M2-branes Coupled to Antisymmetric Fluxes

TL;DR

This paper explores how multiple M2-branes interact with antisymmetric fluxes, focusing on gauge invariance and tensor constraints, especially within the A_4 algebra framework, revealing new insights beyond previous matrix representations.

Contribution

It provides a detailed analysis of gauge invariance conditions and tensor constraints for M2-branes coupled to fluxes, particularly fixing tensor components in the A_4 algebra case, which was not achievable with prior cubic matrix models.

Findings

Fixed tensor components in A_4 algebra case.

Identified additional constraints from dimensional reduction.

Highlighted limitations of previous cubic matrix representations.

Abstract

By turning on antisymmetric background fluxes, we study how multiple M2-branes are coupled to them. Our investigation concentrates on the gauge invariance conditions for the Myers-Chern-Simons action. Furthermore, the dimensional reduction of M2-branes to D2-branes introduces more constraints on the newly introduced tensors. Particularly, for the theory based on A_4 algebra, we are able to fix all components of them up to an overall normalization constant. These results can not be simply obtained from the previously proposed cubic matrix representation for this algebra. We also comment on cubic matrices as the representations of 3-algebras.