Non - singlet Q - deformation of the N = ( 1 , 1 ) gauge multiplet in harmonic superspace

We study a non-anticommutative chiral non-singlet deformation of the N =(1, 1) abelian gauge multiplet in Euclidean harmonic superspace with a product ansatz for the deformation matrix, C (αβ) (ik) = c (αβ) b (ik). This choice allows us to obtain in closed form the gauge transformations and the unbroken N =(1, 0) supersymmetry transformations preserving the Wess-Zumino gauge, as well as the bosonic sector of the N =(1, 0) invariant action. This should be contrasted with the generic choice for which the analogous results are known only to a few orders in the deformation parameters. As in the case of a singlet deformation, the bosonic action can be cast in a form where it differs from the free action merely by a scalar factor. The latter is now given by cosh 2 (2 ¯ φ c αβ c αβ b ik b ik) , with ¯ φ being one of two scalar fields of the N =(1, 1) vector multiplet. We compare our results with previous studies of non-singlet deformations, including the degenerate case b (ik) b (ik) = 0 which preserves the N =(1, 1 2) fraction of N =(1, 1) supersymmetry.