A renormalizable N=1/2 SYM theory with interacting matter

Abstract

We consider nonanticommutative SYM theories with chiral matter in the adjoint representation of the SU(N) x 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.

LaTex, 38 pages, 3 figures

References in corpus (27)

• String Theory and Noncommutative Geometry
• Non-commutative superspace from string theory
• Noncommutative Superspace, N=1/2 Supersymmetry, Field Theory and String Theory
• Non(anti)commutative Superspace
• Some Aspects of Deformations of Supersymmetric Field Theories
• Comments on Noncommutative Superspace
• N=1/2 Wess-Zumino model is renormalizable
• Two-loop Renormalization for Nonanticommutative N=1/2 Supersymmetric WZ Model
• Deformed Superspace, N=1/2 Supersymmetry and (Non)Renormalization Theorems
• Supersymmetry in noncommutative superspaces
• Renormalizability of N=1/2 Wess-Zumino model in superspace
• Nilpotent deformations of N=2 superspace
• Renormalizability of Non(anti)commutative Gauge Theories with N=1/2 Supersymmetry
• Non-anticommutative N=2 super-Yang-Mills theory with singlet deformation
• Wilsonian Proof for Renormalizability of N=1/2 Supersymmetric Field Theories
• Non(anti)commutative Superspace, UV/IR Mixing & Open Wilson Lines
• Non-anticommutative chiral singlet deformation of N=(1,1) gauge theory
• N=1/2 gauge theory and its instanton moduli space from open strings in R-R background
• One-Loop Perturbative Corrections to non(anti)commutativity Parameter of N=1/2 Supersymmetric U(N) Gauge Theory
• One-loop renormalisation of N=1/2 supersymmetric gauge theory
• Covariant quantization of N=1/2 SYM theories and supergauge invariance
• One-loop renormalisation of general N=1/2 supersymmetric gauge theory
• Non(anti)commutative SYM theory: Renormalization in superspace
• Nonanticommutative superspace and N= 1/2 WZ model
• One-loop renormalisation of N=1/2 supersymmetric gauge theory with a superpotential
• The non-anticommutative supersymmetric Wess-Zumino model
• Renormalizability of non-anticommutative N=(1,1) theories with singlet deformation

Cited by in corpus (7)

• D-deformed Wess-Zumino model and its renormalizability properties
• Nonanticommutative U(1) SYM theories: Renormalization, fixed points and infrared stability
• A renormalisable non-anticommutative SU(N)xU(1) gauge theory in components
• Twisted SUSY: twisted symmetry versus renormalizability
• Renormalisation of the non-anticommutativity parameter at two loops
• One-Loop Renormalizable Wess-Zumino Model on Bosonic-Fermionic Noncommutative Superspace
• The role of field redefinition on renormalisability of a general $N=\frac{1}{2}$ supersymmetric gauge theories