Path-integral approach to anomalies at finite temperature

The non-Abelian chiral anomaly for a fermion interacting with an external vector field in any even dimension and the conformal anomaly, in the limit of flat space–time, for a self-interacting scalar field are shown to be independent of temperature using a simple path-integral approach that employs dimensional regularization. The chiral anomaly is used as an example to show that the methods used to study the dimensionally regularized anomaly at finite temperature are readily transferable to the case of ζ-function regularization. The conformal anomaly in (super) string theory at finite temperature is briefly discussed in the light of known results. Some subtleties concerning the use of infrared cutoffs in a dimensionally regularized approach to the computation of the one-loop effective action at finite temperature are considered in an appendix.