Current Algebra of Super WZNW Models

TL;DR

This paper derives the current algebra structure of supersymmetric principal chiral models with a Wess-Zumino term, revealing a quadratic algebra with intertwining fields connecting right and left sectors, extending known bosonic results.

Contribution

It introduces the supersymmetric extension of the current algebra, showing the emergence of a quadratic algebra and the role of intertwining fields in connecting sectors.

Findings

At the critical point, two commuting super Kac-Moody algebras are obtained.

In general, the algebra is quadratic due to boson-fermion mixing.

Intertwining fields connect right and left sectors in the supersymmetric model.

Abstract

We derive the current algebra of supersymmetric principal chiral models with a Wess-Zumino term. At the critical point one obtains two commuting super Kac-Moody algebra as expected, but in general there are intertwining fields connecting both right and left sectors, analogously to the bosonic case. Moreover, in the present supersymmetric extension we have a quadratic algebra, rather than an affine Lie algebra, due to the mixing between bosonic and fermionic fields since the purely fermionic sector displays a Lie algebra as well.