Twisted $sl(3, {\bf C})^{(2)}_k$ Current Algebra: Free Field Representation and Screening Currents

TL;DR

This paper constructs a free field representation of the twisted $sl(3,C)^{(2)}_k$ current algebra, including primary fields and screening currents, motivated by applications in $AdS_3$ black hole entropy.

Contribution

It provides the first explicit free field realization and screening currents for the twisted $sl(3,C)^{(2)}_k$ algebra, expanding tools for related theoretical physics applications.

Findings

Free field representation of the twisted algebra obtained

Explicit primary fields and screening currents constructed

Potential applications in $AdS_3$ black hole entropy analysis

Abstract

Motivated by applications of twisted current algebras in description of the entropy of $Ads_3$ black hole, we investigate the simplest twisted current algebra $sl(3,{\bf C})^{(2)}_k$. Free field representation of the twisted algebra and the corresponding twisted Sugawara energy-momentum tensor are obtained by using three $(\beta,\gamma)$ pairs and two scalar fields. Primary fields and two screening currents of the first kind are presented.