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.

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

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• On Higher-dimensional Carrollian and Galilean Conformal Field Theories
• Carroll covariant scalar fields in two dimensions
• Boosting to BMS
• From CFTs to theories with Bondi-Metzner-Sachs symmetries: Complexity and out-of-time-ordered correlators
• Carroll fermions in two dimensions
• Intrinsic Approach to $1+1$D Carrollian Conformal Field Theory
• Symmetry group at future null infinity I: Scalar theory
• A BMS-invariant free fermion model
• Horizon Strings as 3d Black Hole Microstates
• Symmetry group at future null infinity II: Vector theory
• Quantization of Carrollian conformal scalar theories
• Symmetry Resolution in non-Lorentzian Field Theories
• Flat Bands and Compact Localised States: A Carrollian roadmap
• Non-Lorentzian Kač-Moody Algebras
• Irrelevant and marginal deformed BMS field theories
• Bulk Reconstruction of Scalar Excitations in Flat${}_3$/CCFT${}_2$ and the Flat Limit from (A)dS${}_3$/CFT${}_2$
• Quantization of Carrollian fermions
• The BRST quantisation of chiral BMS-like field theories
• Thermal Corrections to Rényi Entropy in BMS Field Theory
• Sourced Carrollian Fluids Dual to Black Hole Horizons
• Universal sectors of two-dimensional Carrollian CFTs
• Revisiting the Carrollian Scalar Field
• Character of the highest weight module of BMS algebra realized on codimensional-two boundary
• Conformal Blocks in 2d Carrollian/Galilean CFTs and Excited State Entanglement Entropy
• Strings near BTZ black holes: A Carrollian Chronicle