Chiral Quartic Massive Gravity in Three Dimensions

We study New Massive Gravity (NMG) with Chern-Simons (CS), cubic, and quartic terms under the Comp\`ere-Song-Strominger (CSS) boundary conditions. By employing a semi-product of a Virasoro and a $U(1)$ Kac-Moody current algebra as the asymptotic symmetry algebra, we calculate the entropy of BTZ black holes via the degeneracy of states belonging to a Warped-CFT. Then, we compute the linearized energy excitations using the representations of the algebra $U(1)\times SL(2, R)_{R}$ and demonstrate that the energies of excitations are non-negative at two chiral points in the parameter space.