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Quantum gauge theories on noncommutative 3-d space

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arxiv 1312.6145 v3 pith:ULEMV2JS submitted 2013-12-20 hep-th math-phmath.MP

classification hep-thmath-phmath.MP
keywords gaugemodelsmasslessmathbbnoncommutativeactioncomputationfunctions
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abstract

We consider a class of gauge invariant models on the noncommutative space $\mathbb{R}^3_\lambda$, 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 $\mathbb{R}^3_\lambda$ 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 $\sigma$-term. Its global symmetry does not fit with the one of the classical action, reminiscent to an explicit global symmetry breaking term.

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  1. Yang-Mills Field in the $\kappa$-space-time

    hep-th 2024-11 conditional novelty 6.0 of 10

    A first-order SU(N) Yang-Mills theory on κ-deformed spacetime is constructed, with field strengths rescaled by probe-energy-dependent factors and an SU(N)-invariant Lagrangian.

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