Fractional Hydrodynamic Transport from the Witten Anomaly

TL;DR

This paper explores how 't Hooft anomalies in certain high-temperature quantum field theories lead to novel fractional hydrodynamic transport phenomena, revealing quantized conductivities linked to topological properties of the symmetry groups.

Contribution

It introduces a new class of fractional transport effects arising from global anomalies in relativistic quantum field theories with specific symmetry groups.

Findings

Prediction of fractional conductivities in high-temperature regimes

Connection between anomalies and topologically quantized transport

Identification of 2-torsion in bordism groups related to these effects

Abstract

We study the physical consequences of 't Hooft anomalies in the high-temperature limit of relativistic quantum field theories with $SU(2)$, or more generally $USp(2N)$, global symmetry. The global anomaly afflicting these symmetry groups results in new transport phenomena akin to the chiral magnetic and chiral vortical effect, predicting conductivities that are fractionally quantised in units of a half, reflecting the 2-torsion in the bordism groups $\Omega^\text{Spin}_5(BUSp(2N))\cong \mathbb{Z}_2$.