Six-Dimensional (1,0) Superconformal Models and Higher Gauge Theory

TL;DR

This paper explores the gauge structure of a six-dimensional superconformal field theory, revealing its relation to higher gauge theory and describing its algebraic underpinnings like weak Courant-Dorfman and homotopy Lie algebras.

Contribution

It identifies the gauge structure as a weak Courant-Dorfman algebra and links it to higher gauge theory, providing new insights into the algebraic framework of superconformal models.

Findings

Gauge structure is a weak Courant-Dorfman algebra.

Superconformal theory relates to higher gauge theory.

Examples include Lie 2-algebras and differential crossed modules.

Abstract

We analyze the gauge structure of a recently proposed superconformal field theory in six dimensions. We find that this structure amounts to a weak Courant-Dorfman algebra, which, in turn, can be interpreted as a strong homotopy Lie algebra. This suggests that the superconformal field theory is closely related to higher gauge theory, describing the parallel transport of extended objects. Indeed we find that, under certain restrictions, the field content and gauge transformations reduce to those of higher gauge theory. We also present a number of interesting examples of admissible gauge structures such as the structure Lie 2-algebra of an abelian gerbe, differential crossed modules, the 3-algebras of M2-brane models and string Lie 2-algebras.