Non-singlet Q-deformation of the 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 (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 (2φ c αβ c αβ b ik b ik ) , withφ 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.1 A more complete list of references can be found e.g. in [12].

Non-singlet Q-deformed N=(1,0) and N=(1Castro1, Quevedo2 2006Physics Letters BSelf Cite8000View full textAdd to dashboardCite

“…For the pure bosonic case [15] we found a closed from of the action using (2.7) and moreover, we were able to redefine the fields in such a way that the Lagrangian took a particular factorized form cosh 2 (2φ…”

“…In the sequel, we use all conventions in [15]. Note that all operators are left derivations unless explicitly stated.…”

“…Therefore, implementing (2.9), the supersymmetry is broken down to N = (1, 1/2) recovering the 1/4 fraction generated byQ 2α . The exact expressions for non-singlet gauge and supersymmetric transformations for the U(1) vector multiplet with (2.9) were first constructed in [18], where the authors also constructed the N = (1, 1/2) invariant action in components to first order in the deformation C. In [15] we constructed the bosonic action using the maximally space-time and R-symmetry preserving parameters in (2.7) for the generic case and with b ij restricted to…”

“…It remains to solve the coupled system of equations (3.8), plug the solutions into (3.4) and integrate in the harmonic variables using the list of integrals in Appendix B of [15]. Due to the complexity of this calculation, it was performed with help of a symbolic algebra computer package, resulting into a very lengthy action in components which for our further analysis is not necessary to present here.…”

“…From the corresponding gauge variations we directly propose the minimal Seiberg-Witten like map which take us back to the standard form of the gauge transformations. In [15] we obtained the full set of exact variations, they are …”