Localization of Gauged Linear Sigma Model for KK5-branes

TL;DR

This paper investigates the quantum properties of the gauged linear sigma model's target space for KK5-branes, revealing instanton effects depend on the Taub-NUT space's asymptotic radius, using supersymmetric localization.

Contribution

It provides an exact sphere partition function for GLSM of KK5-branes and analyzes instanton effects related to the Taub-NUT geometry.

Findings

Instanton contributions vanish when the asymptotic radius is non-zero.

The sphere partition function is computed exactly using localization.

World-sheet instanton effects are characterized in the KK5-brane background.

Abstract

We study quantum aspects of the target space of the non-linear sigma model which is a low-energy effective theory of the gauged linear sigma model (GLSM). As such, we especially compute the exact sphere partition function of GLSM for KK$5$-branes whose background geometry is a Taub-NUT space, using the supersymmetric localization technique on the Coulomb branch. From the sphere partition function, we distill the world-sheet instanton effects. In particular, we show that concerning the single-centered Taub-NUT space, the instanton contributions exist only if the asymptotic radius of the $S^1$ fiber in the Taub-NUT space is zero.