Covariant Mickelsson-Faddeev extensions of gauge and diffeomorphism algebras

TL;DR

This paper introduces new algebraic extensions related to gauge and diffeomorphism symmetries in higher dimensions, expanding the mathematical framework for understanding these structures in theoretical physics.

Contribution

It constructs novel extensions of current and diffeomorphism algebras in dimensions greater than three, aligning with existing classifications and incorporating higher Casimir operators.

Findings

New extensions of current and diffeomorphism algebras in N>3 dimensions.

Compatibility with Dzhumadil'daev's classification of cocycles.

Extension depending on the fourth Casimir operator in N>=5 dimensions.

Abstract

We construct new extensions of current and diffeomorphism algebras in N>3 dimensions, which are related to the Mickelsson-Faddeev algebra. The result is compatible with Dzhumadil'daev's classification of diffeomorphism cocycles. We also construct an extension of the current algebra in N>=5 dimensions which depends on the fourth Casimir operator.