M5 branes on $\mathbb{R}^{1,1} \times$Taub-NUT

TL;DR

This paper investigates M5 branes on a singular Taub-NUT space, resolving gauge anomalies and supersymmetry issues by introducing a 2d gauged chiral WZW theory and mass terms, resulting in a consistent 2d effective theory.

Contribution

It presents a novel method to restore supersymmetry and gauge invariance in the 5d theory derived from M5 branes on a singular fibration by adding a 2d gauged WZW model and mass terms.

Findings

Successfully cancels gauge anomaly.

Restores supersymmetry in the effective theory.

Provides a consistent framework for M5 branes on singular spaces.

Abstract

We study M5 branes on $\mathbb{R}^{1,1} \times$Taub-NUT that we view as a singular fibration. Reducing the M5 branes along the fiber gives 5d SYM. Due to the singularity, this 5d theory has a gauge anomaly and it is not supersymmetric. To cure these problems we add a supersymmetric gauged chiral WZW theory on the 2d submanifold where the circle fiber vanishes. In addition we add a mass term for the five scalar fields located on this submanifold. With all this, we obtain a fully supersymmetric and gauge invariant theory.