One-loop perturbative corrections to non(anti)commutativity parameter of supersymmetric U(N) gauge theory

Abstract

Perturbative corrections to N = 1 2 supersymmetric U (N ) gauge theory at one-loop order are studied. It is shown that whereas the quantum corrections to N = 1 sector of the theory are not affected by the C-deformation, the non(anti)commutativity parameter C receives one-loop perturbative corrections. These perturbative corrections are computed by performing an explicit one-loop calculation of the three and four-point functions of the theory. The running of the non(anti)commutativity parameter C is also studied using an appropriate Callan-Symanzik equation.1 alishah@theory.ipm.ac.ir 2 ahmad@theory.ipm.ac.ir 3 sadooghi@theory.ipm.ac.ir V (y, θ,θ) = −θσ µθ A µ + iθθθλ − iθθθ α λ α +

One-loop renormalisation of N=1/2 supersymmetric gauge theory

“…We shall try to give sufficient details of our calculations in order to enable the interested reader to check them. The one-loop calculation of the divergences in pure N = 1 2 gauge theory has been performed before [7] but we disagree with this result as we shall explain. The original non-anticommutative theory defined in superfields appears to require a U (N ) gauge group [2] [3].…”

A renormalizableN= 1/2 SYM theory with interacting matter

“…The same analysis can be carried on also for deformed gauge theories (a first attempt can be found in [15]). In [16], for SU(N ) ⊗ U(1) SYM theory with massive chiral matter in the adjoint representation of the gauge group we have found a general action for the pure gauge sector which is N = 1/2 supergauge invariant and one-loop renormalizable.…”

On renormalizability of non-anticommutativeN=(1, 0) theories with singlet deformation

“…For example, for the non-anticommutative Wess-Zumino model it was shown that only a single new divergent term should be added to the classical action, and the model where such an extra term is added from the very beginning is renormalizable in the usual sense [12,13,14,15]. The non-anticommutative super Yang-Mills model was also proved to be renormalizable using component field formulations [15,16,17,18] and superspace techniques [19]. Note that, in N = (1/2, 0) gauge theories, quantum computations in components also produce new field structures which are not present in the classical action but, in contrast to the Wess-Zumino model, can be removed from the effective action by a simple shift of the gaugino field [18].…”