The supersymmetric version of the Green-Schwarz anomaly cancellation mechanism

Abstract The N = 1, D = 10 Supergravity-Super-Yang-Mills (SUGRA-SYM) theory is plagued by ABBJ gauge and Lorentz anomalies which are cancelled via the Green-Schwarz anomaly cancellation mechanism. Due to the fact that the ABBJ anomalies are not invariant under supersymmetry (SUSY) transformations one concludes that the theory is plagued also by a SUSY anomaly. For the gauge groups SO (32) and E 8 × E 8 we compute this SUSY anomaly, by solving a coupled cohomology problem, and we show that it can be cancelled by subtracting from the action the known Green-Schwarz counterterm, the same which cancels also the ABBJ anomaly, the expected result. Finally, we argue that the corresponding mechanism does not apply in the dual SUGRA-SYM, related to the heterotic five-brane.