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

2017

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

Batlle, Carles, Campello, Victor, Gomis, Joaquim

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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.

Built on

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2010
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G. Barnich and C. Troessaert, “Supertranslations call for superrotations,” PoS, 010 (2010), Ann. U. Craiova Phys. 21
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2011
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G. Barnich, A. Gomberoff and H. A. González, “Three-dimensional Bondi-Metzner-Sachs invariant two-dimensional field theories as the flat limit of Liouville theory,” Phys. Rev. D 87
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2013

Then

T. He, V. Lysov, P. Mitra and A. Strominger, “BMS supertranslations and WeinbergÕs soft graviton theorem,” JHEP 1505
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2015
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M. Campiglia and A. Laddha, “Asymptotic symmetries of QED and Weinberg’s soft photon theorem,” JHEP 1507
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2015
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G. Barnich and B. Oblak, “Notes on the BMS group in three dimensions: II. Coadjoint representation,” JHEP 1503
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2015
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M. Campiglia and A. Laddha, “Asymptotic symmetries of gravity and soft theorems for massive particles,” JHEP 1512
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2015
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A. Strominger and A. Zhiboedov, “Gravitational Memory, BMS Supertranslations and Soft Theorems,” JHEP 1601

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