Gauge fields on noncommutative geometries with curvature
arXiv:1003.2284 · doi:10.1007/JHEP07(2010)010
Abstract
It was shown recently that the lagrangian of the Grosse-Wulkenhaar model can be written as lagrangian of the scalar field propagating in a curved noncommutative space. In this interpretation, renormalizability of the model is related to the interaction with the background curvature which introduces explicit coordinate dependence in the action. In this paper we construct the gauge field on the same noncommutative space: since covariant derivatives contain coordinates, the Yang-Mills action is again coordinate dependent. To obtain a two-dimensional model we reduce to a subspace, which results in splitting of the degrees of freedom into a gauge and a scalar. We define the gauge fixing and show the BRST invariance of the quantum action.
18 pages
References in corpus (10)
- Noncommutative Induced Gauge Theory
- A translation-invariant renormalizable non-commutative scalar model
- Induced Gauge Theory on a Noncommutative Space
- On the Problem of Renormalizability in Non-Commutative Gauge Field Models - A Critical Review
- On the vacuum states for noncommutative gauge theory
- Non-Commutative U(1) Gauge Theory on R**4 with Oscillator Term and BRST Symmetry
- Loop Calculations for the Non-Commutative U(1) Gauge Field Model with Oscillator Term
- On Non-Commutative U*(1) Gauge Models and Renormalizability
- Improved Localization of a Renormalizable Non-Commutative Translation Invariant U(1) Gauge Model
- Kaluza-Klein Aspects of Noncommutative Geometry
Cited by in corpus (8)
- Gauge Theories on Deformed Spaces
- Slavnov-Taylor identities, non-commutative gauge theories and infrared divergences
- On the Origin of the Harmonic Term in Noncommutative Quantum Field Theory
- Renormalization footprints in the phase diagram of the Grosse-Wulkenhaar model
- One-loop structure of the U(1) gauge model on the truncated Heisenberg space
- Quantization of a gauge theory on a curved noncommutative space
- Laplacian on fuzzy de Sitter space
- Spinors on a curved noncommutative space: coupling to torsion and the Gross-Neveu model