BMS-invariant free scalar model

Abstract

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 (${\mathrm{BMS}}_{3}$) is generated by the super-rotation generators that form a Virasoro subalgebra with central charge ${c}_{L}$, together with mutually commuting super-translation generators. The super-rotation and supertranslation generators have nontrivial commutation relations with another central charge ${c}_{M}$. In this paper, we study a free scalar theory in two dimensions exhibiting ${\mathrm{BMS}}_{3}$ symmetry, which can also be understood as the ultrarelativistic limit of a free scalar ${\mathrm{CFT}}_{2}$ in the flipped representation. 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 latter of which is also shown explicitly to be modular invariant. Is it interesting to note that our model has vanishing ${c}_{M}$, a feature also shared by the so-called flat space chiral gravity in Bagchi et al. [Flat-Space Chiral Gravity, Phys. Rev. Lett. 109, 151301 (2012)].