Perturbative BF-Yang-Mills theory on noncommutative R^4

Details Perturbative BF-Yang-Mills theory on noncommutative R^4 Perturbative BF-Yang-Mills theory on noncommutative R^4

1999-12-05

arxiv.org/abs/hep-th/9912036v2

Nucl.Phys. B585 (2000) 554-566

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, 4 figures, latex, version to appear in NPB

Scientific paper

10.1016/S0550-3213(00)00364-3

A U(1) BF-Yang-Mills theory on noncommutative ${\mathbb{R}}^4$ is presented and in this formulation the U(1) Yang-Mills theory on noncommutative ${\mathbb{R}}^4$ is seen as a deformation of the pure BF theory. Quantization using BRST symmetry formalism is discussed and Feynman rules are given. Computations at one-loop order have been performed and their renormalization studied. It is shown that the U(1) BFYM on noncommutative ${\mathbb{R}}^4$ is asymptotically free and its UV-behaviour in the computation of the $\beta$-function is like the usual SU(N) commutative BFYM and Yang Mills theories.

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