D-branes and fractional instantons on a twisted four torus: the moduli space as an N=2 supersymmetric Higgs branch

TL;DR

This paper investigates self-dual instantons with fractional topological charge in SU(N) Yang-Mills theory on a twisted four torus, using D-brane embeddings to analyze their moduli space as an N=2 supersymmetric Higgs branch.

Contribution

It constructs a brane-based parameterization of the instanton moduli space with manifest hyper-K"ahler structure, simplifying previous field theory approaches.

Findings

Identifies the local moduli space with the Higgs branch of an N=2 supersymmetric theory.

Provides a hyper-K"ahler parameterization of the moduli space.

Suggests a path to understanding the global structure of instanton moduli spaces.

Abstract

We study self-dual instantons of topological charge $Q=r/N$, for any natural $r$, in $SU(N)$ Yang-Mills theory on a four torus with 't Hooft twists, by embedding them into worldvolume theories of $D$-branes. To study their moduli, we construct the wrapped intersecting brane configurations dual to general constant field strength instanton backgrounds. We show that, locally, the moduli space is identified with the Higgs branch of an $N=2$ supersymmetric theory. This parameterization of the moduli space is equivalent to one recently found in field theory, but is obtained with significantly less effort and has manifest hyper-K\" ahler structure. Our hope is that combining different perspectives on instantons on the twisted torus will help understand the still unknown global structure of the moduli space for general solutions with $Q=r/N$ as well as the nature of instantons with all moduli turned on -- when some $Q<1$ and all $Q \ge 1$ instantons become space-time dependent. For integer $Q$, these are expected to match the ADHM solution in an appropriately taken infinite volume limit.