  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.
