BMS-invariant free scalar model

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 (BMS3) is generated by the super-rotation generators that form a Virasoro subalgebra with central charge cL, together with mutually commuting super-translation generators. The super-rotation and supertranslation generators have nontrivial commutation relations with another central charge cM. In this paper, we study a free scalar theory in two dimensions exhibiting BMS3 symmetry, which can also be understood as the ultrarelativistic limit of a free scalar CFT2 in the flipped representation. Upon canonical quantization on the highest weight vacuum, the central charges are found to be cL = 2 and cM = 0. Because of the vanishing central charge cM = 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 cM, 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)].

Automated summary

This paper investigates a free scalar theory in two dimensions exhibiting BMS3 symmetry, finding central charges cL = 2 and cM = 0 upon canonical quantization on the highest weight vacuum, leading to novel properties such as the existence of primary states forming a multiplet and an enlarged version of BMS modules called staggered modules.