Exact WKB Analysis of N = 2 Gauge Theories

TL;DR

This paper applies exact WKB analysis to N=2 SU(2) gauge theories, deriving differential equations from conformal field theory, and explores their monodromy and Stokes phenomena in relation to Seiberg-Witten data.

Contribution

It provides a novel exact WKB framework for analyzing N=2 gauge theories and connects monodromy data with Seiberg-Witten theory using Borel resummation.

Findings

Confirmed differential equations via saddle-point analysis.

Computed monodromy groups from deformed Seiberg-Witten data.

Linked Borel resummed monodromies with traditional variables.

Abstract

We study N = 2 supersymmetric gauge theories with gauge group SU(2) coupled to fundamental flavours, covering all asymptotically free and conformal cases. We re-derive, from the conformal field theory perspective, the differential equations satisfied by omega deformed instanton partition functions. We confirm their validity at leading order in one of the deformation parameters via a saddle-point analysis of the partition function. In the semi-classical limit we show that these differential equations take a form amenable to exact WKB analysis. We compute the monodromy group associated to the differential equations in terms of deformed and Borel resummed Seiberg-Witten data. For each case, we study pairs of Stokes graphs that are related by flips and pops, and show that the monodromy groups allow one to confirm the Stokes automorphisms that arise as the phase of the deformation parameter is varied. Finally, we relate the Borel resummed monodromies with the traditional Seiberg-Witten variables in the semi-classical limit.