Heat kernels on the AdS sub(2) cone and logarithmic corrections to extremal black hole entropy

(ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image).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 ... = 4 vector multiplet about a ... sub( )Norbifold of the nearhorizon geometry of quarter-BPS black holes in ... = 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 ... sub( )Norbifolds of higher-dimensional spheres and hyperboloids.