Galilean conformal algebra in two dimensions and cosmological topologically massive gravity

We consider a realization of the Galilean conformal algebra (GCA) in two-dimensional space-time on the AdS boundary of a particular three-dimensional gravity theory, the so-called cosmological topologically massive gravity (CTMG), which includes the gravitational Chern-Simons term and the negative cosmological constant. The infinite-dimensional GCA in two dimensions is obtained from the Virasoro algebra for the relativistic CFT by taking a scaling limit t→t, x→ϵx with ϵ→0. The parent relativistic CFT should have left and right central charges of order O(1/ϵ) but opposite in sign in the limit ϵ→0. On the other hand, by Brown-Henneaux's analysis the Virasoro algebra is realized on the boundary of AdS3, but the left and right central charges are asymmetric only by the factor of the gravitational Chern-Simons coupling 1/μ. If μ behaves as of order O(ϵ) under the corresponding limit, we have the GCA with non-trivial centers on AdS boundary of the bulk CTMG. Then we present a new entropy formula for the Galilean field theory from the bulk black hole entropy, which is a non-relativistic counterpart of the Cardy formula. It is also discussed whether it can be reproduced by the microstate counting.