Nonanticommutative U(1) SYM theories: Renormalization, fixed points and infrared stability

Abstract

Renormalizable nonanticommutative SYM theories with chiral matter in the adjoint representation of the gauge group have been recently constructed in [arXiv:0901.3094]. In the present paper we focus on the U*(1) case with matter interacting through a cubic superpotential. For a single flavor, in a superspace setup and manifest background covariant approach we perform the complete one-loop renormalization and compute the beta-functions for all couplings appearing in the action. We then generalize the calculation to the case of SU(3) flavor matter with a cubic superpotential viewed as a nontrivial NAC generalization of the ordinary abelian N=4 SYM and its marginal deformations. We find that, as in the ordinary commutative case, the NAC N=4 theory is one-loop finite. We provide general arguments in support of all-loop finiteness. Instead, deforming the superpotential by marginal operators gives rise to beta-functions which are in general non-vanishing. We study the spectrum of fixed points and the RG flows. We find that nonanticommutativity always makes the fixed points unstable.

1+30 pages, 5 figures

References in corpus (41)

• Deforming field theories with $U(1)\times U(1)$ global symmetry and their gravity duals
• Exactly Marginal Operators and Duality in Four Dimensional N=1 Supersymmetric Gauge Theory
• 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
• Non(anti)commutative Superspace, UV/IR Mixing & Open Wilson Lines
• Wilsonian Proof for Renormalizability of N=1/2 Supersymmetric Field Theories
• 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 renormalisation of N=1/2 supersymmetric gauge theory
• Covariant quantization of N=1/2 SYM theories and supergauge invariance
• On nonanticommutative N=2 sigma-models in two dimensions
• Conformal invariance of the planar beta-deformed N=4 SYM theory requires beta real
• One-loop renormalisation of general N=1/2 supersymmetric gauge theory
• Non(anti)commutative SYM theory: Renormalization in superspace
• D=2, N=2 Supersymmetric sigma models on Non(anti)commutative Superspace
• The three-dimensional non-anticommutative superspace
• Real versus complex beta-deformation of the N=4 planar super Yang-Mills theory
• Nonanticommutative superspace and N= 1/2 WZ model
• Quantum Corrections in 2D SUSY CP^{N-1} Sigma Model on Noncommutative Superspace
• N=2 sigma model Action on Non(anti)commutative Superspace
• The non-anticommutative supersymmetric Wess-Zumino model
• Nonanticommutative Deformation of N=4 SYM Theory: The Myers Effect and Vacuum States
• One-loop renormalisation of N=1/2 supersymmetric gauge theory with a superpotential
• Conformal Invariance = Finiteness and Beta Deformed N=4 SYM Theory
• Renormalizability of non-anticommutative N=(1,1) theories with singlet deformation
• One-loop renormalisation of massive N=1/2 supersymmetric gauge theory
• A renormalizable N=1/2 SYM theory with interacting matter
• One-loop divergences in the two-dimensional non-anticommutative supersymmetric sigma-model
• The non-anticommutative supersymmetric U(1) gauge theory
• Non-anticommutative solitons

Cited by in corpus (4)

• All-Loop Renormalizable Wess-Zumino Model on Bosonic-Fermionic Noncommutative Superspace
• A renormalisable non-anticommutative SU(N)xU(1) gauge theory in components
• Renormalisation of the non-anticommutativity parameter at two loops
• One-Loop Renormalizable Wess-Zumino Model on Bosonic-Fermionic Noncommutative Superspace