Higher Structures, Self-Dual Strings and 6d Superconformal Field Theories

TL;DR

This paper explores the formulation of six-dimensional superconformal field theories using higher gauge theory, introducing non-Abelian self-dual string equations and a related action that shares features with the (2,0)-theory.

Contribution

It presents a mathematically consistent non-Abelian extension of self-dual string equations and formulates a 6d action using higher gauge groups and string structures.

Findings

Non-Abelian self-dual string equations satisfy physical expectations

A 6d action similar to (2,0)-theory is constructed

Higher gauge theory provides a consistent framework

Abstract

I summarize and discuss some recent results on formulating actions of six-dimensional superconformal field theories using the language of higher gauge theory. The latter guarantees mathematical consistency of our constructions and we review crucial aspects of this framework, such as $L_\infty$-algebras and corresponding kinematical data given by higher connections. We then show that there is a mathematically consistent non-Abelian extension of the self-dual string equation which satisfies many physical expectations. Our construction favors a particular higher gauge group leading us to higher principal bundles known as string structures. Using these, we manage to formulate a six-dimensional action which shares many properties with the famous $(2,0)$-theory but also still differs from it in some key points.