Abstract
An interpolating function \( \tilde{F} \) 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 \( \tilde{F} \) in the large-N CFT’s in d dimensions holographically described by the Einstein-Hilbert gravity in the AdS d+1 space. We show that \( \tilde{F} \) is a smooth function of d and correctly interpolates the a coefficients and the free energies. The monotonicity of \( \tilde{F} \) along an RG flow follows from the analytic continuation of the holographic c-theorem to continuous d, which completes the proof of the conjecture.
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Kawano, T., Nakaguchi, Y. & Nishioka, T. Holographic interpolation between a and F . J. High Energ. Phys. 2014, 161 (2014). https://doi.org/10.1007/JHEP12(2014)161
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DOI: https://doi.org/10.1007/JHEP12(2014)161