A renormalizableN= 1/2 SYM theory with interacting matter

Abstract

We consider nonanticommutative SYM theories with chiral matter in the adjoint representation of the SU(N ) ⊗ U(1) gauge group. In a superspace setup and manifest background covariant approach we investigate the one-loop renormalization of the theory when a cubic superpotential is present. The structure of the divergent terms reveals that the theory simply obtained from the ordinary one by trading products for star products is not renormalizable. Moreover, because of the different renormalization undergone by the abelian field compared to the non-abelian ones, the superpotential seems to be incompatible with the requests of renormalizability, gauge and N = 1/2 invariance. However, by a suitable modification of the quadratic action for the U(1) (anti)chiral superfields and the addition of extra couplings, we find an action which is one-loop renormalizable and manifestly N = 1/2 supersymmetric and supergauge invariant. We conclude that interacting matter can be safely introduced in NAC gauge theories, in contrast with previous results.

The role of field redefinition on renormalisability of a generalN=12supersymmetric gauge theories

“…Therefore, one should modify the classical superspace Lagrangian (1) because these terms are not obtained from the original superfield action (1). This point is consistent with results [19][20][21]. They have modified the classical action (1) in order to have one-loop renormalisable theory.…”

“…On the other hand, the authors in [19][20][21] started from the superspace formalism and discussed renormalisability and supergauge invariance. They have argued that suitable deformations of the classical actions are necessary in order to achieve renormalisability at one loop level [19].…”

A renormalisable non-anticommutative supersymmetric SU(N)⊗U(1) gauge theory in components

“…The authors of Ref. [33] worked in superspace; our purpose here is to confirm that a similar procedure can be carried out in the component formalism.…”

“…The problem is that the potential part of the classical action contains terms with different combinations of SU(N) and U(1) chiral fields which mix under N = 1 2 supersymmetry, but for which the Yukawa couplings renormalise differently, at least in the simplest version of the theory. However, recently an elegant solution to this problem has been proposed [33] in which the kinetic terms for the U(1) chiral fields are modified, in such a way that the SU(N) and U(1) chiral fields (and consequently their Yukawa couplings) renormalise in exactly the same way. The authors of Ref.…”

One-loop renormalizable Wess-Zumino model on a bosonic-fermionic noncommutative superspace

“…Moreover, the super Yang-Mills in NAC superspace has been constructed in ref. [26][27][28][29][30][31], we shall explore the super Yang-Mills model on the BFNC superspace and search for its renormalizable formulation by following the way we have utilized for the Wess-Zumino model.…”