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Canonical analysis of the gravitational description of the $T\bar{T}$ deformation (2401.00068v1)

Published 29 Dec 2023 in hep-th

Abstract: 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 Poincar\'e 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.

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References (37)
  1. F. A. Smirnov and A. B. Zamolodchikov, “On space of integrable quantum field theories,” Nucl. Phys. B 915 (2017) 363–383, 1608.05499.
  2. A. Cavaglià, S. Negro, I. M. Szécsényi, and R. Tateo, “T⁢T¯𝑇¯𝑇T\bar{T}italic_T over¯ start_ARG italic_T end_ARG-deformed 2D Quantum Field Theories,” JHEP 10 (2016) 112, 1608.05534.
  3. S. Dubovsky, V. Gorbenko, and M. Mirbabayi, “Asymptotic fragility, near AdS 2 holography and T⁢T¯𝑇¯𝑇T\bar{T}italic_T over¯ start_ARG italic_T end_ARG,” Journal of High Energy Physics 2017 (2017), no. 9, 1–37.
  4. S. Dubovsky, V. Gorbenko, and G. Hernández-Chifflet, “T⁢T¯𝑇¯𝑇T\bar{T}italic_T over¯ start_ARG italic_T end_ARG partition function from topological gravity,” Journal of High Energy Physics 2018 (2018), no. 9, 1–23.
  5. E. A. Mazenc, V. Shyam, and R. M. Soni, “A T⁢T¯𝑇¯𝑇T\bar{T}italic_T over¯ start_ARG italic_T end_ARG Deformation for Curved Spacetimes from 3d Gravity,” 1912.09179.
  6. R. L. Arnowitt, S. Deser, and C. W. Misner, “The Dynamics of general relativity,” Gen. Rel. Grav. 40 (2008) 1997–2027, gr-qc/0405109.
  7. Cambridge University Press, 12, 2010.
  8. A. J. Tolley, “T⁢T¯𝑇¯𝑇T\overline{T}italic_T over¯ start_ARG italic_T end_ARG deformations, massive gravity and non-critical strings,” JHEP 06 (2020) 050, 1911.06142.
  9. C. Itzykson and J. B. Zuber, Quantum Field Theory. International Series In Pure and Applied Physics. McGraw-Hill, New York, 1980.
  10. S. Weinberg, The quantum theory of fields. Cambridge university press, 1995.
  11. C. T. Marc Henneaux, Quantization of gauge systems. Princeton University press, 1991.
  12. E. Witten, “Open Strings On The Rindler Horizon,” JHEP 01 (2019) 126, 1810.11912.
  13. L. Brink and M. Henneaux, PRINCIPLES OF STRING THEORY. 1988.
  14. R. Jackiw, “Two lectures on two-dimensional gravity,” arXiv preprint gr-qc/9511048 (1995).
  15. C. Rovelli, Quantum gravity. Cambridge university press, 2004.
  16. T. Thiemann, Modern canonical quantum general relativity. Cambridge University Press, 2008.
  17. R. Conti, L. Iannella, S. Negro, and R. Tateo, “Generalised Born-Infeld models, Lax operators and the T⁢T¯T¯T\mathrm{T}\overline{\mathrm{T}}roman_T over¯ start_ARG roman_T end_ARG perturbation,” JHEP 11 (2018) 007, 1806.11515.
  18. S. Dubovsky, R. Flauger, and V. Gorbenko, “Solving the Simplest Theory of Quantum Gravity,” JHEP 09 (2012) 133, 1205.6805.
  19. N. Callebaut, J. Kruthoff, and H. Verlinde, “T⁢T¯𝑇¯𝑇T\overline{T}italic_T over¯ start_ARG italic_T end_ARG deformed CFT as a non-critical string,” JHEP 04 (2020) 084, 1910.13578.
  20. S. Frolov, “T⁢T¯𝑇¯𝑇T\overline{T}italic_T over¯ start_ARG italic_T end_ARG Deformation and the Light-Cone Gauge,” Proc. Steklov Inst. Math. 309 (2020) 107–126, 1905.07946.
  21. A. Ireland and V. Shyam, “T⁢T¯𝑇¯𝑇T\overline{T}italic_T over¯ start_ARG italic_T end_ARG deformed YM22{}_{2}start_FLOATSUBSCRIPT 2 end_FLOATSUBSCRIPT on general backgrounds from an integral transformation,” JHEP 07 (2020) 058, 1912.04686.
  22. L. Griguolo, R. Panerai, J. Papalini, and D. Seminara, “Exact T⁢T¯𝑇¯𝑇T\overline{T}italic_T over¯ start_ARG italic_T end_ARG deformation of two-dimensional Yang-Mills theory on the sphere,” JHEP 10 (2022) 134, 2207.05095.
  23. L. Griguolo, R. Panerai, J. Papalini, and D. Seminara, “The phase diagram of T⁢T¯𝑇¯𝑇T\overline{T}italic_T over¯ start_ARG italic_T end_ARG-deformed Yang-Mills theory on the sphere,” JHEP 11 (2022) 078, 2209.06222.
  24. L. Santilli and M. Tierz, “Large N phase transition in T⁢T¯𝑇¯𝑇T\overline{T}italic_T over¯ start_ARG italic_T end_ARG -deformed 2d Yang-Mills theory on the sphere,” JHEP 01 (2019) 054, 1810.05404.
  25. V. Iyer and R. M. Wald, “Some properties of Noether charge and a proposal for dynamical black hole entropy,” Phys. Rev. D 50 (1994) 846–864, gr-qc/9403028.
  26. M. Guica, “An integrable Lorentz-breaking deformation of two-dimensional CFTs,” SciPost Phys. 5 (2018), no. 5, 048, 1710.08415.
  27. A. Bzowski and M. Guica, “The holographic interpretation of J⁢T¯𝐽¯𝑇J\bar{T}italic_J over¯ start_ARG italic_T end_ARG-deformed CFTs,” JHEP 01 (2019) 198, 1803.09753.
  28. S. Chakraborty, A. Giveon, and D. Kutasov, “J⁢T¯𝐽¯𝑇J\overline{T}italic_J over¯ start_ARG italic_T end_ARG deformed CFT22{}_{2}start_FLOATSUBSCRIPT 2 end_FLOATSUBSCRIPT and string theory,” JHEP 10 (2018) 057, 1806.09667.
  29. O. Aharony, S. Datta, A. Giveon, Y. Jiang, and D. Kutasov, “Modular covariance and uniqueness of J⁢T¯𝐽¯𝑇J\bar{T}italic_J over¯ start_ARG italic_T end_ARG deformed CFTs,” JHEP 01 (2019) 085, 1808.08978.
  30. L. Apolo and W. Song, “Strings on warped AdS33{}_{3}start_FLOATSUBSCRIPT 3 end_FLOATSUBSCRIPT via T⁢J¯T¯J\mathrm{T}\bar{\mathrm{J}}roman_T over¯ start_ARG roman_J end_ARG deformations,” JHEP 10 (2018) 165, 1806.10127.
  31. J. Aguilera-Damia, V. I. Giraldo-Rivera, E. A. Mazenc, I. Salazar Landea, and R. M. Soni, “A path integral realization of joint J⁢T¯𝐽¯𝑇J\overline{T}italic_J over¯ start_ARG italic_T end_ARG, T⁢J¯𝑇¯𝐽T\overline{J}italic_T over¯ start_ARG italic_J end_ARG and T⁢T¯𝑇¯𝑇T\overline{T}italic_T over¯ start_ARG italic_T end_ARG flows,” JHEP 07 (2020), no. 07, 085, 1910.06675.
  32. G. Hernández-Chifflet, S. Negro, and A. Sfondrini, “Flow Equations for Generalized T⁢T¯𝑇¯𝑇T\overline{T}italic_T over¯ start_ARG italic_T end_ARG Deformations,” Phys. Rev. Lett. 124 (2020), no. 20, 200601, 1911.12233.
  33. J. Polchinski, “Evaluation of the One Loop String Path Integral,” Commun. Math. Phys. 104 (1986) 37.
  34. E. D’Hoker and D. H. Phong, “The Geometry of String Perturbation Theory,” Rev. Mod. Phys. 60 (1988) 917.
  35. E. Witten, “A Note On The Canonical Formalism for Gravity,” 2212.08270.
  36. J. B. Hartle and K. V. Kuchar, “Path integrals in parametrized theories: The Free relativistic particle,” Phys. Rev. D 34 (1986) 2323–2331.
  37. A. G. Cohen, G. W. Moore, P. C. Nelson, and J. Polchinski, “An Off-Shell Propagator for String Theory,” Nucl. Phys. B 267 (1986) 143–157.

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