The conformal current algebra on supergroups with applications to the spectrum and integrability

TL;DR

This paper derives the current algebra structure for supergroup principal chiral models with Wess-Zumino terms, exploring their primary fields, operator product expansions, and connections to quantum integrability.

Contribution

It introduces a detailed current algebra framework for supergroup models with zero Killing form, linking classical constraints to quantum integrability.

Findings

Current algebra consistent with quantum integrability

Computed conformal dimensions in large radius limit

Defined primary fields matching affine primaries at WZW points

Abstract

We compute the algebra of left and right currents for a principal chiral model with arbitrary Wess-Zumino term on supergroups with zero Killing form. We define primary fields for the current algebra that match the affine primaries at the Wess-Zumino-Witten points. The Maurer-Cartan equation together with current conservation tightly constrain the current-current and current-primary operator product expansions. The Hilbert space of the theory is generated by acting with the currents on primary fields. We compute the conformal dimensions of a subset of these states in the large radius limit. The current algebra is shown to be consistent with the quantum integrability of these models to several orders in perturbation theory.