Chiral U(1) anomaly in D = 4 super Yang-Mills theory coupled to supergravity

We evaluate the chiral U(1) anomaly in D = 4 supersymmetric Yang-Mills theory coupled to supergravity. We consider not only the minimal coupling between the gauge fields and fermions but also the interaction term which mixes gravitino and gaugino. We show that the mixing interaction gives the new contributions to the anomaly. This fact suggests necessity for reexamination of the Green-Schwarz anomaly cancellation mechanism. (author)