Noncommutative gauge theories on \( \mathbb{R}_{\theta}^2 \) as matrix models. (English) Zbl 1342.81309
Summary: 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, indicate that only one class of symmetric vacua should lead to fast decaying propagators. The quantum stability of the vacuum is briefly discussed.
MSC:
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 81T75 | Noncommutative geometry methods in quantum field theory |
Keywords:
non-commutative geometry; gauge symmetry; matrix models; field theories in lower dimensionsReferences:
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