On the $β$-Function and Conformal Anomaly of Noncommutative QED with Adjoint Matter Fields

Details On the $β$-Function and Conformal Anomaly of Noncommutative QED with Adjoint Matter Fields On the $β$-Function and Conformal Anomaly of Noncommutative QED with Adjoint Matter Fields

2002-06-17

arxiv.org/abs/hep-th/0206137v1

Int.J.Mod.Phys. A18 (2003) 2591-2608

Physics

High Energy Physics

High Energy Physics - Theory

1+17 pages, LaTeX, axodraw.sty, 3 figures. Diploma thesis of M. Mohammadi. Email correspondence please to <sadooghi@theory.ipm

Scientific paper

10.1142/S0217751X0301231X

In the first part of this work, a perturbative analysis up to one-loop order is carried out to determine the one-loop $\beta$-function of noncommutative U(1) gauge theory with matter fields in the adjoint representation. In the second part, the conformal anomaly of the same theory is calculated using the Fujikawa's path integral method. The value of the one-loop $\beta$-function calculated in both methods coincides. As it turns out, noncommutative QED with matter fields in the adjoint representation is asymptotically free for the number of flavor degrees of freedom $N_{f}<3$.

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