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 \( \mathcal{N} \) = 4 vector multiplet about a \( \mathbb{Z} \) N orbifold of the nearhorizon geometry of quarter-BPS black holes in \( \mathcal{N} \) = 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 \( \mathbb{Z} \) N orbifolds of higher-dimensional spheres and hyperboloids.
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Gupta, R.K., Lal, S. & Thakur, S. Heat kernels on the AdS2 cone and logarithmic corrections to extremal black hole entropy. J. High Energ. Phys. 2014, 43 (2014). https://doi.org/10.1007/JHEP03(2014)043
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DOI: https://doi.org/10.1007/JHEP03(2014)043