Gauged Wess–Zumino model in noncommutative Minkowski superspace

Abstract

We develop a gauged Wess-Zumino model in noncommutative Minkowski superspace. This is the natural extension of the work of Carlson and Nazaryan, which extended N = 1/2 supersymmetry written over deformed Euclidean superspace to Minkowski superspace. We investigate the interaction of the vector and chiral superfields. Noncommutativity is implemented by replacing products with star products. Although, in general, our star product is nonassociative, we prove that it is associative to the first order in the deformation parameter C. We show that our model reproduces the N = 1/2 theory in the appropriate limit, namely when the deformation parametersCαβ = 0. Essentially, we find the N = 1/2 theory and a conjugate copy. As in the N = 1/2 theory, a reparameterization of the gauge parameter, vector superfield and chiral superfield are necessary to write standard C-independent gauge theory. However, our choice of parameterization differs from that used in the N = 1/2 supersymmetry, which leads to some unexpected new terms.a similar paper has been submitted to JHEP testbetter@yahoo.com 1

Noncommutativity and Non-Anticommutativity Perturbative Quantum Gravity

“…The RR background in string theory leads to a non-anticommutative gauge theory [10]- [13]. Thus, many models based on non-anticommutative gauge theory have also been studied [14]- [15]. Similarly, in analogy with noncommutative case, a superconformal non-anticommutative gauge theory on the boundary of anti-de Sitter spacetime will be dual to non-anticommutative gravity in the bulk of that anti-de Sitter spacetime.…”

Cryptoreality of nonanticommutative Hamiltonians

“…[3,4] and references therein), the deformation is performed in Euclidean rather than Minkowski space-time. The reason is that in Minkowski space it seems impossible to preserve both supersymmetry and reality of the action after deformation, still retaining simple properties of the corresponding ⋆-product (e.g., associativity and nilpotency) [5]. As discussed in [1], Euclidean NAC theories are of interest in stringy perspectives 2 .…”

Supersymmetric Duality in Deformed Superloop Space

“…Such noncommutative deformation of ordinary field theories has motivated the study of non-anticommutative deformation of supersymmetric field theories [5]- [6]. The non-anticommutative deformation of supersymmetric gauge theories has also been studied [7]- [8]. In this deformation, the Grassmann coordinate of a superspace are promoted to non-anticommutating coordinates.…”