Whitham Deformations and Tau Functions in N = 2 Supersymmetric Gauge Theories

TL;DR

This paper explores the relationship between integrable systems, Whitham deformations, and tau functions in N=2 supersymmetric gauge theories, revealing new mathematical structures and their implications for topologically twisted theories.

Contribution

It provides an explicit construction of Whitham deformations of Seiberg-Witten curves and links tau functions to the blowup formula in topologically twisted theories.

Findings

Explicit Whitham deformation construction for classical gauge groups

Application to contact terms in the u-plane integral

Connection between tau functions and blowup formulas

Abstract

We review new aspects of integrable systems discovered recently in N=2 supersymmetric gauge theories and their topologically twisted versions. The main topics are (i) an explicit construction of Whitham deformations of the Seiberg-Witten curves for classical gauge groups, (ii) its application to contact terms in the u-plane integral of topologically twisted theories, and (iii) a connection between the tau functions and the blowup formula in topologically twisted theories.