Results 11  20
of
131
A holomorphic and background independent partition function for matrix models and topological strings
, 2009
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Holomorphic anomaly in gauge theories and matrix models
, 2006
"... We use the holomorphic anomaly equation to solve the gravitational corrections to SeibergWitten theory and a twocut matrix model, which is related by the DijkgraafVafa conjecture to the topological Bmodel on a local CalabiYau manifold. In both cases we construct propagators that give a recursiv ..."
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Cited by 36 (12 self)
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We use the holomorphic anomaly equation to solve the gravitational corrections to SeibergWitten theory and a twocut matrix model, which is related by the DijkgraafVafa conjecture to the topological Bmodel on a local CalabiYau manifold. In both cases we construct propagators that give a recursive solution in the genus modulo a holomorphic ambiguity. In the case of SeibergWitten theory the gravitational corrections can be expressed in closed form as quasimodular functions of Γ(2). In the matrix model we fix the holomorphic ambiguity up to genus two. The latter result establishes the DijkgraafVafa conjecture at that genus and yields a new method for solving the matrix model at fixed genus in closed form in terms of generalized hypergeometric functions.
Derivation of CalabiYau crystals from ChernSimons gauge theory
 JHEP
"... We derive new crystal melting models from ChernSimons theory on the threesphere. Via large N duality, these models compute amplitudes for Amodel on the resolved conifold. The crystal is bounded by two walls whose distance corresponds to the Kähler modulus of the geometry. An interesting phenomeno ..."
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Cited by 34 (3 self)
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We derive new crystal melting models from ChernSimons theory on the threesphere. Via large N duality, these models compute amplitudes for Amodel on the resolved conifold. The crystal is bounded by two walls whose distance corresponds to the Kähler modulus of the geometry. An interesting phenomenon is found where the Kähler modulus is shifted by the presence of noncompact Dbranes. We also discuss the idea of using the crystal models as means of proving more general large N dualities to all Topological string theory [1, 2] is currently undergoing a drastic paradigm change. Reshetikhin, Okounkov, and Vafa [3] realized that various amplitudes for topological A model on C 3 can be expressed in terms of classical statistical models of a melting crystal. Iqbal, Nekrasov, and Vafa [4] proposed to interpret the crystals in terms of
Unquenched flavor and tropical geometry in strongly coupled Chern–Simons–matter theories
, 2011
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Exact Results for Wilson Loops in Superconformal ChernSimons Theories with Matter
, 909
"... Abstract: We use localization techniques to compute the expectation values of supersymmetric Wilson loops in ChernSimons theories with matter. We find the pathintegral reduces to a nonGaussian matrix model. The Wilson loops we consider preserve a single complex supersymmetry, and exist in any N = ..."
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Cited by 29 (0 self)
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Abstract: We use localization techniques to compute the expectation values of supersymmetric Wilson loops in ChernSimons theories with matter. We find the pathintegral reduces to a nonGaussian matrix model. The Wilson loops we consider preserve a single complex supersymmetry, and exist in any N = 2 theory, though the localization requires superconformal symmetry. We present explicit results for the cases of pure ChernSimons theory with gauge group U(N), showing agreement with the known results, and ABJM, showing agreement with perturbative calculations. Our method applies to other theories, such as GaiottoWitten theories, BLG, and their variants.
Matrix Models, Integrable Structures, and Tduality of Type 0 String Theory
"... Instanton matrix models (IMM) for two dimensional string theories are obtained from the matrix quantum mechanics (MQM) of the Tdual theory. In this paper we study the connection between the IMM and MQM, which amounts to understand Tduality from the viewpoint of matrix models. We show that type 0A ..."
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Cited by 27 (0 self)
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Instanton matrix models (IMM) for two dimensional string theories are obtained from the matrix quantum mechanics (MQM) of the Tdual theory. In this paper we study the connection between the IMM and MQM, which amounts to understand Tduality from the viewpoint of matrix models. We show that type 0A and type 0B matrix models perturbed by purely closed string momentum modes (or purely winding modes) have the integrable structure of Toda hierarchies, extending the well known results for c = 1 string. In particular, we show that type 0A(0B) MQM perturbed by momentum modes has the same integrable structure as type 0B(0A) MQM perturbed by winding modes, which is a nontrivial check of the Tduality between the matrix models. The MQM deformed by NSNS winding modes are used to study type 0 string in 2D black holes. We also find an intriguing connection between the IMM and the MQM via tachyon condensation. The array of alternating Dinstantons and antiDinstantons separated at the critical distance plays a key role in this picture. We discuss its implications on sDbranes in two dimensional
Nonperturbative effects and the refined topological string
, 2013
"... The partition function of ABJM theory on the threesphere has nonperturbative corrections due to membrane instantons in the Mtheory dual. We show that the full series of membrane instanton corrections is completely determined by the refined topological string on the Calabi–Yau manifold known as lo ..."
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Cited by 23 (7 self)
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The partition function of ABJM theory on the threesphere has nonperturbative corrections due to membrane instantons in the Mtheory dual. We show that the full series of membrane instanton corrections is completely determined by the refined topological string on the Calabi–Yau manifold known as local P1 × P1, in the Nekrasov–Shatashvili limit. Our result can be interpreted as a firstprinciples derivation of the full series of nonperturbative effects for the closed topological string on this Calabi–Yau background. Based on this, we make a proposal for the nonperturbative free energy of topological strings on general, local Calabi–Yau manifolds.