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: | , , |
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| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
SpringerOpen
2021
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| Materias: | |
| Acceso en línea: | https://doaj.org/article/c1620e89eb3b4e8cb518c81906039296 |
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| Sumario: | 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. |
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