N = 3 AND N = 4 SUPERCONFORMAL WZNW SIGMA MODELS IN SUPERSPACE II: THE N = 4 CASE

Abstract

The issues related to the U (1) × O (4) N = 4 superconformal WZNW sigma models [with the bosonic target spaces U (1) × SU (2) and U (1) × U (1) × O (4)] are investigated in the framework of a 2D N = 4 superspace. We define the corresponding N = 4 supercurrents, both on classical and quantum levels, in terms of the basic primary N = 4 WZNW superfields and show that the generalized Sugawara form for the dimension 3/2 and 2 component currents directly follows from the constraints on the basic superfields. The N = 4 superfield analog of the Knizhnik–Zamolodchikov equation for conformal blocks in WZNW sigma models is derived. We also analyze the N = 4 WZNW superfields from the standpoint of two SU(2) N = 4 SCAs entering as subalgebras into the underlying U (1) × O (4) N = 4 SCA. We demonstrate that in the linearizing limit the U (1) × SU (2) WZNW model reproduces the recently discussed SU(2) N = 4 superconformal system of free chiral superfields.