Global gravitational anomalies and transport

Subham Dutta Chowdhury,Justin R David

doi:10.1007/jhep12(2016)116

Subham Dutta Chowdhury, Justin R David

Open Access

https://doi.org/10.1007/jhep12(2016)116

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Abstract

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'. We then perform a direct perturbative calculation for the contribution of the self dual tensor in d = 6 to the parity odd transport coefficient using the Feynman rules proposed by Gaume and Witten. The result for the transport coefficient agrees with that obtained using matching of global anomalies.

Highlights

We show that the result obtained for the parity odd transport for gravitinos using global anomaly matching is consistent with the direct perturbative calculation
We have used the method of global anomaly matching put forward in [20] for theories with chiral gravitinos and self dual tensors to determine thermal effective actions and parity odd transport coefficients
Our analysis in d = 6 shows that the second Pontryagin class does not contribute to the topological η invariant and does not contribute to transport

Summary

Introduction

A second aim of the paper is to evaluate the contribution of self dual tensors to parity odd transport coefficient in d = 6 perturbatively using the Feynman rules for these fields put forward by [21] This calculation will check the consistency of the result obtained using the matching global anomalies. This was confirmed by evaluating the expectation of the thermal helicity [24] for theories with gravitinos and later in [16], by the direct perturbative evaluation of the contribution of gravitinos to the transport coefficient using the Kubo formula To highlight this fact, let us naively apply the method of consistency of the Euclidean vacuum [17, 18] to determine the contribution of gravitinos to transport coefficients.

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Results

Conclusion