Quantum gauge theories on noncommutative 3-d space

Abstract

We consider a class of gauge invariant models on the noncommutative space ${\mathbb{R}}_{\lambda }^3$, a deformation of ${\mathbb{R}}^3$. Focusing on massless models with no linear $A_i$ dependence, we obtain noncommutative gauge models for which the computation of the propagator can be done in a convenient gauge. We find that the infrared singularity of the massless propagator disappears in the computation of the correlation functions. We show that massless gauge invariant models on ${\mathbb{R}}_{\lambda }^3$ have quantum instabilities of the vacuum, signaled by the occurrence of non vanishing 1-point functions for some but not all of the components of the gauge potential. The tadpole contribution to the effective action cannot be interpreted as a standard $\sigma$-term. Its global symmetry does not fit with the one of the classical action, reminiscent to an explicit global symmetry breaking term.

31 pages. Section 2 modified with two new subsections about derivations of the algebra and the integration measure. References added

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• Matrix Bases for Star Products: a Review
• Exact Partition Functions for Gauge Theories on ${\mathbb{R}}_{\lambda }^3$
• Noncommutative gauge theories on ${\mathbb{R}}_{\lambda }^3$: Perturbatively finite models
• Thermodynamics of Quantum Phase Transitions of a Dirac oscillator in a homogenous magnetic field
• Seiberg-Witten map and quantum phase effects for neutral Dirac particle on noncommutatiave plane
• A novel approach to non-commutative gauge theory
• Four-Dimensional Gravity on a Covariant Noncommutative Space (II)
• Involutive representations of coordinate algebras and quantum spaces
• Twisted BRST symmetry in gauge theories on $\kappa$-Minkowski
• Vacuum energy and the cosmological constant problem in $\kappa$-Poincaré invariant field theories
• $\mathcal{P}\mathcal{T}$-symmetric quantum field theory on the noncommutative spacetime
• Lie-Poisson gauge theories and $\kappa$-Minkowski electrodynamics
• Gravity as a Gauge Theory on Three-Dimensional Noncommutative spaces
• Derivation based differential calculi for noncommutative algebras deforming a class of three dimensional spaces
• The Gribov problem in Noncommutative gauge theory
• Quantum instability of gauge theories on $\kappa$-Minkowski space
• Field theories on $\rho$-deformed Minkowski space-time
• Poisson electrodynamics on $\kappa$-Minkowski space-time
• Two-particle system in Coulomb potential for twist-deformed space-time
• Spectral theorem in noncommutative field theories: Jacobi dynamics
• Quantum spaces, central extensions of Lie groups and related quantum field theories
• Complex (super)-matrix models with external sources and $q$-ensembles of Chern-Simons and ABJ(M) type
• Four-dimensional noncommutative deformations of $U(1)$ gauge theory and $L_{\infty }$ bootstrap