Topic
Topological string theory
About: Topological string theory is a research topic. Over the lifetime, 1206 publications have been published within this topic receiving 54758 citations.
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TL;DR: In this paper, the authors study mass-deformed N = 2 gauge theories from various points of view, including (p, q)-brane webs in type II string theory using Nekrasov's instanton calculus, (refined) topological string using the topological vertex formalism and M theory via the elliptic genus of certain M-strings configurations.
Abstract: We study mass-deformed N = 2 gauge theories from various points of view. Their partition functions can be computed via three dual approaches: firstly, (p,q)-brane webs in type II string theory using Nekrasov's instanton calculus, secondly, the (refined) topological string using the topological vertex formalism and thirdly, M theory via the elliptic genus of certain M-strings configurations. We argue for a large class of theories that these approaches yield the same gauge theory partition function which we study in detail. To make their modular properties more tangible, we consider a fourth approach by connecting the partition function to the equivariant elliptic genus of ℂ2 through a (singular) theta-transform. This form appears naturally as a specific class of one-loop scattering amplitudes in type II string theory on T2, which we calculate explicitly.
77 citations
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TL;DR: In this paper, the authors analyze the N = 2 dual pair of string theories in four dimensions introduced by Ferrara, Harvey, Strominger and Vafa and show that a second discrete degree of freedom must be switched on in addition to the known Wilson line to achieve a nonperturbatively consistent theory.
76 citations
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TL;DR: In this paper, a systematic formulation of the higher genus expansion in topological string theory is considered and a simple way of evaluating genus zero correlation functions is developed for higher genera.
Abstract: A systematic formulation of the higher genus expansion in topological string theory is considered. We also develop a simple way of evaluating genus zero correlation functions. At higher genera we derive some interesting formulas for the free energy in the A1 and A2 models. We present some evidence that topological minimal models associated with Lie algebras other than the A-D-E type do not have a consistent higher genus expansion beyond genus one. We also present some new results on the CP1 model at higher genera.
76 citations
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TL;DR: In this article, it was shown that the Laplace transform of the counting functions satisfies the Eynard-Orantin topological recursion, and that the B-model partition function satisfies the KP equations.
Abstract: It is predicted that the principal specialization of the partition function of a B-model topological string theory, that is mirror dual to an A-model enumerative geometry problem, satisfies a Schroedinger equation, and that the characteristic variety of the Schroedinger operator gives the spectral curve of the B-model theory, when an algebraic K-theory obstruction vanishes. In this paper we present two concrete mathematical A-model examples whose mirror dual partners exhibit these predicted features on the B-model side. The A-model examples we discuss are the generalized Catalan numbers of an arbitrary genus and the single Hurwitz numbers. In each case, we show that the Laplace transform of the counting functions satisfies the Eynard-Orantin topological recursion, that the B-model partition function satisfies the KP equations, and that the principal specialization of the partition function satisfies a Schroedinger equation whose total symbol is exactly the Lagrangian immersion of the spectral curve of the Eynard-Orantin theory.
76 citations
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TL;DR: An examination of the Schwinger - Dyson equations of U(n) lattice Yang-Mills theory as mentioned in this paper shows that this theory is exactly equivalent to a theory of strings that interact with one another only through their topology.
75 citations