Five-dimensional gauge theory and compactification on a torus

TL;DR

This paper investigates a five-dimensional supersymmetric gauge theory compactified on a torus, analyzing its moduli space, instanton corrections, and string theory embeddings, revealing new insights into its geometric and quantum properties.

Contribution

It provides a detailed computation of the moduli space metric, instanton effects, and their string theory interpretations, advancing understanding of 5D gauge theories on compact spaces.

Findings

One-loop corrections to the moduli space metric are explicitly computed.

Instanton corrections are interpreted as worldsheet and D1-brane effects in string theory.

Partition functions of M5 branes and N=4 SYM are used to analyze zero-mode path integrals.

Abstract

We study five-dimensional minimally supersymmetric gauge theory compactified on a torus down to three dimensions, and its embedding into string/M-theory using geometric engineering. The moduli space on the Coulomb branch is hyperkaehler equipped with a metric with modular transformation properties. We determine the one-loop corrections to the metric and show that they can be interpreted as worldsheet and D1-brane instantons in type IIB string theory. Furthermore, we analyze instanton corrections coming from the solitonic BPS magnetic string wrapped over the torus. In particular, we show how to compute the path-integral for the zero-modes from the partition function of the M5 brane, or, using a 2d/4d correspondence, from the partition function of N=4 SYM theory on a Hirzebruch surface.