Differential operator realizations of superalgebras and free field representations of corresponding current algebras

TL;DR

This paper constructs explicit differential operator and free field representations of certain superalgebras and their current algebras, providing tools for studying their structure and applications in theoretical physics.

Contribution

It introduces new explicit differential operator realizations and free field representations for the superalgebras osp(2r|2n) and osp(2r+1|2n), including energy-momentum tensors and screening currents.

Findings

Explicit differential operator representations for osp(2r|2n) and osp(2r+1|2n)

Free field realizations of corresponding current superalgebras at arbitrary level

Construction of energy-momentum tensors and screening currents

Abstract

Based on the particular orderings introduced for the positive roots of finite dimensional basic Lie superalgebras, we construct the explicit differential operator representations of the $osp(2r|2n)$ and $osp(2r+1|2n)$ superalgebras and the explicit free field realizations of the corresponding current superalgebras $osp(2r|2n)_k$ and $osp(2r+1|2n)_k$ at an arbitrary level $k$. The free field representations of the corresponding energy-momentum tensors and screening currents of the first kind are also presented.