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| Natura: | Preprint |
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2023
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| Accesso online: | https://arxiv.org/abs/2401.00068 |
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| _version_ | 1866908607876956160 |
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| author | Benítez, Florencia Hernández-Chifflet, Guzmán Mato, Esteban |
| author_facet | Benítez, Florencia Hernández-Chifflet, Guzmán Mato, Esteban |
| contents | The description of the $T\bar{T}$ deformation in terms of two-dimensional gravity is analyzed from the Hamiltonian point of view, in a manner analogous to the ADM description of general relativity. We find that the Hamiltonian constraints of the theory imply relations between target-space momentum at finite volume which are equivalent to the $T\bar{T}$ finite volume flow equations. This fully-quantum $T\bar{T}$ result emerges already at the classical level within the gravitational theory. We exemplify the analysis for the case when the undeformed sector is a collection of $D-2$ free massless scalars, where it is shown that -- somewhat non-trivially -- the target-space two-dimensional Poincaré symmetry is extended to $D$ dimensions. The connection between canonical quantization of this constrained Hamiltonian system and previous path integral quantizations is also discussed. We extend our analysis to the ``gravitational'' description of $J\bar{T}$-type deformations, where it is found that the flow equations obtained involve deformations that twist the spatial boundary conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00068 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Canonical analysis of the gravitational description of the $T\bar{T}$ deformation Benítez, Florencia Hernández-Chifflet, Guzmán Mato, Esteban High Energy Physics - Theory The description of the $T\bar{T}$ deformation in terms of two-dimensional gravity is analyzed from the Hamiltonian point of view, in a manner analogous to the ADM description of general relativity. We find that the Hamiltonian constraints of the theory imply relations between target-space momentum at finite volume which are equivalent to the $T\bar{T}$ finite volume flow equations. This fully-quantum $T\bar{T}$ result emerges already at the classical level within the gravitational theory. We exemplify the analysis for the case when the undeformed sector is a collection of $D-2$ free massless scalars, where it is shown that -- somewhat non-trivially -- the target-space two-dimensional Poincaré symmetry is extended to $D$ dimensions. The connection between canonical quantization of this constrained Hamiltonian system and previous path integral quantizations is also discussed. We extend our analysis to the ``gravitational'' description of $J\bar{T}$-type deformations, where it is found that the flow equations obtained involve deformations that twist the spatial boundary conditions. |
| title | Canonical analysis of the gravitational description of the $T\bar{T}$ deformation |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2401.00068 |