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].
We employ the non-linear realization techniques to relate the N = 1 chiral, and the N = 2 vector multiplets to the Goldstone spin 1/2 superfield arising from partial supersymmetry breaking of N = 2 and N = 3 respectively. In both cases, we obtain a family of non-linear transformation laws realizing an extra supersymmetry. In the N = 2 case, we find an invariant action which is the low energy limit of the supersymmetric Born-Infeld theory expected to describe a D3-brane in six dimensions.
We define a noncommutative and nonanticommutative associative product for general supersymplectic forms, allowing the explicit treatment of non(anti)commutative field theories from general nonconstant string backgrounds like a graviphoton field. We propose a generalization of deformation quantizationà la Fedosov to superspace, which considers noncommutativity in the tangent bundle instead of base space, by defining the Weyl super product of elements of Weyl super algebra bundles. Super Poincaré symmetry is not broken and chirality seems not to be compromised in our formulation. We show that, for a particular case, the projection of the Weyl super product to the base space gives rise the Moyal product for non(anti)commutative theories.
In this paper we construct N = (1, 0) and N = (1, 1/2) non-singlet Q-deformed supersymmetric U(1) actions in components. We obtain an exact expression for the enhanced supersymmetry action by turning off particular degrees of freedom of the deformation tensor. We analyze the behavior of the action upon restoring weekly some of the deformation parameters, obtaining a non trivial interaction term between a scalar and the gauge field, breaking the supersymmetry down to N = (1, 0).Additionally, we present the corresponding set of unbroken supersymmetry transformations. We work in harmonic superspace in four Euclidean dimensions.
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