Generalized Massive Gravity and Galilean Conformal Algebra in two dimensions

Abstract

Galilean conformal algebra (GCA) in two dimensions arises as contraction of two copies of the centrally extended Virasoro algebra ($t\rightarrow t, x\rightarrow\epsilon x$ with $\epsilon\rightarrow 0$). The central charges of GCA can be expressed in term of Virasoro central charges. For finite and non-zero GCA central charges, the Virasoro central charges must behave as asymmetric form $O(1)\pm O(\frac{1}{\epsilon})$. We propose that, the bulk description for 2d GCA with asymmetric central charges is given by general massive gravity (GMG) in three dimensions. It can be seen that, if the gravitational Chern-Simons coupling $\frac{1}{\mu}$ behaves as of order O($\frac{1}{\epsilon}$) or ($\mu\rightarrow\epsilon\mu$), the central charges of GMG have the above $\epsilon$ dependence. So, in non-relativistic scaling limit $\mu\rightarrow\epsilon\mu$, we calculated GCA parameters and finite entropy in term of gravity parameters mass and angular momentum of GMG.