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Canonical analysis of the gravitational description of the TT¯ deformation

Florencia Benítez*, Guzmán Hernández-Chifflet†, and Esteban Mato‡

  • *Contact author: florenciab@fing.edu.uy
  • †Contact author: guzmanhc@fing.edu.uy
  • ‡Contact author: emato@fing.edu.uy
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Phys. Rev. D 113, 046015 – Published 19 February, 2026

DOI: https://doi.org/10.1103/9g3f-nc1f

Abstract

The description of the TT¯ deformation in terms of two-dimensional gravity is analyzed from the Hamiltonian point of view, in a manner analogous to the Arnowitt-Deser-Misner description of general relativity. We find that the Hamiltonian constraints of the theory imply relations between target-space momentum at finite volume that are equivalent to the TT¯ finite-volume flow equations. This fully quantum TT¯ 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 nontrivially—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 JT¯-type deformations, where it is found that the flow equations obtained involve deformations that twist the spatial boundary conditions.

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Phys. Rev. D 113, 046015– Published 19 February, 2026
  • Received 30 October 2025
  • Accepted 26 January 2026
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