Symmetries of P-Branes

TL;DR

This paper investigates the symmetry properties of bosonic p-branes in curved backgrounds, focusing on gauge invariances, the role of form fields, and the potential for infinite-dimensional symmetry algebras.

Contribution

It constructs generators for gauge transformations and explores the possibility of Kac-Moody-like symmetries for p-branes in curved spaces.

Findings

Constructed Yang-Mills and tensor gauge transformation generators.

Identified the role of (p+1)-form in cancelling Schwinger terms.

Discussed the existence of infinite-dimensional symmetry algebras.

Abstract

Using canonical methods, we study the invariance properties of a bosonic $p$--brane propagating in a curved background locally diffeomorphic to $M\times G$, where $M$ is spacetime and $G$ a group manifold. The action is that of a gauged sigma model in $p+1$ dimensions coupled to a Yang--Mills field and a $(p+1)$--form in $M$. We construct the generators of Yang-Mills and tensor gauge transformations and exhibit the role of the $(p+1)$--form in cancelling the potential Schwinger terms. We also discuss the Noether currents associated with the global symmetries of the action and the question of the existence of infinite dimensional symmetry algebras, analogous to the Kac-Moody symmetry of the string.