English

Quantum gauge theories on noncommutative 3-d space

High Energy Physics - Theory 2014-08-20 v3 Mathematical Physics math.MP

Abstract

We consider a class of gauge invariant models on the noncommutative space Rλ3\mathbb{R}^3_\lambda, a deformation of R3\mathbb{R}^3. Focusing on massless models with no linear AiA_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 Rλ3\mathbb{R}^3_\lambda 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 σ\sigma-term. Its global symmetry does not fit with the one of the classical action, reminiscent to an explicit global symmetry breaking term.

Keywords

Cite

@article{arxiv.1312.6145,
  title  = {Quantum gauge theories on noncommutative 3-d space},
  author = {Antoine Géré and Patrizia Vitale and Jean-Christophe Wallet},
  journal= {arXiv preprint arXiv:1312.6145},
  year   = {2014}
}

Comments

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

R2 v1 2026-06-22T02:33:03.701Z