On explicit free field realizations of current algebras

TL;DR

This paper constructs explicit free field representations for various current algebras, providing detailed formulas for energy-momentum tensors and screening currents, which are essential for understanding their structure and applications.

Contribution

It introduces explicit free field realizations for $so(2n)_k$, $so(2n+1)_k$, and $sp(2n)_k$ current algebras, including energy-momentum tensors and screening currents.

Findings

Explicit free field representations derived for multiple current algebras

Formulas for energy-momentum tensors in free field form

Screening currents of the first kind explicitly constructed

Abstract

We construct the explicit free field representations of the current algebras $so(2n)_k$, $so(2n+1)_k$ and $sp(2n)_k$ for a generic positive integer $n$ and an arbitrary level $k$. The corresponding energy-momentum tensors and screening currents of the first kind are also given in terms of free fields.