Peng-xiang HaoYau Mathematical Sciences Center, Tsinghua University, Beijing 100084, ChinaWei SongDepartment of Mathematical Sciences, Tsinghua University, Beijing 100084, China; Peng Huanwu Center for Fundamental Theory, Hefei, Anhui 230026, ChinaXianjin XieYau Mathematical Sciences Center, Tsinghua University, Beijing 100084, ChinaYuan ZhongYau Mathematical Sciences Center, Tsinghua University, Beijing 100084, China
arXiv subject: High Energy Physics - Theory (hep-th)mathscidoc:2204.74001
2021.11
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 which form a Virasoro sub-algebra with central charge cL, together with mutually-commuting super-translation generators. The super-rotation and super-translation generators have non-trivial 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 ultra-relativistic limit of a free scalar CFT2. 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 later of which is also shown explicitly to be modular invariant.