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

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.