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arXiv · hep-th/9610011

Heat-kernel Coefficients and Spectra of the Vector Laplacians on Spherical Domains with Conical Singularities

Lara De Nardo·Dmitri V. Fursaev·Gennaro Miele
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Abstract

The spherical domains $S^d_β$ with conical singularities are a convenient arena for studying the properties of tensor Laplacians on arbitrary manifolds with such a kind of singular points. In this paper the vector Laplacian on $S^d_β$ is considered and its spectrum is calculated exactly for any dimension $d$. This enables one to find the Schwinger-DeWitt coefficients of this operator by using the residues of the $ζ$-function. In particular, the second coefficient, defining the conformal anomaly, is explicitly calculated on $S^d_β$ and its generalization to arbitrary manifolds is found. As an application of this result, the standard renormalization of the one-loop effective action of gauge fields is demonstrated to be sufficient to remove the ultraviolet divergences up to the first order in the conical deficit angle.

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Lara De Nardo, Dmitri V. Fursaev, Gennaro Miele. 1996-10-22. Heat-kernel Coefficients and Spectra of the Vector Laplacians on Spherical Domains with Conical Singularities. https://doi.org/10.1088/0264-9381%2F14%2F5%2F013

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