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Root-$T \overline{T}$ Deformed Boundary Conditions in Holography (2304.08723v3)

Published 18 Apr 2023 in hep-th, gr-qc, math-ph, and math.MP

Abstract: We develop the holographic dictionary for pure $\mathrm{AdS}_3$ gravity where the Lagrangian of the dual $2d$ conformal field theory has been deformed by an arbitrary function of the energy-momentum tensor. In addition to the $T \overline{T}$ deformation, examples of such functions include a class of marginal stress tensor deformations which are special because they leave the generating functional of connected correlators unchanged up to a redefinition of the source and expectation value. Within this marginal class, we identify the unique deformation that commutes with the $T \overline{T}$ flow, which is the root-$T \overline{T}$ operator, and write down the modified boundary conditions corresponding to this root-$T \overline{T}$ deformation. We also identify the unique marginal stress tensor flow for the cylinder spectrum of the dual CFT which commutes with the inviscid Burgers' flow driven by $T \overline{T}$, and we propose this unique flow as a candidate root-$T \overline{T}$ deformation of the energy levels. We study BTZ black holes in $\mathrm{AdS}_3$ subject to root-$T \overline{T}$ deformed boundary conditions, and find that their masses flow in a way which is identical to that of our candidate root-$T \overline{T}$ energy flow equation, which offers evidence that this flow is the correct one. Finally, we also obtain the root-$T \overline{T}$ deformed boundary conditions for the gauge field in the Chern-Simons formulation of $\mathrm{AdS}_3$ gravity.

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References (79)
  1. E. Witten, “Multitrace operators, boundary conditions, and AdS/CFTAdSCFT\mathrm{AdS}/\mathrm{CFT}roman_AdS / roman_CFT correspondence,” hep-th/0112258.
  2. A. B. Zamolodchikov, “Expectation value of composite field T anti-T in two-dimensional quantum field theory,” hep-th/0401146.
  3. F. A. Smirnov and A. B. Zamolodchikov, “On space of integrable quantum field theories,” Nucl. Phys. B915 (2017) 363–383, 1608.05499.
  4. 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.
  5. 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.
  6. B. Chen, J. Hou, and J. Tian, “Lax connections in TT-deformed integrable field theories,” Chin. Phys. C 45 (2021), no. 9, 093112, 2102.01470.
  7. M. Baggio, A. Sfondrini, G. Tartaglino-Mazzucchelli, and H. Walsh, “On T⁢T¯𝑇¯𝑇T\overline{T}italic_T over¯ start_ARG italic_T end_ARG deformations and supersymmetry,” JHEP 06 (2019) 063, 1811.00533.
  8. C.-K. Chang, C. Ferko, and S. Sethi, “Supersymmetry and T⁢T¯𝑇¯𝑇T\overline{T}italic_T over¯ start_ARG italic_T end_ARG deformations,” JHEP 04 (2019) 131, 1811.01895.
  9. H. Jiang, A. Sfondrini, and G. Tartaglino-Mazzucchelli, “T⁢T¯𝑇¯𝑇T\bar{T}italic_T over¯ start_ARG italic_T end_ARG deformations with 𝒩=(0,2)𝒩02\mathcal{N}=(0,2)caligraphic_N = ( 0 , 2 ) supersymmetry,” Phys. Rev. D100 (2019), no. 4, 046017, 1904.04760.
  10. C.-K. Chang, C. Ferko, S. Sethi, A. Sfondrini, and G. Tartaglino-Mazzucchelli, “T⁢T¯𝑇¯𝑇T\bar{T}italic_T over¯ start_ARG italic_T end_ARG flows and (2,2) supersymmetry,” Phys. Rev. D 101 (2020), no. 2, 026008, 1906.00467.
  11. C. Ferko, H. Jiang, S. Sethi, and G. Tartaglino-Mazzucchelli, “Non-linear supersymmetry and T⁢T¯𝑇¯𝑇T\overline{T}italic_T over¯ start_ARG italic_T end_ARG-like flows,” JHEP 02 (2020) 016, 1910.01599.
  12. PhD thesis, Chicago U., 2021. 2112.14647.
  13. S. Ebert, C. Ferko, H.-Y. Sun, and Z. Sun, “T⁢T¯𝑇¯𝑇T\overline{T}italic_T over¯ start_ARG italic_T end_ARG deformations of supersymmetric quantum mechanics,” JHEP 08 (2022) 121, 2204.05897.
  14. S. Dubovsky, V. Gorbenko, and M. Mirbabayi, “Asymptotic fragility, near AdS22{}_{2}start_FLOATSUBSCRIPT 2 end_FLOATSUBSCRIPT holography and T⁢T¯𝑇¯𝑇T\overline{T}italic_T over¯ start_ARG italic_T end_ARG,” JHEP 09 (2017) 136, 1706.06604.
  15. J. Cardy, “The T⁢T¯𝑇¯𝑇T\overline{T}italic_T over¯ start_ARG italic_T end_ARG deformation of quantum field theory as random geometry,” JHEP 10 (2018) 186, 1801.06895.
  16. S. Datta and Y. Jiang, “T⁢T¯𝑇¯𝑇T\bar{T}italic_T over¯ start_ARG italic_T end_ARG deformed partition functions,” JHEP 08 (2018) 106, 1806.07426.
  17. O. Aharony, S. Datta, A. Giveon, Y. Jiang, and D. Kutasov, “Modular invariance and uniqueness of T⁢T¯𝑇¯𝑇T\bar{T}italic_T over¯ start_ARG italic_T end_ARG deformed CFT,” JHEP 01 (2019) 086, 1808.02492.
  18. M. Guica and R. Monten, “T⁢T¯𝑇¯𝑇T\bar{T}italic_T over¯ start_ARG italic_T end_ARG and the mirage of a bulk cutoff,” SciPost Phys. 10 (2021), no. 2, 024, 1906.11251.
  19. C. Ferko, A. Sfondrini, L. Smith, and G. Tartaglino-Mazzucchelli, “Root-T⁢T¯𝑇¯𝑇T\bar{T}italic_T over¯ start_ARG italic_T end_ARG Deformations in Two-Dimensional Quantum Field Theories,” Phys. Rev. Lett. 129 (2022), no. 20, 201604, 2206.10515.
  20. R. Borsato, C. Ferko, and A. Sfondrini, “On the Classical Integrability of Root-T⁢T¯𝑇¯𝑇T\bar{T}italic_T over¯ start_ARG italic_T end_ARG Flows,” 2209.14274.
  21. I. Bandos, K. Lechner, D. Sorokin, and P. K. Townsend, “A non-linear duality-invariant conformal extension of Maxwell’s equations,” Phys. Rev. D 102 (2020) 121703, 2007.09092.
  22. I. Bandos, K. Lechner, D. Sorokin, and P. K. Townsend, “On p-form gauge theories and their conformal limits,” JHEP 03 (2021) 022, 2012.09286.
  23. I. Bandos, K. Lechner, D. Sorokin, and P. K. Townsend, “ModMax meets Susy,” JHEP 10 (2021) 031, 2106.07547.
  24. K. Lechner, P. Marchetti, A. Sainaghi, and D. P. Sorokin, “Maximally symmetric nonlinear extension of electrodynamics and charged particles,” Phys. Rev. D 106 (2022), no. 1, 016009, 2206.04657.
  25. H. Babaei-Aghbolagh, K. B. Velni, D. M. Yekta, and H. Mohammadzadeh, “Emergence of non-linear electrodynamic theories from T⁢T¯𝑇¯𝑇T\bar{T}italic_T over¯ start_ARG italic_T end_ARG-like deformations,” 2202.11156.
  26. C. Ferko, L. Smith, and G. Tartaglino-Mazzucchelli, “On Current-Squared Flows and ModMax Theories,” SciPost Phys. 13 (2022), no. 2, 012, 2203.01085.
  27. C. Ferko, L. Smith, and G. Tartaglino-Mazzucchelli, “Stress Tensor Flows, Birefringence in Non-Linear Electrodynamics, and Supersymmetry,” 2301.10411.
  28. C. Ferko, Y. Hu, Z. Huang, K. Koutrolikos, and G. Tartaglino-Mazzucchelli, “T⁢T¯𝑇¯𝑇T\overline{T}italic_T over¯ start_ARG italic_T end_ARG-Like Flows and 3⁢d3𝑑3d3 italic_d Nonlinear Supersymmetry,” 2302.10410.
  29. H. Babaei-Aghbolagh, K. Babaei Velni, D. Mahdavian Yekta, and H. Mohammadzadeh, “Marginal TT¯-like deformation and modified Maxwell theories in two dimensions,” Phys. Rev. D 106 (2022), no. 8, 086022, 2206.12677.
  30. R. Conti, J. Romano, and R. Tateo, “Metric approach to a T⁢T¯T¯T\mathrm{T}\overline{\mathrm{T}}roman_T over¯ start_ARG roman_T end_ARG-like deformation in arbitrary dimensions,” JHEP 09 (2022) 085, 2206.03415.
  31. J. A. García and R. A. Sánchez-Isidro, “T⁢T¯𝑇¯𝑇\sqrt{T\overline{T}}square-root start_ARG italic_T over¯ start_ARG italic_T end_ARG end_ARG-deformed oscillator inspired by ModMax,” Eur. Phys. J. Plus 138 (2023), no. 2, 114, 2209.06296.
  32. P. Rodríguez, D. Tempo, and R. Troncoso, “Mapping relativistic to ultra/non-relativistic conformal symmetries in 2D and finite T⁢T¯𝑇¯𝑇\sqrt{T\overline{T}}square-root start_ARG italic_T over¯ start_ARG italic_T end_ARG end_ARG deformations,” JHEP 11 (2021) 133, 2106.09750.
  33. A. Bagchi, A. Banerjee, and H. Muraki, “Boosting to BMS,” JHEP 09 (2022) 251, 2205.05094.
  34. D. Tempo and R. Troncoso, “Nonlinear automorphism of the conformal algebra in 2D and continuous T⁢T¯𝑇¯𝑇\sqrt{T\overline{T}}square-root start_ARG italic_T over¯ start_ARG italic_T end_ARG end_ARG deformations,” JHEP 12 (2022) 129, 2210.00059.
  35. J. Hou, “T⁢T¯𝑇¯𝑇T\overline{T}italic_T over¯ start_ARG italic_T end_ARG flow as characteristic flows,” JHEP 03 (2023) 243, 2208.05391.
  36. S. S. Gubser and I. R. Klebanov, “A Universal result on central charges in the presence of double trace deformations,” Nucl. Phys. B 656 (2003) 23–36, hep-th/0212138.
  37. I. R. Klebanov and E. Witten, “AdS / CFT correspondence and symmetry breaking,” Nucl. Phys. B 556 (1999) 89–114, hep-th/9905104.
  38. M. Berkooz, A. Sever, and A. Shomer, “’Double trace’ deformations, boundary conditions and space-time singularities,” JHEP 05 (2002) 034, hep-th/0112264.
  39. W. Mueck, “An Improved correspondence formula for AdS / CFT with multitrace operators,” Phys. Lett. B 531 (2002) 301–304, hep-th/0201100.
  40. D. E. Diaz and H. Dorn, “Partition functions and double-trace deformations in AdS/CFT,” JHEP 05 (2007) 046, hep-th/0702163.
  41. T. Hartman and L. Rastelli, “Double-trace deformations, mixed boundary conditions and functional determinants in AdS/CFT,” JHEP 01 (2008) 019, hep-th/0602106.
  42. S. S. Gubser and I. Mitra, “Double trace operators and one loop vacuum energy in AdS / CFT,” Phys. Rev. D 67 (2003) 064018, hep-th/0210093.
  43. I. Papadimitriou, “Multi-Trace Deformations in AdS/CFT: Exploring the Vacuum Structure of the Deformed CFT,” JHEP 05 (2007) 075, hep-th/0703152.
  44. 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.
  45. M. Guica, “T⁢T¯𝑇¯𝑇T\bar{T}italic_T over¯ start_ARG italic_T end_ARG deformations and holography,” CERN Winter School on Supergravity, Strings and Gauge Theory (2020).
  46. K. Nguyen, “Holographic boundary actions in AdS33{}_{3}start_FLOATSUBSCRIPT 3 end_FLOATSUBSCRIPT/CFT22{}_{2}start_FLOATSUBSCRIPT 2 end_FLOATSUBSCRIPT revisited,” JHEP 10 (2021) 218, 2108.01095.
  47. S. Coleman, Aspects of Symmetry: Selected Erice Lectures. Cambridge University Press, 1988.
  48. J. D. Brown and J. W. York, “Quasilocal energy and conserved charges derived from the gravitational action,” Phys. Rev. D 47 (Feb, 1993) 1407–1419.
  49. R. Conti, S. Negro, and R. Tateo, “The T⁢T¯T¯T\mathrm{T}\overline{\mathrm{T}}roman_T over¯ start_ARG roman_T end_ARG perturbation and its geometric interpretation,” JHEP 02 (2019) 085, 1809.09593.
  50. 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.
  51. R. M. Wald and A. Zoupas, “A General definition of ‘conserved quantities’ in general relativity and other theories of gravity,” Phys. Rev. D 61 (2000) 084027, gr-qc/9911095.
  52. P. Kraus, “Lectures on black holes and the AdS(3) / CFT(2) correspondence,” Lect. Notes Phys. 755 (2008) 193–247, hep-th/0609074.
  53. L. Donnay, “Asymptotic dynamics of three-dimensional gravity,” PoS Modave2015 (2016) 001, 1602.09021.
  54. G. Compère and A. Fiorucci, “Advanced Lectures on General Relativity,” 1801.07064.
  55. C. Fefferman and C. R. Graham, “Conformal invariants,” Astérisque (1985).
  56. K. Skenderis and S. N. Solodukhin, “Quantum effective action from the AdS / CFT correspondence,” Phys. Lett. B 472 (2000) 316–322, hep-th/9910023.
  57. J. D. Brown and M. Henneaux, “Central Charges in the Canonical Realization of Asymptotic Symmetries: An Example from Three-Dimensional Gravity,” Commun. Math. Phys. 104 (1986) 207–226.
  58. V. Balasubramanian and P. Kraus, “A stress tensor for anti-de Sitter gravity,” Commun. Math. Phys. 208 (1999) 413–428, hep-th/9902121.
  59. S. de Haro, S. N. Solodukhin, and K. Skenderis, “Holographic reconstruction of space-time and renormalization in the AdS / CFT correspondence,” Commun. Math. Phys. 217 (2001) 595–622, hep-th/0002230.
  60. M. He and Y.-h. Gao, “T⁢T¯/J⁢T¯𝑇¯𝑇𝐽¯𝑇T\bar{T}/J\bar{T}italic_T over¯ start_ARG italic_T end_ARG / italic_J over¯ start_ARG italic_T end_ARG-deformed WZW models from Chern-Simons AdS33{}_{3}start_FLOATSUBSCRIPT 3 end_FLOATSUBSCRIPT gravity with mixed boundary conditions,” Phys. Rev. D 103 (2021), no. 12, 126019, 2012.05726.
  61. M. Banados, “Three-dimensional quantum geometry and black holes,” AIP Conf. Proc. 484 (1999), no. 1, 147–169, hep-th/9901148.
  62. C. Ferko and S. Sethi, “Sequential Flows by Irrelevant Operators,” 2206.04787.
  63. S. Chakraborty, A. Giveon, and D. Kutasov, “T⁢T¯𝑇¯𝑇T\bar{T}italic_T over¯ start_ARG italic_T end_ARG, J⁢T¯𝐽¯𝑇J\bar{T}italic_J over¯ start_ARG italic_T end_ARG, T⁢J¯𝑇¯𝐽T\bar{J}italic_T over¯ start_ARG italic_J end_ARG and String Theory,” 1905.00051.
  64. L. McGough, M. Mezei, and H. Verlinde, “Moving the CFT into the bulk with T⁢T¯𝑇¯𝑇T\overline{T}italic_T over¯ start_ARG italic_T end_ARG,” JHEP 04 (2018) 010, 1611.03470.
  65. T. Hartman, J. Kruthoff, E. Shaghoulian, and A. Tajdini, “Holography at finite cutoff with a T2superscript𝑇2T^{2}italic_T start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT deformation,” JHEP 03 (2019) 004, 1807.11401.
  66. A. Achucarro and P. K. Townsend, “A Chern-Simons Action for Three-Dimensional anti-De Sitter Supergravity Theories,” Phys. Lett. B 180 (1986) 89.
  67. E. Witten, “(2+1)-Dimensional Gravity as an Exactly Soluble System,” Nucl. Phys. B 311 (1988) 46.
  68. T. Regge and C. Teitelboim, “Role of Surface Integrals in the Hamiltonian Formulation of General Relativity,” Annals Phys. 88 (1974) 286.
  69. O. Coussaert, M. Henneaux, and P. van Driel, “The Asymptotic dynamics of three-dimensional Einstein gravity with a negative cosmological constant,” Class. Quant. Grav. 12 (1995) 2961–2966, gr-qc/9506019.
  70. J. de Boer and J. I. Jottar, “Thermodynamics of higher spin black holes in A⁢d⁢S3𝐴𝑑subscript𝑆3AdS_{3}italic_A italic_d italic_S start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT,” JHEP 01 (2014) 023, 1302.0816.
  71. S. Ebert, C. Ferko, H.-Y. Sun, and Z. Sun, “T⁢T¯𝑇¯𝑇T\bar{T}italic_T over¯ start_ARG italic_T end_ARG in JT Gravity and BF Gauge Theory,” SciPost Phys. 13 (2022), no. 4, 096, 2205.07817.
  72. E. Llabrés, “General solutions in Chern-Simons gravity and T⁢T¯𝑇¯𝑇T\overline{T}italic_T over¯ start_ARG italic_T end_ARG-deformations,” JHEP 01 (2021) 039, 1912.13330.
  73. P. Kraus, J. Liu, and D. Marolf, “Cutoff AdS33{}_{3}start_FLOATSUBSCRIPT 3 end_FLOATSUBSCRIPT versus the T⁢T¯𝑇¯𝑇T\overline{T}italic_T over¯ start_ARG italic_T end_ARG deformation,” JHEP 07 (2018) 027, 1801.02714.
  74. S. Ebert, E. Hijano, P. Kraus, R. Monten, and R. M. Myers, “Field Theory of Interacting Boundary Gravitons,” SciPost Phys. 13 (2022), no. 2, 038, 2201.01780.
  75. J. L. Cardy, “Operator Content of Two-Dimensional Conformally Invariant Theories,” Nucl. Phys. B 270 (1986) 186–204.
  76. T. Hartman, C. A. Keller, and B. Stoica, “Universal Spectrum of 2d Conformal Field Theory in the Large c Limit,” JHEP 09 (2014) 118, 1405.5137.
  77. S. Pal and Z. Sun, “Tauberian-Cardy formula with spin,” JHEP 01 (2020) 135, 1910.07727.
  78. To appear.
  79. M. Guica, T. Hartman, W. Song, and A. Strominger, “The Kerr/CFT Correspondence,” Phys. Rev. D80 (2008) 124008, 0809.4266.

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