Results 1  10
of
265
Liouville Correlation Functions from Fourdimensional Gauge Theories
 SIMONS CENTER FOR GEOMETRY AND PHYSICS, STONY BROOK UNIVERSITY
, 2009
"... We conjecture an expression for the Liouville theory conformal blocks and correlation functions on a Riemann surface of genus g and n punctures as the Nekrasov partition function of a certain class of N = 2 SCFTs recently defined by one of the authors. We conduct extensive tests of the conjecture ..."
Abstract

Cited by 394 (22 self)
 Add to MetaCart
(Show Context)
We conjecture an expression for the Liouville theory conformal blocks and correlation functions on a Riemann surface of genus g and n punctures as the Nekrasov partition function of a certain class of N = 2 SCFTs recently defined by one of the authors. We conduct extensive tests of the conjecture at genus 0, 1.
Localization of gauge theory on a foursphere and supersymmetric Wilson loops
, 2007
"... ..."
(Show Context)
AN−1 conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
, 2009
"... We propose a relation between correlation functions in the 2d AN−1 conformal Toda theories and the Nekrasov instanton partition functions in certain conformal N = 2 SU(N) 4d quiver gauge theories. Our proposal generalises the recently uncovered relation between the Liouville theory and SU(2) quivers ..."
Abstract

Cited by 159 (4 self)
 Add to MetaCart
(Show Context)
We propose a relation between correlation functions in the 2d AN−1 conformal Toda theories and the Nekrasov instanton partition functions in certain conformal N = 2 SU(N) 4d quiver gauge theories. Our proposal generalises the recently uncovered relation between the Liouville theory and SU(2) quivers [1]. New features appear in the analysis that have no counterparts in the Liouville case.
Quantization of Integrable Systems and Four Dimensional Gauge Theories
, 2009
"... We study four dimensional N = 2 supersymmetric gauge theory in the Ωbackground with the two dimensional N = 2 superPoincare invariance. We explain how this gauge theory provides the quantization of the classical integrable system underlying the moduli space of vacua of the ordinary four dimension ..."
Abstract

Cited by 115 (3 self)
 Add to MetaCart
We study four dimensional N = 2 supersymmetric gauge theory in the Ωbackground with the two dimensional N = 2 superPoincare invariance. We explain how this gauge theory provides the quantization of the classical integrable system underlying the moduli space of vacua of the ordinary four dimensional N = 2 theory. The εparameter of the Ωbackground is identified with the Planck constant, the twisted chiral ring maps to quantum Hamiltonians, the supersymmetric vacua are identified with Bethe states of quantum integrable systems. This four dimensional gauge theory in its low energy description has two dimensional twisted superpotential which becomes the YangYang function of the integrable system. We present the thermodynamicBetheansatz like formulae for these functions and for the spectra of commuting Hamiltonians following the direct computation in gauge theory. The general construction is illustrated at the examples of the manybody systems, such as the periodic Toda chain, the elliptic CalogeroMoser system, and their relativistic versions, for which we present a complete characterization of the L²spectrum. We very briefly discuss the quantization of Hitchin system.
Topological strings and (almost) modular forms
, 2007
"... The Bmodel topological string theory on a CalabiYau threefold X has a symmetry group Γ, generated by monodromies of the periods of X. This acts on the topological string wave function in a natural way, governed by the quantum mechanics of the phase space H 3 (X). We show that, depending on the cho ..."
Abstract

Cited by 94 (10 self)
 Add to MetaCart
The Bmodel topological string theory on a CalabiYau threefold X has a symmetry group Γ, generated by monodromies of the periods of X. This acts on the topological string wave function in a natural way, governed by the quantum mechanics of the phase space H 3 (X). We show that, depending on the choice of polarization, the genus g topological string amplitude is either a holomorphic quasimodular form or an almost holomorphic modular form of weight 0 under Γ. Moreover, at each genus, certain combinations of genus g amplitudes are both modular and holomorphic. We illustrate this for the local CalabiYau manifolds giving rise to SeibergWitten gauge theories in four dimensions and local IP2 and IP1×IP1. As a byproduct, we also obtain a simple way of relating the topological string amplitudes near different points in the moduli space, which we use to give predictions for GromovWitten invariants of the orbifold C 3 / Z3.
The library of Babel: On the Origin of Gravitational Thermodynamics
"... We show that heavy pure states of gravity can appear to be mixed states to almost all probes. For AdS5 Schwarzschild black holes, our arguments are made using the field theory dual to string theory in such spacetimes. Our results follow from applying information theoretic notions to field theory ope ..."
Abstract

Cited by 86 (16 self)
 Add to MetaCart
(Show Context)
We show that heavy pure states of gravity can appear to be mixed states to almost all probes. For AdS5 Schwarzschild black holes, our arguments are made using the field theory dual to string theory in such spacetimes. Our results follow from applying information theoretic notions to field theory operators capable of describing very heavy states in gravity. For halfBPS states of the theory which are incipient black holes, our account is exact: typical microstates are described in gravity by a spacetime “foam”, the precise details of which are almost invisible to almost all probes. We show that universal lowenergy effective description of a foam of given global charges is via certain singular spacetime geometries. When one of the specified charges is the number of Dbranes, the effective singular geometry is the halfBPS “superstar”. We propose this as the general mechanism by which the effective thermodynamic character of gravity emerges.
Matrix models, geometric engineering and elliptic genera
, 2008
"... We compute the prepotential of N = 2 supersymmetric gauge theories in four dimensions obtained by toroidal compactifications of gauge theories from 6 dimensions, as a function of Kähler and complex moduli of T². We use three different methods to obtain this: matrix models, geometric engineering and ..."
Abstract

Cited by 66 (18 self)
 Add to MetaCart
We compute the prepotential of N = 2 supersymmetric gauge theories in four dimensions obtained by toroidal compactifications of gauge theories from 6 dimensions, as a function of Kähler and complex moduli of T². We use three different methods to obtain this: matrix models, geometric engineering and instanton calculus. Matrix model approach involves summing up planar diagrams of an associated gauge theory on T². Geometric engineering involves considering Ftheory on elliptic threefolds, and using topological vertex to sum up worldsheet instantons. Instanton calculus involves computation of elliptic genera of instanton moduli spaces on R 4. We study the compactifications of N = 2 ∗ theory in detail and establish equivalence of all these three approaches in this case. As a byproduct we geometrically engineer theories with massive adjoint fields. As one application, we show that the moduli space of mass deformed M5branes wrapped on T² combines the Kähler and complex moduli of T² String theory has been rather successful in providing insights into the dynamics of supersymmetric
Instanton counting via affine Lie algebras I: Equivariant . . .
, 2004
"... Let g be a simple complex Lie algebra, G the corresponding simply connected group; let also gaff be the corresponding untwisted affine Lie algebra. For a parabolic subgroup P ⊂ G we introduce a generating function Z aff G,P which roughly speaking counts framed Gbundles on P 2 endowed with a Pst ..."
Abstract

Cited by 63 (6 self)
 Add to MetaCart
Let g be a simple complex Lie algebra, G the corresponding simply connected group; let also gaff be the corresponding untwisted affine Lie algebra. For a parabolic subgroup P ⊂ G we introduce a generating function Z aff G,P which roughly speaking counts framed Gbundles on P 2 endowed with a Pstructure on the horizontal line (the formal definition uses the corresponding Uhlenbeck type compactifications studied in [3]). In the case P = G the function Z aff G,P coincides with Nekrasov’s partition function introduced in [23] and studied thoroughly in [24] and [22] for G = SL(n). In the ”opposite case ” when P is a Borel subgroup of G we show that Z aff G,P is equal (roughly speaking) to the Whittaker matrix coefficient in the universal Verma module for the Lie algebra ˇgaff – the Langlands dual Lie algebra of ˇg. This clarifies somewhat the connection between certain asymptotic of Z aff G,P (studied in loc. cit. for P = G) and the classical affine Toda system. We also explain why the above result gives rise to a calculation of (not yet rigorously defined) equivariant quantum cohomology ring of the affine flag manifold associated with G. In particular, we reprove the results of [13] and [18] about quantum cohomology of ordinary flag manifolds using methods which are totally different from loc. cit. We shall show in a subsequent publication how this allows one to connect certain asymptotic of the function Z aff G,P with the SeibergWitten prepotential (cf. [2], thus proving the main conjecture of [23] for an arbitrary gauge group G (for G = SL(n) it has been proved in [24] and [22] by other methods.
Algebraic methods in random matrices and enumerative geometry
, 2008
"... We review the method of symplectic invariants recently introduced to solve matrix models loop equations, and further extended beyond the context of matrix models. For any given spectral curve, one defines a sequence of differential forms, and a sequence of complex numbers Fg. We recall the definitio ..."
Abstract

Cited by 38 (9 self)
 Add to MetaCart
We review the method of symplectic invariants recently introduced to solve matrix models loop equations, and further extended beyond the context of matrix models. For any given spectral curve, one defines a sequence of differential forms, and a sequence of complex numbers Fg. We recall the definition of the invariants Fg, and we explain their main properties, in particular symplectic invariance, integrability, modularity,... Then, we give several examples of applications, in particular matrix models, enumeration of discrete surfaces (maps), algebraic geometry and topological strings, nonintersecting brownian motions,...