Holographic interpolation between a and F

Abstract

Abstract: An interpolating function (Formula presented.) between the a-anomaly coefficient in even dimensions and the free energy on an odd-dimensional sphere has been proposed recently and is conjectured to monotonically decrease along any renormalization group flow in continuous dimension d. We examine (Formula presented.) in the large-N CFT’s in d dimensions holographically described by the Einstein-Hilbert gravity in the AdSd+1 space. We show that (Formula presented.) is a smooth function of d and correctly interpolates the a coefficients and the free energies. The monotonicity of (Formula presented.) along an RG flow follows from the analytic continuation of the holographic c-theorem to continuous d, which completes the proof of the conjecture.