Towards an M5-Brane Model I: A 6d Superconformal Field Theory

TL;DR

This paper proposes a six-dimensional superconformal field theory action with a non-abelian tensor multiplet, using string Lie 2-algebra as a gauge structure, linking it to known theories and paving the way for an M5-brane model.

Contribution

It introduces a new 6d superconformal field theory action based on string Lie 2-algebra, connecting to 4d SYM and M2-brane models, advancing towards an M5-brane theory.

Findings

Reduces to 4d supersymmetric Yang--Mills for each Dynkin diagram

Deforms the ABJM model into an M2-brane model

Provides a framework for a 6d (2,0)-theory approximation

Abstract

We present an action for a six-dimensional superconformal field theory containing a non-abelian tensor multiplet. All of the ingredients of this action have been available in the literature. We bring these pieces together by choosing the string Lie 2-algebra as a gauge structure, which we motivated in previous work. The kinematical data contains a connection on a categorified principal bundle, which is the appropriate mathematical description of the parallel transport of self-dual strings. Our action can be written down for each of the simply laced Dynkin diagrams, and each case reduces to a four-dimensional supersymmetric Yang--Mills theory with corresponding gauge Lie algebra. Our action also reduces nicely to an M2-brane model which is a deformation of the ABJM model. While this action is certainly not the desired M5-brane model, we regard it as a key stepping stone towards a potential construction of the (2,0)-theory.