Holomorphic Anomaly in Gauge Theories and Matrix Models

Abstract

We use the holomorphic anomaly equation to solve the gravitational corrections to Seiberg-Witten theory and a two-cut matrix model, which is related by the Dijkgraaf-Vafa conjecture to the topological B-model on a local Calabi-Yau manifold. In both cases we construct propagators that give a recursive solution in the genus modulo a holomorphic ambiguity. In the case of Seiberg-Witten theory the gravitational corrections can be expressed in closed form as quasimodular functions of Gamma(2). In the matrix model we fix the holomorphic ambiguity up to genus two. The latter result establishes the Dijkgraaf-Vafa 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.

34 pages, 2 eps figures, expansion at the monopole point corrected and interpreted, and references added

References in corpus (1)

• Observations on the Darboux coordinates for rigid special geometry

Cited by in corpus (22)

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• Extended Holomorphic Anomaly in Gauge Theory
• Resurgent Transseries and the Holomorphic Anomaly: Nonperturbative Closed Strings in Local CP2
• Topological Strings and Quantum Spectral Problems
• Seiberg-Witten theory and matrix models
• M-theoretic matrix models
• Large $N$ Partition Functions of the ABJM Theory
• Direct Integration and Non-Perturbative Effects in Matrix Models
• Exact multi-instantons in topological string theory
• Topological Strings on Grassmannian Calabi-Yau manifolds
• Topological strings and Wilson loops
• Chiral observables and S-duality in N = 2* U(N) gauge theories
• Partition functions of non-Lagrangian theories from the holomorphic anomaly
• Relations on ${\overline{\mathcal{M}}}_{g,n}$ and the negative $r$-spin Witten conjecture
• Penner Type Ensemble for Gauge Theories Revisited
• Large N instantons from topological strings
• Taking limits in topological recursion
• Resurgence of Refined Topological Strings and Dual Partition Functions
• Resurgent Structure of the Topological String and the First Painlevé Equation
• Boson-Fermion Correspondence and Holomorphic Anomaly Equation in 2d Yang-Mills Theory on Torus
• Painlevé Kernels and Surface Defects at Strong Coupling
• Geometric Transition as a Change of Polarization