N=1 super-WZW and N=1, 2, 3, 4 super-KdV models as D=2 current superfield theories

Abstract

We consider the D=2 classical supercurrent field theories with fundamental Poisson-Lie brackets describing the N=1 Kac-Moody (KM) superalgebra and N=1, 2, 3, 4 Virasoro (V) superalgebras in terms of superfields. The most general local supercurrent hamiltonians, with three-current term for the N=1 KM and N=2 V superalgebras, and four-current term for the N=4 V superalgebra are proposed. We obtain the N=1 supersymmetric extension of the classical WZW model and N=1, 2, 3, 4 supersymmetric extensions of KdV equations. The existence of the N=2 KM superalgebra is also discussed.