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

Abstract

In the first part of this work, a perturbative analysis up to one-loop order is carried out to determine the one-loop $β$-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&#39;s path integral method. The value of the one-loop $β$-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 $N_{f}<3$.