Higher Structures, Self-Dual Strings and 6d Superconformal Field Theories: LMS/EPSRC Durham Symposium on Higher Structures in M-Theory

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 (Formula presented.) -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.