Lectures on Higher Structures in M-Theory

TL;DR

This paper provides an overview of higher mathematical structures in M-theory, focusing on multiple M5-branes, higher gauge theory, non-abelian superconformal theories, and higher quantization methods.

Contribution

It introduces new mathematical frameworks for describing higher gauge theories and their applications in M-theory, including global descriptions and connections to loop space.

Findings

Development of higher gauge theory structures for M5-branes

Construction of non-abelian superconformal gauge theories in six dimensions

Discussion of higher quantization and loop space relations

Abstract

These are notes for four lectures on higher structures in M-theory as presented at workshops at the Erwin Schroedinger Institute and Tohoku University. The first lecture gives an overview of systems of multiple M5-branes and introduces the relevant mathematical structures underlying a local description of higher gauge theory. In the second lecture, we develop the corresponding global picture. A construction of non-abelian superconformal gauge theories in six dimensions using twistor spaces is discussed in the third lecture. The last lecture deals with the problem of higher quantization and its relation to loop space. An appendix summarizes the relation between 3-Lie algebras and Lie 2-algebras.