Chern-Simons Forms, Mickelsson-Faddeev Algebras and the P-Branes

TL;DR

This paper explores the mathematical structures underlying p-branes in string theory, linking Chern-Simons forms to Mickelsson-Faddeev algebras, and generalizing known string theory results to higher-dimensional objects.

Contribution

It introduces a generalization of the Kac-Moody algebra to Mickelsson-Faddeev algebra for p-branes with odd p, extending the mathematical framework of string theory.

Findings

Establishes a connection between Chern-Simons terms and algebraic structures in p-branes.

Generalizes the algebraic framework from strings to higher-dimensional p-branes.

Provides insights into gauge invariance and algebraic relations in string theory and p-branes.

Abstract

In string theory, nilpotence of the BRS operator $\d$ for the string functional relates the Chern-Simons term in the gauge-invariant antisymmetric tensor field strength to the central term in the Kac-Moody algebra. We generalize these ideas to p-branes with odd p and find that the Kac-Moody algebra for the string becomes the Mickelsson-Faddeev algebra for the p-brane.