M-Brane Models and Loop Spaces

TL;DR

This paper explores how loop spaces naturally arise in M-brane models, extending monopole constructions to M-branes and translating M5-brane models into loop space, revealing new geometric insights.

Contribution

It extends the ADHMN monopole construction to M-brane models and demonstrates the natural appearance of loop spaces in these theories.

Findings

Extended the ADHMN construction to M-brane models

Mapped solutions from Basu-Harvey to self-dual string equations in loop space

Translated M5-brane models into loop space, revealing geometric structures

Abstract

I review an extension of the ADHMN construction of monopoles to M-brane models. This extended construction gives a map from solutions to the Basu-Harvey equation to solutions to the self-dual string equation transgressed to loop space. Loop spaces appear in fact quite naturally in M-brane models. This is demonstrated by translating a recently proposed M5-brane model to loop space. Finally, I comment on some recent developments related to the loop space approach to M-brane models.