Canonical Realization of (2+1)-dimensional Bondi-Metzner-Sachs symmetry

Abstract

We construct canonical realizations of the ${\mathfrak{bms}}_3$ algebra as symmetry algebras of a free Klein-Gordon (KG) field in $2+1$ dimensions, for both the massive and massless case. We consider two types of realizations, one on-shell, written in terms of the Fourier modes of the scalar field, and the other one off-shell with non-local transformations written in terms of the KG field and its momenta. These realizations contain both supertranslations and superrotations, for which we construct the corresponding Noether charges.

arXiv commentVersion accepted for publication in PRD. Expanded title and expanded discussion about superrotations in the massive case

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Cited by in corpus (14)

• The Holographic Nature of Null Infinity
• Mapping relativistic to ultra/non-relativistic conformal symmetries in 2D and finite $\sqrt{T\bar{T}}$ deformations
• Asymptotic symmetries of three-dimensional Chern-Simons gravity for the Maxwell algebra
• Generalizing the ${\mathfrak{bms}}_3$ and 2D-conformal algebras by expanding the Virasoro algebra
• Massless Scalars and Higher-Spin BMS in Any Dimension
• Semi-simple enlargement of the ${\mathfrak{bms}}_3$ algebra from a $\mathfrak{so}(2,2)\oplus \mathfrak{so}(2,1)$ Chern-Simons theory
• Detector Operators for Celestial Symmetries
• A canonical realization of the Weyl BMS symmetry
• Generalized BMS Algebra at Timelike Infinity
• 1/c deformations of AdS${}_3$ boundary conditions and the Dym hierarchy
• Non-Relativistic BMS algebra
• Polyharmonic Green Functions and Nonlocal BMS Transformations of a Free Scalar Field
• Non Local Global Symmetries of a Free Scalar Field in a Bounded Domain
• BMS in higher space-time dimensions and Non-relativistic BMS