Path integral calculation of heat kernel traces with first order operator insertions

Understand

We study generalized heat kernel coefficients, which appear in the trace of the heat kernel with an insertion of a first-order differential operator, by using a path integral representation.

• These coefficients may be used to study gravitational anomalies, i.e.
• anomalies in the conservation of the stress tensor.
• We use the path integral method to compute the coefficients related to the gravitational anomalies of theories in a non-abelian gauge background and flat space of dimensions 2, 4, and 6.