N=2 supersymmetric Yang-Mills theories and Whitham integrable hierarchies

TL;DR

This paper explores the connection between N=2 super Yang-Mills theories and Whitham hierarchies, introducing new computational methods, interpretations of hierarchy times, and constraints on strong coupling expansions.

Contribution

It develops a recursive method for instanton expansion, interprets hierarchy times as couplings, and derives constraints on strong coupling behavior in N=2 super Yang-Mills theories.

Findings

New recursive method for instanton expansion

Interpretation of hierarchy times as couplings

Constraints on strong coupling expansions near singularities

Abstract

We review recent work on the study of N=2 super Yang-Mills theory with gauge group SU(N) from the point of view of the Whitham hierarchy, mainly focusing on three main results: (i) We develop a new recursive method to compute the whole instanton expansion of the low-energy effective prepotential; (ii) We interpret the slow times of the hierarchy as additional couplings and promote them to spurion superfields that softly break N=2 supersymmetry down to N=0 through deformations associated to higher Casimir operators of the gauge group; (iii) We show that the Seiberg-Witten-Whitham equations provide a set of non-trivial constraints on the form of the strong coupling expansion in the vicinity of the maximal singularities. We use them to check a proposal that we make for the value of the off-diagonal couplings at those points of the moduli space.