Anomaly and Nonplanar Diagrams in Noncommutative Gauge Theories (original) (raw)

On the Anomalies and Schwinger Terms in Noncommutative Gauge Theories

International Journal of Modern Physics A, 2006

Invariant (nonplanar) anomaly of noncommutative QED is reexamined. It is found that just as in ordinary gauge theory UV regularization is needed to discover anomalies, in noncommutative case, in addition, an IR regularization is also required to exhibit existence of invariant anomaly. Thus resolving the controversy in the value of invariant anomaly, an expression for the unintergrated anomaly is found. Schwinger terms of the current algebra of the theory are derived.

The UV and IR origin of non-Abelian chiral gauge anomalies on noncommutative Minkowski spacetime

Journal of Physics A: Mathematical and General, 2001

We discuss both the UV and IR origin of the one-loop triangle gauge anomalies for noncommutative nonabelian chiral gauge theories with fundamental, adjoint and bi-fundamental fermions for U(N) groups. We find that gauge anomalies only come from planar triangle diagrams, the non-planar triangle contributions giving rise to no breaking of the Ward identies. Generally speaking, theories with fundamental and bi-fundamental chiral matter are anomalous. Theories with only adjoint chiral fermions are anomaly free.

Nonplanar Anomalies in Noncommutative Theories and the Green-Schwarz Mechanism

Journal of High Energy Physics, 2002

We discuss nonplanar anomalies in noncommutative gauge theories. In particular we show that a nonplanar anomaly exists when the external noncommutative momentum is zero and that it leads to a non-conservation of the associated axial charge. In the case of nonplanar local anomalies, a cancellation of the anomaly can be achieved by a Green-Schwarz mechanism. In an example of D3 branes placed on an orbifold singularity that leads to a chiral theory, the mechanism involves twisted RR fields which propagate with zero noncommutative momentum. Global anomalies are not cancelled and, in particular, the decay π 0 → 2γ is allowed.

Anomaly cancellation in three-dimensional noncommutative gauge theories

Physics Letters B, 2007

The anomaly found by Callan and Harvey is shown to be cancelled in a three-dimensional noncommutative gauge theory coupled to a fermion with a mass function depending on one spatial coordinate (domain wall mass). This evaluation has been done for the fermion in the fundamental and adjoint representations of the gauge group in the limit of small noncommutativity θ parameter.

Chiral anomalies in noncommutative YM theories

Physics Letters B, 2001

Using cohomological methods we discuss several issues related to chiral anomalies in noncommutative U(N) YM theories in any even dimension. We show that for each dimension there is only one solution of the WZ consistency condition and that there cannot be any reducible anomaly, nor any mixed anomaly when the gauge group is a product group. We also clarify some puzzling aspects of the issue of the anomaly when chiral fermions are in the adjoint representation.

The covariant form of the gauge anomaly on noncommutative R 2n

Nuclear Physics B - NUCL PHYS B, 2002

The covariant form of the non-Abelian gauge anomaly on noncommutative R2n is computed for U(N) groups. Its origin and properties are analyzed. Its connection with the consistent form of the gauge anomaly is established. We show along the way that bi-fundamental U(N)×U(M) chiral matter carries no mixed anomalies, and interpret this result as a consequence of the half-dipole structure which characterizes the charged non-commutative degrees of freedom.

Gravitational Anomalies in Noncommutative Field Theory

Arxiv preprint hep-th/ …, 2004

Abstract: Gravitational axial and chiral anomalies in a noncommutative space are examined through the explicit perturbative computation of one-loop diagrams in various dimensions. The analysis depend on how gravity is coupled to noncommutative matter fields. ...

Anomaly freedom in Seiberg-Witten noncommutative gauge theories

Journal of High Energy Physics, 2003

We show that noncommutative gauge theories with arbitrary compact gauge group defined by means of the Seiberg-Witten map have the same one-loop anomalies as their commutative counterparts. This is done in two steps. By explicitly calculating the µ 1 µ 2 µ 3 µ 4 part of the renormalized effective action, we first find the would-be one-loop anomaly of the theory to all orders in the noncommutativity parameter θ µν . And secondly we isolate in the would-be anomaly radiative corrections which are not BRS trivial. This gives as the only true anomaly occurring in the theory the standard Bardeen anomaly of commutative spacetime, which is set to zero by the usual anomaly cancellation condition.

A noncommutative anomaly through Seiberg-Witten map and non-locally regularized BV quantization

Anomalies are one essential concept for the renormalization of noncommutative (NC) gauge theories. A NC space can be visualized as a deformation of the usual spacetime with the star\starstar-product and can be constructed after the quantization of a given space with its symplectic structure. The Seiberg-Witten (SW) map connects NC fields, transformations parameters and gauge potential to their commutative analogs. In this work we used the SW map to calculate the NC version of the anomaly of the BV quantized chiral Schwinger model with nonlocal regularization.