On the D(-1)/D7-brane systems

TL;DR

This paper investigates non-perturbative effects in 8D supersymmetric U(N) gauge theories using D(-1)/D7-brane systems with fluxes, deriving the open string action, analyzing the moduli space, and computing instanton corrections that depend on the background geometry.

Contribution

It provides an explicit string construction of the open string action, links the vacua to generalized ADHM moduli, and shows how instanton sums relate to solid partitions in specific backgrounds.

Findings

Instanton corrections depend on the curved background and vanish in flat space.

The open string moduli space corresponds to generalized ADHM gauge connections.

In certain backgrounds, instanton partition functions sum over weighted solid partitions.

Abstract

We study non-perturbative effects in supersymmetric U(N) gauge theories in eight dimensions realized by means of D(-1)/D7-brane systems with non-trivial world-volume fluxes turned on. Using an explicit string construction in terms of vertex operators, we derive the action for the open strings ending on the D(-1)-branes and exhibit its BRST structure. The space of vacua for these open strings is shown to be in correspondence with the moduli space of generalized ADHM gauge connections which trigger the non-perturbative corrections in the eight-dimensional theory. These corrections are computed via localization and turn out to depend on the curved background used to localize the integrals on the instanton moduli space, and vanish in flat space. Finally, we show that for specific choices of the background the instanton partition functions reduce to weighted sums of the solid partitions of the integers.