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

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.