$U(1)$--Extended Gauge Algebras in $p$-Loop Space

TL;DR

This paper explores the gauge algebra structure for p-branes coupled to antisymmetric tensor and Yang-Mills fields, revealing a U(1) extension of the gauge algebra in p-loop space.

Contribution

It introduces a novel U(1) extension of the gauge algebra for p-branes coupled to background fields, and constructs gauge-covariant derivatives in p-loop space.

Findings

Yang-Mills generators do not form a closed algebra alone

The combined algebra is a U(1) extension of Yang-Mills algebra

Constructed gauge-covariant derivatives commute with gauge generators

Abstract

We consider, for $p$ odd, a $p$--brane coupled to a $(p+1)$th rank background antisymmetric tensor field and to background Yang-Mills (YM) fields {\it via} a Wess-Zumino term. We obtain the generators of antisymmetric tensor and Yang-Mills gauge transformations acting on $p$--brane wavefunctionals (functions on `$p$-loop space'). The Yang-Mills generators do not form a closed algebra by themselves; instead, the algebra of Yang-Mills and antisymmetric tensor generators is a $U(1)$ extension of the usual algebra of Yang-Mills gauge transformations. We construct the $p$-brane's Hamiltonian and thereby find gauge-covariant functional derivatives acting on $p$--brane wavefunctionals that commute with the YM and $U(1)$ generators.