M-Theory and Maximally Supersymmetric Gauge Theories

TL;DR

This paper reviews the construction of maximally supersymmetric gauge theories in string and M-Theory, emphasizing recent developments in M2-brane theories and discussing open problems related to M5-branes.

Contribution

It highlights the recent construction of M2-brane worldvolume theories and discusses the open problem of formulating the six-dimensional conformal field theory on M5-branes.

Findings

Construction of M2-brane theories supports M-Theory predictions

Discussion of the open problem of M5-brane conformal field theory

Reinforces the connection between quantum field theories and string/M-Theory

Abstract

In this informal review for non-specalists we discuss the construction of maximally supersymmetric gauge theories that arise on the worldvolumes branes in String Theory and M-Theory. Particular focus is made on the relatively recent construction of M2-brane worldvolume theories. In a formal sense, the existence of these quantum field theories can be viewed as predictions of M-Theory. Their construction is therefore a reinforcement of the ideas underlying String Theory and M-Theory. We also briefly discuss the six-dimensional conformal field theory that is expected to arise on M5-branes. The construction of this theory is not only an important open problem for M-Theory but also a significant challenge to our current understanding of quantum field theory more generally.