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 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 $a_2$, 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.

Several changes (including the title). Version to appear in Class Q. Grav. LaTeX, 12 pages

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Cited by in corpus (13)

• Heat kernel expansion: user's manual
• Parity-odd effects and polarization rotation in graphene
• Casimir-Polder effect for a plane with Chern-Simons interaction
• The quest for Casimir repulsion between Chern-Simons surfaces
• The $a_{3/2}$ heat kernel coefficient for oblique boundary conditions
• Casimir force between Chern-Simons surfaces
• Strong ellipticity and spectral properties of chiral bag boundary conditions
• Chiral bag boundary conditions on the ball
• Casimir energy calculations within the formalism of the noncompact lattice QED
• Casimir interaction of two dielectric half spaces with Chern-Simons boundary layers
• New Kernels in Quantum Gravity
• On the (im)possibility of Casimir repulsion between Chern-Simons surfaces
• Casimir-Polder interaction with Chern-Simons boundary layers