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  • Letter
  • Open Access

Logarithmic celestial conformal field theory

Adrien Fiorucci*, Daniel Grumiller†, and Romain Ruzziconi‡

  • Institute for Theoretical Physics, TU Wien Wiedner Hauptstrasse 8–10/136, A-1040 Vienna, Austria

  • *adrien.fiorucci@tuwien.ac.at
  • †grumil@hep.itp.tuwien.ac.at
  • ‡romain.ruzziconi@tuwien.ac.at
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Phys. Rev. D 109, L021902 – Published 19 January, 2024

DOI: https://doi.org/10.1103/PhysRevD.109.L021902

Abstract

We argue that the celestial conformal field theory exhibits patterns of a logarithmic conformal field theory. We uncover a Jordan block structure involving the celestial stress tensor and its logarithmic partner, a composite operator built from the stress tensor and the Liouville field. Using a limiting process whose parameter corresponds to the infrared cutoff of gravity, we perform some basic consistency checks, particularly the calculation of two-point correlators, which reveals the expected logarithmic behavior. We comment on the vanishing value of the central charge in the celestial conformal field theory and explain how the logarithmic partner is relevant for its well-behavedness.

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References (85)

  1. J. de Boer and S. N. Solodukhin, A holographic reduction of Minkowski space-time, Nucl. Phys. B665, 545 (2003).
  2. T. He, P. Mitra, and A. Strominger, 2D Kac-Moody symmetry of 4D Yang-Mills theory, J. High Energy Phys. 10 (2016) 137.
  3. S. Pasterski, S.-H. Shao, and A. Strominger, Flat space amplitudes and conformal symmetry of the celestial sphere, Phys. Rev. D 96, 065026 (2017).
  4. C. Cheung, A. de la Fuente, and R. Sundrum, 4D scattering amplitudes and asymptotic symmetries from 2D CFT, J. High Energy Phys. 01 (2017) 112.
  5. S. Pasterski and S.-H. Shao, Conformal basis for flat space amplitudes, Phys. Rev. D 96, 065022 (2017).
  6. A. Strominger, Lectures on the Infrared Structure of Gravity and Gauge Theory (Princeton University Press, Princeton, NJ, 2018).
  7. S. Pasterski, S.-H. Shao, and A. Strominger, Gluon amplitudes as 2d conformal correlators, Phys. Rev. D 96, 085006 (2017).
  8. L. Donnay, A. Puhm, and A. Strominger, Conformally soft photons and gravitons, J. High Energy Phys. 01 (2019) 184.
  9. T. Adamo, L. Mason, and A. Sharma, Celestial amplitudes and conformal soft theorems, Classical Quantum Gravity 36, 205018 (2019).
  10. A. Puhm, Conformally soft theorem in gravity, J. High Energy Phys. 09 (2020) 130.
  11. A. Guevara, Notes on conformal soft theorems and recursion relations in gravity, arXiv:1906.07810.
  12. D. Kapec, P. Mitra, A.-M. Raclariu, and A. Strominger, 2D stress tensor for 4D gravity, Phys. Rev. Lett. 119, 121601 (2017).
  13. K. Costello, N. M. Paquette, and A. Sharma, Top-down holography in an asymptotically flat spacetime, Phys. Rev. Lett. 130, 061602 (2023).
  14. A. Fotopoulos, S. Stieberger, T. R. Taylor, and B. Zhu, Extended BMS algebra of celestial CFT, J. High Energy Phys. 03 (2020) 130.
  15. S. Banerjee and S. Pasterski, Revisiting the shadow stress tensor in celestial CFT, J. High Energy Phys. 04 (2023) 118.
  16. G. Compère, A. Fiorucci, and R. Ruzziconi, The Λ−BMS4 charge algebra, J. High Energy Phys. 10 (2020) 205.
  17. L. Donnay and R. Ruzziconi, BMS flux algebra in celestial holography, J. High Energy Phys. 11 (2021) 040.
  18. V. Gurarie, c theorem for disordered systems, Nucl. Phys. B546, 765 (1999).
  19. J. Cardy, Logarithmic conformal field theories as limits of ordinary CFTs and some physical applications, J. Phys. A 46, 494001 (2013).
  20. A. Ball, E. Himwich, S. A. Narayanan, S. Pasterski, and A. Strominger, Uplifting AdS3/CFT2 to flat space holography, J. High Energy Phys. 08 (2019) 168.
  21. G. Compère and J. Long, Vacua of the gravitational field, J. High Energy Phys. 07 (2016) 137.
  22. G. Compère, A. Fiorucci, and R. Ruzziconi, Superboost transitions, refraction memory and super-Lorentz charge algebra, J. High Energy Phys. 11 (2018) 200.
  23. V. Gurarie, Logarithmic operators in conformal field theory, Nucl. Phys. B410, 535 (1993).
  24. M. Flohr, Bits and pieces in logarithmic conformal field theory, Int. J. Mod. Phys. A 18, 4497 (2003).
  25. M. R. Gaberdiel, An algebraic approach to logarithmic conformal field theory, Int. J. Mod. Phys. A 18, 4593 (2003).
  26. D. Grumiller, W. Riedler, J. Rosseel, and T. Zojer, Holographic applications of logarithmic conformal field theories, J. Phys. A 46, 494002 (2013).
  27. T. Creutzig and D. Ridout, Logarithmic conformal field theory: Beyond an introduction, J. Phys. A 46, 4006 (2013).
  28. H. Bondi, M. G. J. van der Burg, and A. W. K. Metzner, Gravitational waves in general relativity. VII. Waves from axisymmetric isolated systems, Proc. R. Soc. A269, 21 (1962). 
  29. R. Sachs, Asymptotic symmetries in gravitational theory, Phys. Rev. 128, 2851 (1962).
  30. E. T. Newman and T. W. J. Unti, Behavior of asymptotically flat empty spaces, J. Math. Phys. (N.Y.) 3, 891 (1962).
  31. R. Penrose, Asymptotic properties of fields and space-times, Phys. Rev. Lett. 10, 66 (1963).
  32. R. Penrose, Conformal treatment of infinity, Gen. Relativ. Gravit. 43, 901 (2011).
  33. R. Geroch, Asymptotic structure of space-time, in Asymptotic Structure of Space-Time, edited by F. P. Esposito and L. Witten (Springer, 1977), p. 1, 10.1007/978-1-4684-2343-3_1.
  34. A. Ashtekar and M. Streubel, Symplectic geometry of radiative modes and conserved quantities at null infinity, Proc. R. Soc. A 376, 585 (1981).
  35. A. Ashtekar, Asymptotic quantization of the gravitational field, Phys. Rev. Lett. 46, 573 (1981).
  36. R. M. Wald and A. Zoupas, A General definition of “conserved quantities” in general relativity and other theories of gravity, Phys. Rev. D 61, 084027 (2000).
  37. G. Barnich and C. Troessaert, Aspects of the BMS/CFT correspondence, J. High Energy Phys. 05 (2010) 062.
  38. G. Barnich and C. Troessaert, BMS charge algebra, J. High Energy Phys. 12 (2011) 105.
  39. A. Strominger, On BMS invariance of gravitational scattering, J. High Energy Phys. 07 (2014) 152.
  40. A. Ashtekar, Geometry and physics of null infinity, arXiv:1409.1800.
  41. L. Donnay, A. Fiorucci, Y. Herfray, and R. Ruzziconi, Bridging Carrollian and celestial holography, Phys. Rev. D 107, 126027 (2023).
  42. G. Barnich and C. Troessaert, Symmetries of asymptotically flat 4 dimensional spacetimes at null infinity revisited, Phys. Rev. Lett. 105, 111103 (2010).
  43. D. Christodoulou and S. Klainerman, The Global nonlinear stability of the Minkowski space (Princeton University Press, 1994).
  44. L. Blanchet and T. Damour, Tail transported temporal correlations in the dynamics of a gravitating system, Phys. Rev. D 37, 1410 (1988).
  45. L. Blanchet and G. Schaefer, Gravitational wave tails and binary star systems, Classical Quantum Gravity 10, 2699 (1993).
  46. B. Sahoo and A. Sen, Classical and quantum results on logarithmic terms in the soft theorem in four dimensions, J. High Energy Phys. 02 (2019) 086.
  47. L. Blanchet, G. Compère, G. Faye, R. Oliveri, and A. Seraj, Multipole expansion of gravitational waves: From harmonic to Bondi coordinates, J. High Energy Phys. 02 (2021) 029.
  48. B. Sahoo and A. Sen, Classical soft graviton theorem rewritten, J. High Energy Phys. 01 (2022) 077.
  49. J. Podolsky and R. Steinbauer, Geodesics in space-times with expanding impulsive gravitational waves, Phys. Rev. D 67, 064013 (2003).
  50. J. Podolsky and R. Svarc, Refraction of geodesics by impulsive spherical gravitational waves in constant-curvature spacetimes with a cosmological constant, Phys. Rev. D 81, 124035 (2010).
  51. J. Podolsky, C. Sämann, R. Steinbauer, and R. Svarc, The global uniqueness and C1-regularity of geodesics in expanding impulsive gravitational waves, Classical Quantum Gravity 33, 195010 (2016).
  52. P. M. Zhang, C. Duval, G. W. Gibbons, and P. A. Horvathy, The memory effect for plane gravitational waves, Phys. Lett. B 772, 743 (2017).
  53. P. M. Zhang, C. Duval, G. W. Gibbons, and P. A. Horvathy, Velocity memory effect for polarized gravitational waves, J. Cosmol. Astropart. Phys. 05 (2018) 030.
  54. S. Pasterski, A. Puhm, and E. Trevisani, Revisiting the conformally soft sector with celestial diamonds, J. High Energy Phys. 11 (2021) 143.
  55. L. Donnay, A. Fiorucci, Y. Herfray, and R. Ruzziconi, Carrollian perspective on celestial holography, Phys. Rev. Lett. 129, 071602 (2022).
  56. L. Freidel, D. Pranzetti, and A.-M. Raclariu, A discrete basis for celestial holography, arXiv:2212.12469.
  57. D. Kapec, V. Lysov, S. Pasterski, and A. Strominger, Semiclassical Virasoro symmetry of the quantum gravity S-matrix, J. High Energy Phys. 08 (2014) 058.
  58. A. Fotopoulos and T. R. Taylor, Primary fields in celestial CFT, J. High Energy Phys. 10 (2019) 167.
  59. T. He, D. Kapec, A.-M. Raclariu, and A. Strominger, Loop-corrected Virasoro symmetry of 4D quantum gravity, J. High Energy Phys. 08 (2017) 050.
  60. L. Donnay, K. Nguyen, and R. Ruzziconi, Loop-corrected subleading soft theorem and the celestial stress tensor, J. High Energy Phys. 09 (2022) 063.
  61. S. Pasterski, A comment on loop corrections to the celestial stress tensor, J. High Energy Phys. 01 (2023) 025.
  62. M. Campiglia and A. Laddha, BMS algebra, double soft theorems, and all that, arXiv:2106.14717.
  63. M. Campiglia and J. Peraza, Generalized BMS charge algebra, Phys. Rev. D 101, 104039 (2020).
  64. E. Himwich, S. A. Narayanan, M. Pate, N. Paul, and A. Strominger, The soft S-matrix in gravity, J. High Energy Phys. 09 (2020) 129.
  65. K. Nguyen and J. Salzer, The effective action of superrotation modes, J. High Energy Phys. 02 (2021) 108.
  66. K. Nguyen and J. Salzer, Celestial IR divergences and the effective action of supertranslation modes, J. High Energy Phys. 09 (2021) 144.
  67. V. Balasubramanian and P. Kraus, A stress tensor for anti-de Sitter gravity, Commun. Math. Phys. 208, 413 (1999).
  68. K. Nguyen, Schwarzian transformations at null infinity, Proc. Sci. CORFU2021 (2022) 133.
  69. S. Pasterski and H. Verlinde, Chaos in celestial CFT, J. High Energy Phys. 08 (2022) 106.
  70. J. Cotler, N. Miller, and A. Strominger, An integer basis for celestial amplitudes, J. High Energy Phys. 08 (2023) 192.
  71. R. Bhardwaj, L. Lippstreu, L. Ren, M. Spradlin, A. Yelleshpur Srikant, and A. Volovich, Loop-level gluon OPEs in celestial holography, J. High Energy Phys. 11 (2022) 171.
  72. A. Bagchi, S. Detournay, and D. Grumiller, Flat-space chiral gravity, Phys. Rev. Lett. 109, 151301 (2012).
  73. G. Barnich, Entropy of three-dimensional asymptotically flat cosmological solutions, J. High Energy Phys. 10 (2012) 095.
  74. A. Bagchi, S. Detournay, R. Fareghbal, and J. Simón, Holography of 3D flat cosmological horizons, Phys. Rev. Lett. 110, 141302 (2013).
  75. A. Bagchi, S. Detournay, D. Grumiller, and J. Simon, Cosmic evolution from phase transition of three-dimensional flat space, Phys. Rev. Lett. 111, 181301 (2013).
  76. A. Bagchi, R. Basu, D. Grumiller, and M. Riegler, Entanglement entropy in Galilean conformal field theories and flat holography, Phys. Rev. Lett. 114, 111602 (2015).
  77. A. Bagchi, D. Grumiller, and W. Merbis, Stress tensor correlators in three-dimensional gravity, Phys. Rev. D 93, 061502 (2016).
  78. A. Campoleoni, H. A. Gonzalez, B. Oblak, and M. Riegler, BMS modules in three dimensions, Int. J. Mod. Phys. A 31, 1650068 (2016).
  79. A. Bagchi, M. Gary, and Zodinmawia, Bondi-Metzner-Sachs bootstrap, Phys. Rev. D 96, 025007 (2017).
  80. H. Jiang, W. Song, and Q. Wen, Entanglement entropy in flat holography, J. High Energy Phys. 07 (2017) 142.
  81. E. Hijano, Semi-classical BMS3 blocks and flat holography, J. High Energy Phys. 10 (2018) 044.
  82. D. Grumiller, P. Parekh, and M. Riegler, Local quantum energy conditions in non-Lorentz-invariant quantum field theories, Phys. Rev. Lett. 123, 121602 (2019).
  83. A. Campoleoni, L. Ciambelli, A. Delfante, C. Marteau, P. M. Petropoulos, and R. Ruzziconi, Holographic Lorentz and Carroll frames, J. High Energy Phys. 12 (2022) 007.
  84. A. Bagchi, S. Banerjee, R. Basu, and S. Dutta, Scattering amplitudes: Celestial and Carrollian, Phys. Rev. Lett. 128, 241601 (2022).
  85. A. Bagchi, P. Dhivakar, and S. Dutta, AdS Witten diagrams to Carrollian correlators, J. High Energy Phys. 04 (2023) 135.

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Phys. Rev. D 109, L021902– Published 19 January, 2024
  • Received 24 May 2023
  • Accepted 9 November 2023
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