Superalgebras from $p$-brane actions

TL;DR

This paper explores the structure of superalgebras related to p-branes, revealing how anomalous terms modify supertranslation algebra and how gauge freedom leads to a spectrum of conserved charge algebras, generalizing known superstring superalgebras.

Contribution

It introduces a cohomological framework for superalgebras of p-branes, incorporating gauge freedom and fermionic charges to generalize existing superstring superalgebras.

Findings

Superalgebras contain anomalous terms described by double complex cohomology.

A spectrum of conserved charge algebras arises with free parameters.

The framework generalizes known superstring superalgebras.

Abstract

Two superalgebras associated with $p$-branes are the constraint algebra and the Noether charge algebra. Both contain anomalous terms which modify the standard supertranslation algebra. These anomalous terms have a natural description in terms of double complex cohomology of generalized forms. By retaining fermionic charges and allowing for gauge freedom in the double complex, it is shown that the algebra of conserved charges forms a spectrum with free parameters. The spectrum associated with the Green-Schwarz superstring is shown to contain and generalize the known superalgebras associated with the superstring.