Fractional Hydrodynamic Transport from the Witten Anomaly

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 ${\mathrm{\Omega }}_5^{\text{Spin}}(BUSp(2N))\cong {\mathbb{Z}}_2$.