M-theory from its superalgebra

TL;DR

The paper argues that M-theory and its Type II descendants are encoded in a single overarching superalgebra structure, extended by central charges corresponding to M-branes (M2, M5) and their bound states. It demonstrates how M-theory dualities (M-, T-, S-duality) map branes and charges into IIA/IIB configurations, and how 1/2- and 1/4-BPS states arise from constraints on gamma matrices, leading to a harmonic-function rule for intersecting branes in supergravity. The work highlights a unified framework where brane dynamics, bound states, and worldvolume solitons are consequences of algebraic and geometric structures, with broader implications for constructing supersymmetric field theories on brane intersections. It also sketches future directions, such as exploring fractions below 1/4 and the associated worldvolume theories, within this algebraic paradigm.

Abstract

These lectures explore what can be learnt about M-theory from its superalgebra. The first three lectures introduce the 'basic' branes of M-theory, and type II superstring theories, and show how the duality relations between them are encoded in the respective spacetime superalgebras. The fourth lecture introduces brane intersections and explains how they are encoded in the worldvolume superalgebras.