One-Loop Calculations and Detailed Analysis of the Localized Non-Commutative p^-2U(1) Gauge Model

Abstract

Abstract. This paper carries forward a series of articles describing our enterprise to construct a gauge equivalent for the θ-deformed non-commutative The reason is that this dimensionless operator is invariant with respect to any symmetry of the model, and can be inserted to arbitrary power. In the present article we discuss explicit one-loop calculations, and analyze the mechanism the mentioned problems originate from.

Gauge Theories on Deformed Spaces

“…In this way, the number of fields, sources and ghosts which are necessary for the localization could be reduced (from 30 to 22) without significantly lowering the symmetry content of the theory. However, as was shown by explicit computations in [41], the total number of Feynman graphs which need to be considered (even at one loop order) in the perturbative renormalization procedure is still rather high. Similar to the model by Vilar et al the damping is implemented in a breaking term.…”

“…Therefore, attempts have been made to localize the action by coupling them to unphysical auxiliary fields. There are several ways to implement this, resulting in models with different properties, and even a modified physical content [39,40,41,42]. In this respect one is led to the conclusion that only minimal couplings and the consequent construction of BRST doublet structures for all auxiliary fields result in a stable theory.…”

Translation-Invariant Noncommutative Renormalization

“…The idea behind the model (4.2) was extended to propose a modified U (1) gauge model on the Moyal space [41]. This type of gauge theory has a trivial vacuum; this a crucial difference with respect to gauge theories based on a Grosse-Wulkenhaar-like modification, which were proved to have a highly nontrivial vacuum state [42].…”

On noncommutative quantum field theories and dimensionless insertions

“…One has to use a local form of the above action. Motivated by the work of Vilar et al [4] we have eliminate the non-local terms with the help of auxiliary fields forming BRST-doublet structures [8]:…”

“…Here, we discuss a gauge invariant implementation of the damping behaviour necessary in order to avoid UV/IR mixing; see e.g. [5,6,7,8,4]. However, there are also different ways of implementing IR modifications of the propagator.…”