HyperK\"ahler quotients and N=4 gauge theories in D=2

TL;DR

This paper explores N=4 supersymmetric gauge theories in two dimensions, demonstrating how they lead to sigma-models on HyperK"ahler manifolds via HyperK"ahler quotients, with a focus on ALE manifolds.

Contribution

It provides a detailed analysis of the connection between N=4 gauge theories and HyperK"ahler quotients, including explicit examples involving ALE manifolds.

Findings

N=4 gauge theories in D=2 can be effectively described by sigma-models on HyperK"ahler manifolds.

HyperK"ahler quotients serve as a geometric method to construct these manifolds from gauge theories.

Explicit example of ALE manifolds illustrates the theory's applicability.

Abstract

We consider certain N=4 supersymmetric gauge theories in D=2 coupled to quaternionic matter multiplets in a minimal way. These theories admit as effective theories sigma-models on non-trivial HyperK\"ahler manifolds obtained as HyperK\"ahler quotients. The example of ALE manifolds is discussed. (Based on a talk given by P. Fr\'e at the F. Gursey Memorial Conference, Istanbul, June 1994).