  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 $t\to t$, $x\to\epsilon x$ with $\epsilon\to 0$. The parent relativistic
CFT should have left and right central charges of order
$\mathcal{O}(1/\epsilon)$ but opposite in sign in the limit $\epsilon\to 0$. On
the other hand, by Brown-Henneaux's analysis the Virasoro algebra is realized
on the boundary of AdS$_3$, but the left and right central charges are
asymmetric only by the factor of the gravitational Chern-Simons coupling
$1/\mu$. If $\mu$ behaves as of order $\mathcal{O}(\epsilon)$ 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.

High Energy Physics - Theory