Whitham Hierarchies, Instanton Corrections and Soft Supersymmetry Breaking in N=2 SU(N) Super Yang-Mills Theory

TL;DR

This paper connects Whitham hierarchies with instanton corrections in N=2 SU(N) super Yang-Mills theory, introducing a recursive method for instanton expansion and exploring supersymmetry breaking via hierarchy times.

Contribution

It introduces a new recursive approach to compute instanton expansions using theta functions and links hierarchy times to supersymmetry breaking mechanisms.

Findings

Explicit one and two-instanton corrections for SU(N)

Hierarchy times can be promoted to spurion superfields

Analysis of the SU(3) case in detail

Abstract

We study N=2 super Yang-Mills theory with gauge group SU(N) from the point of view of the Whitham hierarchy. We develop a new recursive method to compute the whole instanton expansion of the prepotential using the theta function associated to the root lattice of the group. Explicit results for the one and two-instanton corrections in SU(N) are presented. Interpreting the slow times of the hierarchy as additional couplings, we show how they can be promoted to spurion superfields that softly break N=2 supersymmetry down to N=0. This provides a family of nonsupersymmetric deformations of the theory, associated to higher Casimir operators of the gauge group. The SU(3) theory is analyzed in some detail.