# The conformal current algebra on supergroups with applications to the spectrum and integrability - High Energy Physics - Theory

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Abstract: We compute the algebra of left and right currents for a principal chiralmodel with arbitrary Wess-Zumino term on supergroups with zero Killing form. Wedefine primary fields for the current algebra that match the affine primariesat the Wess-Zumino-Witten points. The Maurer-Cartan equation together withcurrent conservation tightly constrain the current-current and current-primaryoperator product expansions. The Hilbert space of the theory is generated byacting with the currents on primary fields. We compute the conformal dimensionsof a subset of these states in the large radius limit. The current algebra isshown to be consistent with the quantum integrability of these models toseveral orders in perturbation theory.

Author: ** Raphael Benichou, Jan Troost**

Source: https://arxiv.org/