3D Lovelock gravity and the holographic c -theorem

Abstract

We show that the scalar-tensor theory that arises in a rigorous $D\ensuremath{\rightarrow}3$ 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 $\frac{1}{D\ensuremath{-}3}$, and then setting $D=3$.