Higher-Dimensional Loop Algebras, Non-Abelian Extensions and p-Branes

TL;DR

This paper introduces a novel non-abelian operator algebra that generalizes known algebras in string theory to higher-dimensional p-branes, enabling new mathematical tools like BRST operators and curvature tensors in extended loop spaces.

Contribution

It presents a new algebraic framework for p-branes extending Kac--Moody and Mickelsson--Faddeev algebras, along with associated operators in higher-dimensional loop spaces.

Findings

Development of a new non-abelian algebra for p-branes

Construction of BRST operators in higher dimensions

Formulation of covariant derivatives and curvature tensors

Abstract

We postulate a new type of operator algebra with a non-abelian extension. This algebra generalizes the Kac--Moody algebra in string theory and the Mickelsson--Faddeev algebra in three dimensions to higher-dimensional extended objects ($p$-branes). We then construct new BRST operators, covariant derivatives and curvature tensors in the higher-dimensional generalization of loop space.