M-theory branes and their interactions

TL;DR

This review surveys nonperturbative M-theory brane dynamics by contrasting supergravity brane solutions with worldvolume descriptions, and by examining how membranes end on five-branes via self-dual strings. It highlights three complementary probes of degrees of freedom—entropy/thermodynamics, absorption cross sections, and anomalies—revealing characteristic scalings such as $N^{3/2}$ for membranes and $N^{3}$ for five-branes, and it discusses the Basu–Harvey construction and its generalizations for membranes ending on calibrated five-branes. A significant focus is on the membrane boundary theory, open-membrane noncommutativity, and the fuzzy funnel picture, together with proposals for nonassociative membrane theories based on 3-algebras. The article also surveys AdS/CFT perspectives, anomaly inflow mechanisms, and the ongoing quest to unify these approaches into a coherent nonperturbative M-theory framework, underscoring many open questions and potential routes forward.

Abstract

In recent years there has been some progress in understanding how one might model the interactions of branes in M-theory despite not having a fundamental perturbative description. The goal of this review is to describe different approaches to M-theory branes and their interactions. This includes: a review of M-theory branes themselves and their properties; brane interactions; the self-dual string and its properties; the role of anomalies in learning about brane systems; the recent work of Basu and Harvey with subsequent developments; and how these complimentary approaches might fit together.