Dimensional reduction of M5 branes

Andreas Gustavsson

doi:10.1103/physrevd.105.046010

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.

Highlights

There is a supersymmetric (2,0) Abelian tensor multiplet in R1;5 which has a self-dual three-form, five scalar fields and four real Weyl fermionic fields
If the supersymmetry parameter is constant along the circle, it will survive as a supersymmetry under dimensional reduction
Χ and ζ form two components in an SUð2ÞR Majorana spinor which is a zero mode spinor upon dimensional reduction with an R-gauge field turned on and the mass of these fermions is induced from that R-gauge field in the six-dimensional theory

Summary

INTRODUCTION

There is a supersymmetric (2,0) Abelian tensor multiplet in R1;5 which has a self-dual three-form, five scalar fields and four real Weyl fermionic fields. There can be exceptions where a truncated non-Abelian generalization can be found that is supersymmetric This argument shows that the critical term to analyze in the supersymmetry variation of the non-Abelian Lagrangian will be the terms that are cubic in the fermionic fields. In Appendix A we review a 6d formulation of non-Abelian 5d SYM where one introduces an auxiliary geometrical vector field [4,5,6] and present the closure relations that one gets for these supersymmetry variations and it was this analysis that originally led us to consider the two examples that we are presenting in this paper These two examples are following from making the two Weyl projections in Eqs.

The small vector multiplet

A dual description with an R-gauge field

NULL REDUCTION

DISCUSSION

A RST ðA1Þ

A MNP φA