Superfield covariant analysis of the divergence structure of noncommutative supersymmetric QED${}_4$

Abstract

Commutative supersymmetric Yang-Mills is known to be renormalizable for $\mathcal{N}=1,2$, while finite for $\mathcal{N}=4$. However, in the noncommutative version of the model (NCSQED${}_4$) the UV/IR mechanism gives rise to infrared divergences which may spoil the perturbative expansion. In this work we pursue the study of the consistency of NCSQED${}_4$ by working systematically within the covariant superfield formulation. In the Landau gauge, it has already been shown for $\mathcal{N}=1$ that the gauge field two-point function is free of harmful UV/IR infrared singularities, in the one-loop approximation. Here we show that this result holds without restrictions on the number of allowed supersymmetries and for any arbitrary covariant gauge. We also investigate the divergence structure of the gauge field three-point function in the one-loop approximation. It is first proved that the cancellation of the leading UV/IR infrared divergences is a gauge invariant statement. Surprisingly, we have also found that there exist subleading harmful UV/IR infrared singularities whose cancellation only takes place in a particular covariant gauge. Thus, we conclude that these last mentioned singularities are in the gauge sector and, therefore, do not jeopardize the perturbative expansion and/or the renormalization of the theory.

arXiv comment36 pages, 11 figures. Minor corrections

References in corpus (26)

• String Theory and Noncommutative Geometry
• Noncommutative Field Theory
• Quantum Field Theory on Noncommutative Spaces
• Noncommutative Perturbative Dynamics
• The IR/UV Connection in the Non-Commutative Gauge Theories
• Perturbative analysis on infrared aspects of noncommutative QED on R^4
• Testing Non-commutative QED, Constructing Non-commutative MHD
• Perturbative analysis on infrared and ultraviolet aspects of noncommutative QED on R^4
• Comments on Perturbative Dynamics of Non-Commutative Yang-Mills Theory
• Some Aspects of Deformations of Supersymmetric Field Theories
• Gauge-fixing independence of IR divergences in non-commutative U(1), perturbative tachyonic instabilities and supersymmetry
• Noncommutative SO(n) and Sp(n) Gauge Theories
• Renormalization of noncommutative U(N) gauge theories
• UV/IR Mixing via Closed Strings and Tachyonic Instabilities
• A Consistent Noncommutative Field Theory: the Wess-Zumino Model
• Noncommutative $\mathcal{N}=1,2$ super U(N) Yang-Mills: UV/IR mixing and effective action results at one loop
• Noncommutative Quantum Field Theories
• Noncommutative perturbation in superspace
• The Three-Dimensional Noncommutative Nonlinear Sigma Model in Superspace
• The one-loop effective action of noncommutative {\cal N}=4 super Yang-Mills is gauge invariant
• Superfield Effective Action in the Noncommutative Wess-Zumino Model
• Spontaneous Symmetry Breaking in Noncommutative Field Theory
• One-loop four-point function in noncommutative {\cal N}=4 Yang-Mills theory
• Non-commutative U(1) Super-Yang-Mills Theory: Perturbative Self-Energy Corrections
• Interacting Dipoles from Matrix Formulation of Noncommutative Gauge Theories
• UV-IR mixing and the quantum consistency of noncommutative gauge theories

Cited by in corpus (27)

• Gravitational signatures of a non--commutative stable black hole
• Thermodynamics and evaporation of a modified Schwarzschild black hole in a non--commutative gauge theory
• Towards a consistent noncommutative supersymmetric Yang-Mills theory: superfield covariant analysis
• Effects of non-commutative geometry on black hole properties
• Quantum duality under the theta-exact Seiberg-Witten map
• Noncommutative Maxwell-Chern-Simons theory in three dimensions and its dual
• Equivalence of quantum field theories related by the theta-exact Seiberg-Witten map
• Geodesics, accretion disk, gravitational lensing, time delay, and effects on neutrinos induced by a non-commutative black hole
• Properties of an axisymmetric Lorentzian non-commutative black hole
• Noncommutative Correction to the Aharonov-Bohm Scattering: a Field Theory Approach
• On the consistency of the three-dimensional noncommutative supersymmetric Yang-Mills theory
• Non-commutativity in Hayward spacetime
• On the finiteness of the noncommutative supersymmetric Maxwell-Chern-Simons theory
• The coupling of fermions to the three-dimensional noncommutative $C{P}^{N-1}$ model: minimal and supersymmetric extensions
• Lorentz symmetry breaking in the noncommutative Wess-Zumino model: One loop corrections
• Inferring the covariant $\Theta$-exact noncommutative coupling in the top quark pair production at linear colliders
• A Review of Noncommutative Field Theories
• Super Yang-Mills and theta-exact Seiberg-Witten map: Absence of quadratic noncommutative IR divergences
• Non-commutative Duality: High Spin Fields and $C{P}^1$ Model with Hopf Term
• $C{P}^{(N-1)}$ model in aether-superspace
• Slavnov-Taylor identities for noncommutative QED${}_4$
• N=1/2 Supersymmetric gauge theory in noncommutative space
• Quasinormal modes and greybody factor of charged black hole in non-commutative geometry
• Axisymmetric black hole in a non-commutative gauge theory: classical and quantum gravity effects
• Thermostatistical analysis and negative heat capacities of Yukawa and Lee-Wick potentials in noncommutative phase spaces
• Asymptotic Expansions of Feynman Amplitudes in a Generic Covariant Gauge
• Noncommutative Theories, Seiberg-Witten Map and Gravity