Global gravitational anomalies and transport

Understand

We investigate the constraints imposed by global gravitational anomalies on parity odd induced transport coefficients in even dimensions for theories with chiral fermions, gravitinos and self dual tensors.

• The $\eta$-invariant for the large diffeomorphism corresponding to the $T$ transformation on a torus constraints the coefficients in the thermal effective action up to mod 2.
• We show that the result obtained for the parity odd transport for gravitinos using global anomaly matching is consistent with the direct perturbative calculation.
• In $d=6$ we see that the second Pontryagin class in the anomaly polynomial does not contribute to the $\eta$-invariant which provides a topological explanation of this observation in the `replacement rule'.