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 $D=3$.

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

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Cited by in corpus (10)

• Regular BTZ black holes from an infinite tower of corrections
• Nonlocal Massive Gravity from Einstein Gravity
• Microscopic entropy of static black holes in 3d Lovelock gravities
• $c$-functions in Higher-derivative Flows Across Dimensions
• Scaling symmetry, Smarr relation, and the extended first law in lower-dimensional Lovelock gravity
• Cosmic acceleration in Lovelock quantum gravity
• AdS${}_3$ black holes with primary Proca hair from a regularized Gauss-Bonnet coupling
• Regular AdS${}_3$ black holes from regularized Gauss-Bonnet coupling
• Klein-Gordon and Schrödinger solutions in Lovelock quantum gravity
• Explicit Entropic Proofs of Irreversibility Theorems for Holographic RG Flows