The Borel-resummed quantum periods and the Fredholm determinant of the modified Mathieu operator are computed from TBA equations and topological string theory, with high-precision numerical tests against WKB and direct spectral data.
Wall Crossing and Instantons in Compactified Gauge Theory
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abstract
We calculate the leading weak-coupling instanton contribution to the moduli-space metric of N=2 supersymmetric Yang-Mills theory with gauge group SU(2) compactified on R^3 x S^1. The results are in precise agreement with the semiclassical expansion of the exact metric recently conjectured by Gaiotto, Moore and Neitzke based on considerations related to wall-crossing in the corresponding four-dimensional theory.
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Non-perturbative approaches to the quantum Seiberg-Witten curve
The Borel-resummed quantum periods and the Fredholm determinant of the modified Mathieu operator are computed from TBA equations and topological string theory, with high-precision numerical tests against WKB and direct spectral data.