The u ( 2 | 2 ) 1 WZW model

Abstract

WZW models based on super Lie algebras play an important role for the description of string theory on AdS spaces. In particular, for the case of AdS 3 × S 3 with pure NS-NS flux the super Lie algebra of psu ( 1 , 1 | 2 ) k appears in the hybrid formalism, and higher dimensional AdS spaces can be described in terms of related supergroup cosets. In this paper we study the WZW models based on u ( 2 | 2 ) 1 and psu ( 2 | 2 ) 1 that may play a role for the worldsheet theory that is dual to free super Yang-Mills in 4D.