A 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 (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.

arXiv comment59 pages, 5 figures. v2, minor revision: typos correted and some statement rephrased

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• A BMS-invariant free fermion model
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• Quantization of Carrollian conformal scalar theories
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• Non-Lorentzian Kač-Moody Algebras
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• The BRST quantisation of chiral BMS-like field theories
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• Universal sectors of two-dimensional Carrollian CFTs
• Revisiting the Carrollian Scalar Field
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