in 1949, and reunited with them after a 30-year separation for the first time in 1979. Two sisters and one brother are now deceased, and his younger brother, who also has three daughters, lives a comfortable life in retirement in Kunming, China. It has been a pleasure to assemble this collection of papers on the occasion of Fred's 80th birthday, and we wish to thank him for providing much of the biographical information on which this introduction is based. We are also grateful to all the contributors for providing such a diverse and decidedly very modern panorama of the topic of lattice models and integrability, and for meeting the strict deadlines necessary to ensure the completion of this issue before the year 2012 draws to an end. Fred Wu continues to be a highly productive, imaginative scientist, and we look forward to a continuing body of excellent work. Meanwhile, we wish him many more years of a happy and healthy life. 1Wu met Tony Guttmann at the University of Newcastle, Australia, back in 1973 when Guttmann invited him to visit. Over the years their paths have crossed countless times at conferences and workshops, and during Wu's visits to Australia and Guttmann's to America; their families became close friends in the process, with Wu's wife Jane assisting Guttmann's wife Susette in her professional duties when they both visited Taiwan. 2Wu met Larry Glasser in 1968 at MIT and also visited him later at Clarkson. They collaborated in 2003 on a paper later published in the Ramanujan Journal in 2005, in which they evaluated an integral for the entropy of spanning trees on the triangular lattice. 3Wu and Jean-Marie Maillard enjoyed joint research grants, organised between the NSF and the CNRS. They also got together frequently in Taiwan and at conferences including one in Paris on the Yang-Baxter equation in 1992. They have many joint papers, including one of Wu's favorites, a 1992 J. Phys. A: Math. Gen. paper on thermal transmissivity. In that paper they put the loosely defined term transmissivity onto a rigorous footing. 4Henk Blöte and Wu first met in 1973 in Delft. Since then they have visited each other frequently, as Blöte made regular visits to the University of Rhode Island (near Boston) and Beijing Normal University, intersecting those of Wu. They first collaborated in a 1989 paper in which they obtained a closed-form expression for the critical curve of the honeycomb antiferromagnetic Ising model and checked the formula against finite-size analysis. This combination of checking an a priori derivation against high-precision numerical analysis set the tone of Wu's later collaborations with Blöte and his students. 5Youjin Deng obtained his PhD in 2004 under the direction of Blöte at Delft. Wu served on Deng's Dissertation Committee and participated in his graduation ceremony. 6Through Wu's recent works on the Potts model he got to know Bob Ziff well. They exchanged preprints and e-mails, and often had lengthy discussions on minute points, including the use and origin of the term 'hemp-leaf lattice'. 7Wu and Murray Batchelor met at the Australia National University in 1990 and again in 1995, and their paths have crossed at many conferences and workshops. 8Wenan Guo likewise obtained his PhD under the supervision of Blöte in Delft. Wu and Guo know each other well from Wu's visits to the Beijing Normal University where he is an honorary professor. He has collaborated with Guo, on the subject of finite-size analysis using the transfer matrix approach, in several of his recent papers. 9Wu first met John Essam at King's College, London in 1978. Followoing Wu's 2006 closed-form expression of the corner-to-corner resistance of an M × N resistor network in the form of a double summation, they combined forces in 2008 at a workshop in Cambridge, and derived the asymptotic expansion of that expression. 10Nickolay Izmailian holds positions in Armenia and Taiwan. Wu and Izmailian collaborated in a paper in 2000 on the exact solution of a 6-vertex model with bond defects. Most recently they collaborated on the exact enumeration of dimers on a cylinder with a single boundary defect. 11Wu's acquaintance with Jesper Jacobsen goes back to this period, when the latter pointed out this fact in a comment to Wu's first paper on this subject. They have since crossed paths on various occasions, most recently at a 2008 workshop at the Isaac Newton Institute in Cambridge. 12Jerry Barry is another long-term collaborator of Wu's. They have met at numerous conferences and workshops. In one meeting in 1989, Barry called Wu's attention to a three-dimensional spin model on the pyrochlore lattice that appeared to be soluble. They soon solved the Ising model on that lattice. In 1997 they collaborated on a paper obtaining the phase diagram of a ternary polymer model.