Heat kernel coefficients for Chern-Simons boundary conditions in QED

Abstract

We consider the four-dimensional Euclidean Maxwell theory with a Chern-Simons term on the boundary. The corresponding gauge-invariant boundary conditions become dependent on tangential derivatives. Taking the 4-sphere as a particular example, we calculate explicitly a number of the first heat kernel coefficients and obtain the general formulae that yield any desired coefficient. A remarkable observation is that the coefficient , which defines the 1-loop counterterm and the conformal anomaly, does not depend on the Chern-Simons coupling constant, while the heat kernel itself becomes singular at a certain (critical) value of the coupling. This could be a reflection of a general property of Chern-Simons theories.