Abstract
We develop new techniques to efficiently evaluate heat kernel coefficients for the Laplacian in the short-time expansion on spheres and hyperboloids with conical singularities. We then apply these techniques to explicitly compute the logarithmic contribution to black hole entropy from an N=4 vector multiplet about a Z(N) orbifold of the near-horizon geometry of quarter--BPS black holes in N=4 supergravity. We find that this vanishes, matching perfectly with the prediction from the microstate counting. We also discuss possible generalisations of our heat kernel results to higher-spin fields over Z(N) orbifolds of higher-dimensional spheres and hyperboloids.
Highlights
One of the main successes of string theory as a theory of quantum gravity has been to provide a statistical interpretation of black hole entropy [1]
We apply these techniques to explicitly compute the logarithmic contribution to black hole entropy from an N = 4 vector multiplet about a ZN orbifold of the nearhorizon geometry of quarter-BPS black holes in N = 4 supergravity
The near horizon geometry of such black holes is always of the form AdS2 ⊗ K where K is a compact manifold. It was proposed in [16] that the full quantum answer for the microscopic degeneracy associated with the black hole horizon is contained in the quantum entropy function, defined as the string path integral over all spacetimes which asymptote to the black hole near horizon geometry
Summary
One of the main successes of string theory as a theory of quantum gravity has been to provide a statistical interpretation of black hole entropy [1]. A non-trivial test of this proposal is that the leading quantum corrections in the large charge limit, which scale as log (charges), to the semi-classical Bekenstein-Hawking formula as predicted from the string computation can be reproduced from the quantum entropy function for N = 4 and N = 8 string theory [24, 25] This is obtained by expanding the quantum entropy function about the saddle-point defined by the near- horizon geometry of the black hole. These geometries are essentially ZN orbifolds of the near horizon geometry of the black hole in question. We propose a quantum test of the proposal of [16] analogous to the tests performed in [24, 25]
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