The supersymmetric version of the Green--Schwarz anomaly cancellation mechanism

TL;DR

This paper extends the Green-Schwarz anomaly cancellation mechanism to include supersymmetry anomalies in 10-dimensional supergravity-super-Yang-Mills theories, demonstrating their cancellation for specific gauge groups.

Contribution

It computes the supersymmetry anomaly in 10D supergravity-super-Yang-Mills theories and shows it can be canceled by the same Green-Schwarz counterterm used for gauge anomalies.

Findings

Supersymmetry anomalies are computed for $SO(32)$ and $E_8 imes E_8$.

The Green-Schwarz counterterm cancels both gauge and SUSY anomalies.

The mechanism does not apply to the dual heterotic five-brane scenario.

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 $E_8\times E_8$ 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.