Pure N=2 Super Yang-Mills and Exact WKB

Abstract

We apply exact WKB methods to the study of the partition function of pure N=2 epsilon_i-deformed gauge theory in four dimensions in the context of the 2d/4d correspondence. We study the partition function at leading order in epsilon_2/epsilon_1 (i.e. at large central charge) and in an expansion in epsilon_1. We find corrections of the form ~ exp[- SW periods / epsilon_1] to this expansion. We attribute these to the exchange of the order of summation over gauge instanton number and over powers of epsilon_1 when passing from the Nekrasov form of the partition function to the topological string theory inspired form. We conjecture that such corrections should be computable from a worldsheet perspective on the partition function. Our results follow upon the determination of the Stokes graphs associated to the Mathieu equation with complex parameters and the application of exact WKB techniques to compute the Mathieu characteristic exponent.

arXiv comment44 pages, 5 figures

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Cited by in corpus (9)

• Matrix models from operators and topological strings, 2
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• Quantum Geometry of Resurgent Perturbative/Nonperturbative Relations
• Comments on Exact Quantization Conditions and Non-Perturbative Topological Strings
• Exact WKB analysis and TBA equations for the Mathieu equation
• Quantum periods for $\mathcal{N}=2$ $SU(2)$ SQCD around the superconformal point
• On Chebyshev Wells: Periods, Deformations, and Resurgence
• Quantum periods and TBA equations for $\mathcal{N}=2SU(2)N_f=2$ SQCD with flavor symmetry
• Exact Chern-Simons / Topological String duality