Chiral Gauge Anomalies on Noncommutative R^4

We discuss the noncommutative counterparts of chiral gauge theories and compute the associated anomalies.Comment: 11 pages, plain tex. Further comments on the main result have been added. Version to appear in Phys. Lett.

Paramagnetic dominance, the sign of the beta function and UV/IR mixing in non-commutative U(1)

U(1) gauge theory on non-commutative Minkowski space-time in the Feynman-'t Hooft background gauge is studied. In particular, UV divergences and non-commutative IR divergent contributions to the two, three and four-point functions are explicitly computed at one loop. We show that the negative sign of the beta function results from paramagnetism --producing UV charge anti-screening-- prevailing over diamagnetism --giving rise toUV charge screening. This dominance in the field theory setting corresponds to tachyon magnification dominance in the string theory framework. Our calculations provide an explicit realization of UV/IR mixing and lead to an IR renormalization of the coupling constant, where now paramagnetic contributions produce screening and diamagnetic contributions anti-screening.Comment: 39 pages, 7 eps figures; typos corrected, few comments adde

The BRS invariance of noncommutative U(N) Yang-Mills theory at the one-loop level

We show that U(N) Yang-Mills theory on noncommutative Minkowski space-time can be renormalized, in a BRS invariant way, at the one-loop level, by multiplicative dimensional renormalization of its coupling constant, its gauge parameter and its fields. It is shown that the Slavnov-Taylor equation, the gauge-fixing equation and the ghost equation hold, up to order $\hbar$, for the MS renormalized noncommutative U(N) Yang-Mills theory. We give the value of the pole part of every 1PI diagram which is UV divergent.Comment: Corrected typos. Version to appear in Nuclear Physics

Action principles, restoration of BRS symmetry and the renormalization group equation for chiral non-Abelian gauge theories in dimensional renormalization with a non-anticommuting γ5\gamma_5

The one-loop renormalization of a general chiral gauge theory without scalar and Majorana fields is fully worked out within Breitenlohner and Maison dimensional renormalization scheme. The coefficients of the anomalous terms introduced in the Slavnov-Taylor equations by the minimal subtraction algorithm are calculated and the asymmetric counterterms needed to restore the BRS symmetry, if the anomaly cancellation conditions are met, are computed. The renormalization group equation and its coefficients are worked out in the anomaly free case. The computations draw heavily from the existence of action principles and BRS cohomology theory.Comment: 86 pages, 14 figures, one table, plane te

Computing noncommutative Chern-Simons theory radiative corrections on the back of an envelope

We show that the renormalized U(N) noncommutative Chern-Simons theory can be defined in perturbation theory so that there are no loop corrections to the 1PI functional of the theory in an arbitrary homogeneous axial (time-like, light-like or space-like) gauge. We define the free propagators of the fields of the theory by using the Leibbrandt-Mandelstam prescription --which allows Wick rotation and is consistent with power-counting-- and regularize its Green functions with the help of a family of regulators which explicitly preserve the infinitesimal vector Grassmann symmetry of the theory. We also show that in perturbation theory the nonvanishing Green functions of the elementary fields of the theory are products of the free propagators.Comment: In memory of Professor G. Leibbrand