CONES, SPINS AND HEAT KERNELS

The heat kernels of Laplacians for spin-1/2, spin-1, spin-3/2 and spin -2 fields, and the asymptotic expansion of their traces are studied on manifolds with conical singularities. The exact mode-by-mode analysis is carried out for 2-dimensional domains and then extended to arbitra ry dimensions. The corrections to the first Schwinger-DeWitt coefficie nts in the trace expansion, due to conical singularities, are found fo r all the above spins. The results for spins 1/2 and 1 resemble the sc alar case. However, the heat kernels of the Lichnerowicz spin-2 operat or and the spin-3/2 Laplacian show a new feature. When the conical ang le deficit vanishes the limiting values of their traces differ from th e corresponding values computed on the smooth manifold. The reason for the discrepancy is breaking of the local translational isometries nea r a conical singularity. As an application, the results are used to fi nd the ultraviolet divergences in the quantum corrections to the black hole entropy for all these spins.