Non-singlet Q-deformation of the [formula omitted] gauge multiplet in harmonic superspace

Abstract

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 ( i k ) ( α β ) = c ( α β ) b ( i k ) . 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 α β c α β b i k b i k ) , 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 ( i k ) b ( i k ) = 0 which preserves the N = ( 1 , 1 2 ) fraction of N = ( 1 , 1 ) supersymmetry.