Noncommutative gauge theories on ${\mathbb{R}}_{\theta }^2$ as matrix models

Abstract

We study a class of noncommutative gauge theory models on 2-dimensional Moyal space from the viewpoint of matrix models and explore some related properties. Expanding the action around symmetric vacua generates non local matrix models with polynomial interaction terms. For a particular vacuum, we can invert the kinetic operator which is related to a Jacobi operator. The resulting propagator can be expressed in terms of Chebyschev polynomials of second kind. We show that non vanishing correlations exist at large separations. General considerations on the kinetic operators stemming from the other class of symmetric vacua, indicates that only one class of symmetric vacua should lead to fast decaying propagators. The quantum stability of the vacuum is briefly discussed.

22 pages. References and subsections added. Discussion in Section 4 improved

References in corpus (18)

• Algebras of distributions suitable for phase-space quantum mechanics. I
• Vanishing of Beta Function of Non Commutative ${\Phi }_4^4$ Theory to all orders
• Noncommutative Induced Gauge Theory
• Algebras of distributions suitable for phase-space quantum mechanics. II. Topologies on the Moyal algebra
• Induced Gauge Theory on a Noncommutative Space
• Vacuum configurations for renormalizable non-commutative scalar models
• Emergent Gravity, Matrix Models and UV/IR Mixing
• On the vacuum states for noncommutative gauge theory
• Noncommutative field theories on $R_{\lambda }^3$: Towards UV/IR mixing freedom
• Renormalization of the Orientable Non-commutative Gross-Neveu Model
• Non-Commutative U(1) Gauge Theory on R**4 with Oscillator Term and BRST Symmetry
• Translation Invariance, Commutation Relations and Ultraviolet/Infrared Mixing
• On the 1-loop effective action for the IKKT model and non-commutative branes
• Connes distance by examples: Homothetic spectral metric spaces
• One-loop Beta Functions for the Orientable Non-commutative Gross-Neveu Model
• Noncommutative Induced Gauge Theories on Moyal Spaces
• A nontrivial solvable noncommutative ϕ^3 model in 4 dimensions
• Slavnov-Taylor identities, non-commutative gauge theories and infrared divergences

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