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142
Matrix Model as a Mirror of ChernSimons Theory
, 2002
"... Using mirror symmetry, we show that ChernSimons theory on certain manifolds such as lens spaces reduces to a novel class of Hermitian matrix models, where the measure is that of unitary matrix models. We show that this agrees with the more conventional canonical quantization of ChernSimons theory. ..."
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Cited by 131 (24 self)
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Using mirror symmetry, we show that ChernSimons theory on certain manifolds such as lens spaces reduces to a novel class of Hermitian matrix models, where the measure is that of unitary matrix models. We show that this agrees with the more conventional canonical quantization of ChernSimons theory. Moreover, large N dualities in this context lead to computation of all genus Amodel topological amplitudes on toric CalabiYau manifolds in terms of matrix integrals. In the context of type IIA superstring compactifications on these CalabiYau manifolds with wrapped D6 branes (which are dual to Mtheory on G2 manifolds) this leads to engineering and solving Fterms for N = 1 supersymmetric gauge theories with superpotentials involving certain multitrace operators
Lectures on localization and matrix models in Supersymmetric Chern–simons–matter Theories
, 2012
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Soft matrix models and ChernSimons partition functions,” Mod
 Phys. Lett. A
, 2004
"... Abstract. We study the properties of matrix models with soft confining potentials. Their precise mathematical characterization is that their weight function is not determined by its moments. Relying on simple considerations from the moment problem and orthogonal polynomials, we show general features ..."
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Cited by 41 (14 self)
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Abstract. We study the properties of matrix models with soft confining potentials. Their precise mathematical characterization is that their weight function is not determined by its moments. Relying on simple considerations from the moment problem and orthogonal polynomials, we show general features of their density of states, correlation functions and loop averages. Some examples are worked out in detail. In addition, some of these models are equivalent, by a simple mapping, to matrix models that have appeared recently in connection with ChernSimons theory. The models can be solved with q deformed orthogonal polynomials (StieltjesWigert polynomials), and the deformation parameter turns out to be the usual q parameter in ChernSimons theory. In this way, we give a matrix model computation of the ChernSimons partition function on S 3 and show that there are an infinite number of matrix models with this partition function. 1.
A holomorphic and background independent partition function for matrix models and topological strings
, 2009
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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