  The BMS (Bondi-van der Burg-Metzner-Sachs) symmetry arises as the asymptotic
symmetry of flat spacetime at null infinity. In particular, the BMS algebra for
three dimensional flat spacetime (BMS$_3$) is generated by the super-rotation
generators which form a Virasoro sub-algebra with central charge $c_L$,
together with mutually-commuting super-translation generators. The
super-rotation and super-translation generators have non-trivial commutation
relations with another central charge $c_M$. In this paper, we study a free
scalar theory in two dimensions exhibiting BMS$_3$ symmetry, which can also be
understood as the ultra-relativistic limit of a free scalar CFT$_2$. Upon
canonical quantization on the highest weight vacuum, the central charges are
found to be $c_L=2$ and $c_M=0$. Because of the vanishing central charge
$c_M=0$, the theory features novel properties: there exist primary states which
form a multiplet, and the Hilbert space can be organized by an enlarged version
of BMS modules dubbed the staggered modules. We further calculate correlation
functions and the torus partition function, the later of which is also shown
explicitly to be modular invariant.
