Dimensional reduction of M5 branes

TL;DR

This paper investigates the dimensional reduction of M5 branes on circle bundles, focusing on supersymmetry preservation with non-constant parameters, and explores conditions for non-Abelian generalizations, especially along null directions.

Contribution

It provides a method to obtain supersymmetric five-dimensional theories from M5 branes with non-constant supersymmetry parameters, highlighting conditions for non-Abelian extensions.

Findings

Abelian case yields supersymmetric 5D theories with nonzero fermionic modes.

Non-Abelian supersymmetric reduction is possible only under specific circumstances.

Null direction reduction admits a non-Abelian supersymmetric generalization.

Abstract

We study dimensional reduction of M5 branes on a circle bundle when the supersymmetry parameter is not constant along the circle. When the gauge group is Abelian and the fields appear quadratically in the Lagrangian, we can always obtain a supersymmetric five-dimensional theory by keeping fermionic nonzero modes that match with the corresponding nonzero modes of the supersymmetry parameter, and by keeping the zero modes for the bosonic fields as usual. But a supersymmetric non-Abelian generalization can be found only under special circumstances. One instance where we find a non-Abelian supersymmetric generalization is when we perform dimensional reduction along a null direction.