Deformed solitons in a 2-dimensional non(anti)commutative Wess-Zumino model

In this paper we examine a deformation of the 1/2 BPS kink solitons of a WZ model with a cubic superpotential in two Euclidean dimensions caused by introducing non(anti)commutativity in the superspace formulation of the theory. The spacetime Lagrangian of the deformed model consists of the ordinary WZ terms plus corrections in the form of a kinetic and a cubic term for the auxiliary field, both in proportion to the determinant of the non(anti)commutativity parameters Cαβ. We compute the correction to the 'orbit' equation, relating the auxiliary and the scalar fields together, and subsequently derive the modifications to the BPS equation and to its solution up to first order in λ≡det(Cαβ). We give a description of the deformed solitons in terms of the 1/2 BPS states of an effective N=1 supersymmetric non-linear σ-model in two dimensions, using which we derive the first-order correction to the BPS mass formula for these solitons.