A nonabelian M5 brane Lagrangian in a supergravity background

TL;DR

This paper proposes a nonabelian Lagrangian for M5 branes with (2,0) superconformal symmetry that can be coupled to supergravity backgrounds, requiring a symmetry-breaking constraint involving a Killing direction.

Contribution

It introduces a novel nonabelian M5 brane Lagrangian that maintains superconformal symmetry under specific constraints and can interact with supergravity backgrounds.

Findings

Lagrangian exhibits (2,0) superconformal symmetry with constraints

Couples consistently to supergravity backgrounds

Requires symmetry breaking via a Killing direction constraint

Abstract

We present a nonabelian Lagrangian that appears to have $(2,0)$ superconformal symmetry and that can be coupled to a supergravity background. But for our construction to work, we have to break this superconformal symmetry by imposing as a constraint on top of the Lagrangian that the fields have vanishing Lie derivatives along a Killing direction.