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-bymode analysis is carried out for 2-dimensional domains and then extended to arbitrary dimensions. The...

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Bibliographic Details
Published in:Nuclear physics. B 1997-01, Vol.484 (3), p.697-723
Main Authors: Fursaev, Dmitri V., Miele, Gennaro
Format: Article
Language:English
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Summary: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-bymode analysis is carried out for 2-dimensional domains and then extended to arbitrary dimensions. The corrections to the first Schwinger-DeWitt coefficients in the trace expansion, due to conical singularities, are found for all the above spins. The results for spins 1 2 and 1 resemble the scalar case. However, the heat kernels of the Lichnerowicz spin-2 operator and the spin- 3 2 Laplacian show a new feature. When the conical angle deficit vanishes the limiting values of their traces differ from the corresponding values computed on the smooth manifold. The reason for the discrepancy is breaking of the local translational isometries near a conical singularity. As an application, the results are used to find the ultraviolet divergences in the quantum corrections to the black hole entropy for all these spins.
ISSN:0550-3213
1873-1562
DOI:10.1016/S0550-3213(96)00631-1