Heat Kernel Coefficients for Chern-Simons Boundary Conditions in QED

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 four-sphere as a particular example, we calculate explicitly a number of the first heat kernel coefficients and obtain the general formulas that yields any desired coefficient. A remarkable observation is that the coefficient a2, which defines the one– 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. PACS: 11.15.-q, 02.30.Gp, 12.20.-m E-mail address: [email protected], [email protected] E-mail address: [email protected] . On leave from: Department of Theoretical Physics, St. Petersburg University, 198904 St. Petersburg, Russia 1