Gravitational Anomalies in Noncommutative Field Theory

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. DelbourgoSalam computation of the gravitational axial anomaly contribution to the pion decay into two photons, is studied in detail in this context. In the process we show that the two-dimensional chiral pure gravitational Weyl anomaly does not receive noncommutative corrections. Pure gravitational chiral anomaly in 4k + 2 dimensions with matter fields being chiral fermions of spin-12 and spin3 2 , is discussed and a noncommutative correction is found in both cases. Mixed anomalies are finally considered for both cases.