Non(anti)commutative SYM theory: Renormalization in superspace

Abstract

We present a systematic investigation of one-loop renormalizability for nonanticommutative N=1/2, U(N) SYM theory in superspace. We first discuss classical gauge invariance of the pure gauge theory and show that in contradistinction to the ordinary anticommutative case, different representations of supercovariant derivatives and field strengths do not lead to equivalent descriptions of the theory. Subsequently we develop background field methods which allow us to compute a manifestly covariant gauge effective action. One-loop evaluation of divergent contributions reveals that the theory simply obtained from the ordinary one by trading products for star products is not renormalizable. In the case of SYM with no matter we present a N=1/2 improved action which we show to be one-loop renormalizable and which is perfectly compatible with the algebraic structure of the star product. For this action we compute the beta functions. A brief discussion on the inclusion of chiral matter is also presented.

Latex file, 59 pages, 10 figures, One reference added

References in corpus (30)

• Noncommutative Perturbative Dynamics
• 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
• Superstrings in Graviphoton Background and N=1/2+3/2 Supersymmetry
• Comments on Noncommutative Superspace
• Supersymmetric Gauge Theories 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
• Wilsonian Proof for Renormalizability of N=1/2 Supersymmetric Field Theories
• Non(anti)commutative Superspace, UV/IR Mixing & Open Wilson Lines
• N=1/2 gauge theory and its instanton moduli space from open strings in R-R background
• Drinfeld-Twisted Supersymmetry and Non-Anticommutative Superspace
• One-loop renormalisation of N=1/2 supersymmetric gauge theory
• Covariant quantization of N=1/2 SYM theories and supergauge invariance
• N=1/2 quiver gauge theories from open strings with R-R fluxes
• One-loop renormalisation of general N=1/2 supersymmetric gauge theory
• Non-Anti-Commutative deformation of effective potentials in supersymmetric gauge theories
• Chiral effective potential in $\mathcal{N}=1/2$ non-commutative Wess-Zumino model
• Generic chiral superfield model on nonanticommutative N=1/2 superspace
• Nonanticommutative Deformation of N=4 SYM Theory: The Myers Effect and Vacuum States
• Chiral Models in Noncommutative N=1/2 Four Dimensional Superspace
• Construction of the effective action in nonanticommutative supersymmetric field theories
• Renormalisation of supersymmetric gauge theory in the uneliminated component formalism

Cited by in corpus (22)

• On quantum properties of the four-dimensional generic chiral superfield model
• One-loop renormalisation of N=1/2 supersymmetric gauge theory with a superpotential
• The non-anticommutative supersymmetric Wess-Zumino model
• Non-singlet Q-deformed N=(1,0) and N=(1,1/2) U(1) actions
• A renormalizable N=1/2 SYM theory with interacting matter
• D-deformed Wess-Zumino model and its renormalizability properties
• AdS/CFT Duality for Non-Anticommutative Supersymmetric Gauge Theory
• The non-anticommutative supersymmetric U(1) gauge theory
• One-loop divergences in the two-dimensional non-anticommutative supersymmetric sigma-model
• Supersymmetric Nambu$-$Jona-Lasinio Model on $\mathcal{N}=1/2$ four-dimensional Non(anti)commutative Superspace
• Nonanticommutative U(1) SYM theories: Renormalization, fixed points and infrared stability
• N=1/2 Supersymmetric gauge theory in noncommutative space
• A renormalisable non-anticommutative SU(N)xU(1) gauge theory in components
• Vector-multiplet effective action in the non-anticommutative charged hypermultiplet model
• Twisted SUSY: twisted symmetry versus renormalizability
• Twisted Supersymmetry in a Deformed Wess-Zumino Model in (2+1) Dimensions
• Renormalisation of the non-anticommutativity parameter at two loops
• Comments on the role of field redefinition on renormalisation of $N=\frac{1}{2}$ supersymmetric pure gauge theory
• One-Loop Renormalizable Wess-Zumino Model on Bosonic-Fermionic Noncommutative Superspace
• On the alternative formulation of the three-dimensional noncommutative superspace
• The role of field redefinition on renormalisability of a general $N=\frac{1}{2}$ supersymmetric gauge theories
• Noncommutative $\mathcal{N}=2$ Chern-Simons-matter model