Microscopic entropy of static black holes in 3d Lovelock gravities

We give a microscopic derivation of the semi-classical entropy of static black holes in 3d Lovelock gravities, which are certain 3d Horndeski theories that were recently discovered from higher-dimensional Lovelock gravities via various methods and admit novel black hole solutions analogous to higher-dimensional ones. Assuming the ground state is described by the soliton obtained from the black hole solution by performing a double Wick rotation, we reproduce the semi-classical entropy from Cardy formula without central charges for the asymptotic growth of the number of states. We explain in detail how the mass of the soliton, which is needed in the Cardy formula, can be computed in the mini-superspace formalism.