Mapping relativistic to ultra/non-relativistic conformal symmetries in 2D and finite T T ¯ $$ \sqrt{T\overline{T}} $$ deformations

Mapping relativistic to ultra/non-relativistic conformal symmetries in 2D and finite T T ¯ $$ \sqrt{T\overline{T}} $$ deformations

Abstract The conformal symmetry algebra in 2D (Diff(S 1)⊕Diff(S 1)) is shown to be related to its ultra/non-relativistic version (BMS3≈GCA2) through a nonlinear map of the generators, without any sort of limiting process. For a generic classical CFT2, the BMS3 generators then emerge as composites bu...

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Autores principales: Pablo Rodríguez, David Tempo, Ricardo Troncoso
Formato: article
Lenguaje:EN
Publicado: SpringerOpen 2021
Materias:
Conformal and W Symmetry
Space-Time Symmetries
Nuclear and particle physics. Atomic energy. Radioactivity
QC770-798
Acceso en línea:https://doaj.org/article/c1620e89eb3b4e8cb518c81906039296
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spelling oai:doaj.org-article:c1620e89eb3b4e8cb518c819060392962021-11-21T12:41:28ZMapping relativistic to ultra/non-relativistic conformal symmetries in 2D and finite T T ¯ $$ \sqrt{T\overline{T}} $$ deformations10.1007/JHEP11(2021)1331029-8479https://doaj.org/article/c1620e89eb3b4e8cb518c819060392962021-11-01T00:00:00Zhttps://doi.org/10.1007/JHEP11(2021)133https://doaj.org/toc/1029-8479Abstract The conformal symmetry algebra in 2D (Diff(S 1)⊕Diff(S 1)) is shown to be related to its ultra/non-relativistic version (BMS3≈GCA2) through a nonlinear map of the generators, without any sort of limiting process. For a generic classical CFT2, the BMS3 generators then emerge as composites built out from the chiral (holomorphic) components of the stress-energy tensor, T and T ¯ $$ \overline{T} $$ , closing in the Poisson brackets at equal time slices. Nevertheless, supertranslation generators do not span Noetherian symmetries. BMS3 becomes a bona fide symmetry once the CFT2 is marginally deformed by the addition of a T T ¯ $$ \sqrt{T\overline{T}} $$ term to the Hamiltonian. The generic deformed theory is manifestly invariant under diffeomorphisms and local scalings, but it is no longer a CFT2 because its energy and momentum densities fulfill the BMS3 algebra. The deformation can also be described through the original CFT2 on a curved metric whose Beltrami differentials are determined by the variation of the deformed Hamiltonian with respect to T and T ¯ $$ \overline{T} $$ . BMS3 symmetries then arise from deformed conformal Killing equations, corresponding to diffeomorphisms that preserve the deformed metric and stress-energy tensor up to local scalings. As an example, we briefly address the deformation of N free bosons, which coincides with ultra-relativistic limits only for N = 1. Furthermore, Cardy formula and the S-modular transformation of the torus become mapped to their corresponding BMS3 (or flat) versions.Pablo RodríguezDavid TempoRicardo TroncosoSpringerOpenarticleConformal and W SymmetrySpace-Time SymmetriesNuclear and particle physics. Atomic energy. RadioactivityQC770-798ENJournal of High Energy Physics, Vol 2021, Iss 11, Pp 1-15 (2021)
institution DOAJ
collection DOAJ
language EN
topic Conformal and W Symmetry
Space-Time Symmetries
Nuclear and particle physics. Atomic energy. Radioactivity
QC770-798
spellingShingle Conformal and W Symmetry
Space-Time Symmetries
Nuclear and particle physics. Atomic energy. Radioactivity
QC770-798
Pablo Rodríguez
David Tempo
Ricardo Troncoso
Mapping relativistic to ultra/non-relativistic conformal symmetries in 2D and finite T T ¯ $$ \sqrt{T\overline{T}} $$ deformations
description Abstract The conformal symmetry algebra in 2D (Diff(S 1)⊕Diff(S 1)) is shown to be related to its ultra/non-relativistic version (BMS3≈GCA2) through a nonlinear map of the generators, without any sort of limiting process. For a generic classical CFT2, the BMS3 generators then emerge as composites built out from the chiral (holomorphic) components of the stress-energy tensor, T and T ¯ $$ \overline{T} $$ , closing in the Poisson brackets at equal time slices. Nevertheless, supertranslation generators do not span Noetherian symmetries. BMS3 becomes a bona fide symmetry once the CFT2 is marginally deformed by the addition of a T T ¯ $$ \sqrt{T\overline{T}} $$ term to the Hamiltonian. The generic deformed theory is manifestly invariant under diffeomorphisms and local scalings, but it is no longer a CFT2 because its energy and momentum densities fulfill the BMS3 algebra. The deformation can also be described through the original CFT2 on a curved metric whose Beltrami differentials are determined by the variation of the deformed Hamiltonian with respect to T and T ¯ $$ \overline{T} $$ . BMS3 symmetries then arise from deformed conformal Killing equations, corresponding to diffeomorphisms that preserve the deformed metric and stress-energy tensor up to local scalings. As an example, we briefly address the deformation of N free bosons, which coincides with ultra-relativistic limits only for N = 1. Furthermore, Cardy formula and the S-modular transformation of the torus become mapped to their corresponding BMS3 (or flat) versions.
format article
author Pablo Rodríguez
David Tempo
Ricardo Troncoso
author_facet Pablo Rodríguez
David Tempo
Ricardo Troncoso
author_sort Pablo Rodríguez
title Mapping relativistic to ultra/non-relativistic conformal symmetries in 2D and finite T T ¯ $$ \sqrt{T\overline{T}} $$ deformations
title_short Mapping relativistic to ultra/non-relativistic conformal symmetries in 2D and finite T T ¯ $$ \sqrt{T\overline{T}} $$ deformations
title_full Mapping relativistic to ultra/non-relativistic conformal symmetries in 2D and finite T T ¯ $$ \sqrt{T\overline{T}} $$ deformations
title_fullStr Mapping relativistic to ultra/non-relativistic conformal symmetries in 2D and finite T T ¯ $$ \sqrt{T\overline{T}} $$ deformations
title_full_unstemmed Mapping relativistic to ultra/non-relativistic conformal symmetries in 2D and finite T T ¯ $$ \sqrt{T\overline{T}} $$ deformations
title_sort mapping relativistic to ultra/non-relativistic conformal symmetries in 2d and finite t t ¯ $$ \sqrt{t\overline{t}} $$ deformations
publisher SpringerOpen
publishDate 2021
url https://doaj.org/article/c1620e89eb3b4e8cb518c81906039296
work_keys_str_mv AT pablorodriguez mappingrelativistictoultranonrelativisticconformalsymmetriesin2dandfinitettsqrttoverlinetdeformations
AT davidtempo mappingrelativistictoultranonrelativisticconformalsymmetriesin2dandfinitettsqrttoverlinetdeformations
AT ricardotroncoso mappingrelativistictoultranonrelativisticconformalsymmetriesin2dandfinitettsqrttoverlinetdeformations
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