3D Lovelock Gravity and the Holographic c-Theorem

TL;DR

This paper demonstrates that a specific scalar-tensor theory derived from a limit of Lovelock gravity in three dimensions supports a holographic c-theorem, with the c-function aligning with the Weyl anomaly coefficient at the UV fixed point.

Contribution

It establishes the existence of a holographic c-theorem in a scalar-tensor theory from a D→3 limit of Lovelock gravity, confirming the c-function's consistency with Weyl anomaly calculations.

Findings

The scalar-tensor theory admits a holographic c-theorem.

The c-function value matches the Weyl anomaly coefficient at the UV fixed point.

The c-function derived matches the one from the naive limit approach.

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 $D=3$.