An Exact Elliptic Superpotential for N=1^* Deformations of Finite N=2 Gauge Theories

TL;DR

This paper derives an exact elliptic superpotential for N=1* deformations of finite N=2 gauge theories, revealing the vacuum structure and duality symmetries using M-theory and mirror symmetry techniques.

Contribution

It provides the first exact, modular covariant superpotential formula for these theories, connecting gauge theory vacua with integrable systems and duality symmetries.

Findings

Exact superpotential formula for N=1* deformations

Vacuum structure permuted by extended duality

Connection to elliptic Calogero-Moser integrable system

Abstract

We study relevant deformations of the N=2 superconformal theory on the world-volume of N D3 branes at an A_{k-1} singularity. In particular, we determine the vacuum structure of the mass-deformed theory with N=1 supersymmetry and show how the different vacua are permuted by an extended duality symmetry. We then obtain exact, modular covariant formulae (for all k, N and arbitrary gauge couplings) for the holomorphic observables in the massive vacua in two different ways: by lifting to M-theory, and by compactification to three dimensions and subsequent use of mirror symmetry. In the latter case, we find an exact superpotential for the model which coincides with a certain combination of the quadratic Hamiltonians of the spin generalization of the elliptic Calogero-Moser integrable system.