Anomalous transport at weak coupling

Abstract

We evaluate the contribution of chiral fermions in $d=2,4,6$, chiral bosons, a chiral gravitino like theory in $d=2$ and chiral gravitinos in $d=6$ to all the leading parity odd transport coefficients at one loop. This is done by using finite temperature field theory to evaluate the relevant Kubo formulae. For chiral fermions and chiral bosons the relation between the parity odd transport coefficient and the microscopic anomalies including gravitational anomalies agree with that found by using the general methods of hydrodynamics and the argument involving the consistency of the Euclidean vacuum. For the gravitino like theory in $d=2$ and chiral gravitinos in $d=6$, we show that relation between the pure gravitational anomaly and parity odd transport breaks down. From the perturbative calculation we clearly identify the terms that contribute to the anomaly polynomial, but not to the transport coefficient for gravitinos. We also develop a simple method for evaluating the angular integrals in the one loop diagrams involved in the Kubo formulae. Finally we show that charge diffusion mode of an ideal 2 dimensional Weyl gas in the presence of a finite chemical potential acquires a speed, which is equal to half the speed of light.

70 pages, 13 figures, typos corrected, added clarifications and a reference

References in corpus (11)

• Gravitational Anomaly and Transport
• Chiral Magnetic conductivity
• Towards hydrodynamics without an entropy current
• Thermodynamics, gravitational anomalies and cones
• Cardy Formulae for SUSY Theories in d=4 and d=6
• (Non)-Renormalization of the Chiral Vortical Effect Coefficient
• Hydrodynamics in 1+1 dimensions with gravitational anomalies
• Anomalies and the Helicity of the Thermal State
• Two dimensional hydrodynamics with gauge and gravitational anomalies
• Hydrodynamics of R-charged D1-branes
• Chiral Magnetic and Vortical Effects in Higher Dimensions at Weak Coupling