WZW in the lightlike directions

TL;DR

This paper explores the dimensional reduction of M5 branes along lightlike directions, revealing a six-dimensional gauge theory with anomalies that can be canceled by a WZW model in two lightlike dimensions.

Contribution

It introduces a covariant reformulation of the reduced gauge theory and demonstrates anomaly cancellation via a WZW model in lightlike directions.

Findings

The six-dimensional gauge theory exhibits gauge anomalies on certain Lorentzian manifolds.

Adding a WZW theory in lightlike directions cancels the gauge anomaly.

The reformulation provides insights into lightlike dimensional reductions and anomaly cancellation.

Abstract

Dimensional reduction of the M5 brane on a Lorentzian manifold along a lightlike direction results in a five-dimensional gauge theory, which can be reformulated covariantly in six dimensions, where one puts the Lie derivatives along the lightlike direction of all fields to zero as constraints. Without imposing these constraints, we have a nonsupersymmetric six-dimensional gauge theory that we may expect shall have a six dimensional gauge symmetry. However this gauge symmetry has an anomaly for certain Lorentzian six-manifolds. We show that this gauge anomaly can be canceled by adding a WZW theory in the 2d space that is spanned by two lightlike directions.