New Derivation of Off-Shell Representations of the Multi-dimensional Affine and Virasoro Algebras

TL;DR

This paper simplifies the derivation of off-shell representations of multi-dimensional affine and Virasoro algebras using standard operator product expansion methods and a more accessible formalism.

Contribution

It introduces a clearer, more field-like approach to deriving off-shell representations of these complex algebras, improving accessibility and understanding.

Findings

Simplified derivation of algebra representations

Use of standard OPE methods

More accessible formalism

Abstract

Algebras of currents and diffeomorphisms in arbitrary dimension have extensions which generalize the affine and Virasoro algebras on the circle. A large class of off-shell representations was discovered in Comm. Math. Phys. 214 (2000) 469--491. That paper is not so accessible due to a slightly non-standard normal ordering formalism and cumbersome $p$-jet calculations. The purpose of the present paper is to simplify the derivation using standard OPE methods and a more field-like formalism.