One-loop renormalization of generalN=12supersymmetric gauge theory

Abstract

We investigate the one-loop renormalisability of a general N = 1 2 supersymmetric gauge theory coupled to chiral matter, and show the existence of an N = 1 2 supersymmetric SU (N ) × U (1) theory which is renormalisable at one loop.

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

“…However, they do not spoil the renormalizability since they can be completely absorbed into a redefinition of the second scalar field φ. This situation is very similar to the N = (1/2, 0) gauge model studied in [18], where it was shown that the nonanticommutative interaction also generates new terms in the effective action which can be eliminated from the theory by a shift of the gaugino field. Third, we demonstrate that the appropriate change of fields in the classical actions (a Seiberg-Witten-like map) [6,7] allows one to completely avoid any divergence in the effective action.…”

“…But due to lacking of the propagator φφ , no loops with such vertices can be constructed. This situation is completely analogous to the N = (1/2, 0) SYM model considered in [18] where it was demonstrated that the quantum computations in this model generate the divergent terms which are not present in the classical action, but these extra divergencies can be removed by a simple shift of the gaugino field (the lowest component in N = (1, 1) gauge multiplet). In our case the divergencies can also be removed by the shift of lowest component of N = (1, 1) gauge multiplet (scalar field).…”

“…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].…”

Gauged Wess–Zumino model in noncommutative Minkowski superspace

“…Secondly, there are numerous papers investigating N = 1/2 supersymmetry [15]- [43] and it would be interesting to find complementary results for the N = 0 case where possible. We could try to find the dual results for, instantons as in [16]- [21], or renormalization as in [22]- [29] , or the possibility of residual supersymmetry as in [30], or the Seiberg Witten map as in [31]. We do not attempt to give a complete account of the N = 1/2 developments, we just wish to point out the variety of novel directions future research might take.…”

Gauge theory in deformed % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfKttLearuqr1ngBPrgarmWu51MyVXgatC % vAUfeBSjuyZL2yd9gzLbvyNv2CaeHbd9wDYLwzYbItLDharyavP1wz % ZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbb % L8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaqpe % pae9pg0FirpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaaiaabeqaam % aaeaqbaaGcbaWefv3ySLgznfgDOfdarCqr1ngBPrginfgDObYtUvga % iyaacqWFneVtaaa!4628! $$ \mathcal{N} $$ = (1, 1) superspace

“…These theories possess a number of attractive properties. For example, it was established in [15,16,17,18,19] that the N =1/2 supersymmetric Wess-Zumino model and the N =1/2 supersymmetric gauge theory inherit the renormalizability of their undeformed prototypes. In the Lagrangians of these models, non-anticommutative deformations (1.3) give rise to additional terms polynomial in the deformation parameters C αβ .…”