One-loop structure of the U(1) gauge model on the truncated Heisenberg space

Abstract

We calculate divergent one-loop corrections to the propagators of the U(1) gauge theory on the truncated Heisenberg space, which is one of the extensions of the Grosse-Wulkenhaar model. The model is purely geometric, based on the Yang-Mills action; the corresponding gauge-fixed theory is BRST invariant. We quantize perturbatively and, along with the usual wave-function and mass renormalizations, we find divergent nonlocal terms of the ${\square }^{-1}$ and ${\square }^{-2}$ type. We discuss the meaning of these terms and possible improvements of the model.

arXiv comment29 pages

References in corpus (28)

• Noncommutative Field Theory
• Physical Aspects of the Space-Time Torsion
• Gauge Theory on Noncommutative Spaces
• Renormalisation of ϕ^4-theory on noncommutative R^4 in the matrix base
• Perturbative analysis on infrared aspects of noncommutative QED on R^4
• Duality in Scalar Field Theory on Noncommutative Phase Spaces
• Renormalisation of ϕ^4-theory on noncommutative R^2 in the matrix base
• Vanishing of Beta Function of Non Commutative ${\Phi }_4^4$ Theory to all orders
• Noncommutative Induced Gauge Theory
• The β-function in duality-covariant noncommutative ϕ^4-theory
• Scaling Limits of the Fuzzy Sphere at one Loop
• Renormalization of Non-Commutative Phi^4_4 Field Theory in x Space
• Renormalization of noncommutative phi 4-theory by multi-scale analysis
• Gauge-fixing independence of IR divergences in non-commutative U(1), perturbative tachyonic instabilities and supersymmetry
• A translation-invariant renormalizable non-commutative scalar model
• Induced Gauge Theory on a Noncommutative Space
• Translation-invariant models for non-commutative gauge fields
• One-Loop Calculations for a Translation Invariant Non-Commutative Gauge Model
• Renormalization of the Orientable Non-commutative Gross-Neveu Model
• Non-Commutative U(1) Gauge Theory on R**4 with Oscillator Term and BRST Symmetry
• 8D-spectral triple on 4D-Moyal space and the vacuum of noncommutative gauge theory
• Geometry of the Grosse-Wulkenhaar Model
• Noncommutative gauge theories on ${\mathbb{R}}_{\theta }^2$ as matrix models
• On Non-Commutative U*(1) Gauge Models and Renormalizability
• A New Approach to Non-Commutative U(N) Gauge Fields
• Gauge Independence of IR singularities in Non-Commutative QFT - and Interpolating Gauges
• Gauge fields on noncommutative geometries with curvature
• Quantization of a gauge theory on a curved noncommutative space

Cited by in corpus (5)

• Detecting scaling in phase transitions on the truncated Heisenberg algebra
• Renormalization footprints in the phase diagram of the Grosse-Wulkenhaar model
• Approximate treatment of noncommutative curvature in quartic matrix model
• Phase transitions in a ${\Phi }^4$ matrix model on a curved noncommutative space
• Pinpointing Triple Point of Noncommutative Matrix Model with Curvature