Anomaly and Nonplanar Diagrams in Noncommutative Gauge Theories

Abstract

Anomalies arising from nonplanar triangle diagrams of noncommutative gauge theory are studied. Local chiral gauge anomalies for both noncommutative U(1) and U(N) gauge theories with adjoint matter fields are shown to vanish. For noncommutative QED with fundamental matters, due to UV/IR mixing a finite anomaly emerges from the nonplanar contributions. It involves a generalized ⋆-product of gauge fields.

On non-commutative super Yang–Mills

“…Supersymmetry requires the divergence of the U(1) R to be controlled by the one-loop beta function. In the present case the one-loop beta function does not vanish and thus neither does the Ranomaly (see [30] for a related discussion). Neither of them is smooth in the θ → 0 limit.…”

Noncommutative field theory

“…Anomalies have been studied in (Ardalan and Sadooghi, 2000;Gracia-Bondia and Martin, 2000;Martin, 2001;Bonora, Schnabl, and Tomasiello, 2000b). Gauge anomalies appear to be directly analogous to those of conventional theory, consistent with their topological origin, and can be described using fairly straightforward noncommutative generalizations of the WessZumino consistency conditions, descent equations, etc.…”

Heat kernel, effective action and anomalies in noncommutative theories

“…In this case, some non-planar contributions to the anomalies should appear leading interesting physical consequences (cf. the discussion in [45,40,46]). …”