3D Lovelock Gravity and the Holographic c-Theorem

Abstract

We show that the scalar-tensor theory that arises in a rigorous $D\to 3$ limit of Lovelock gravity up to cubic order admits a holographic c-theorem and verify that the value of the c-function at the UV fixed point matches with the Weyl anomaly coefficient (up to an irrelevant factor). The constructed c-function is the same as one that follows from the "naive limit", which is obtained by scaling the couplings by a factor of $\frac{1}{D-3}$, and then setting $D=3$.

arXiv comment9 pages; v2: minor changes; v3: more minor changes, version to appear in PRD

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• Microscopic entropy of static black holes in 3d Lovelock gravities
• $c$-functions in Higher-derivative Flows Across Dimensions
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