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  • Letter
  • Open Access

Holographic dictionary from bulk reduction

Wen-Bin Liu* and Jiang Long†

  • School of Physics, Huazhong University of Science and Technology, Luoyu Road 1037, Wuhan, Hubei 430074, China

  • *liuwenbin0036@hust.edu.cn
  • †longjiang@hust.edu.cn
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Phys. Rev. D 109, L061901 – Published 5 March, 2024

DOI: https://doi.org/10.1103/PhysRevD.109.L061901

Abstract

We propose a holographic dictionary which comes from reducing the bulk theories in an asymptotically flat spacetime to its null infinity. A general boundary theory is characterized by a fundamental field, an infinite tower of descendant fields, constraints among the fundamental field and its descendants, as well as a symplectic form. For the Carrollian diffeomorphisms, we can construct the corresponding Hamiltonians which are also the fluxes from the bulk, and whose quantum operators realize this algebra with a divergent central charge. This central charge reflects the propagating degrees of freedom and can be regularized. For the spinning theory, we need a helicity flux operator to close the algebra which relates to the duality transformation.

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References (71)

  1. A. Strominger, On BMS invariance of gravitational scattering, J. High Energy Phys. 07 (2014) 152.
  2. A. Strominger, Lectures on the infrared structure of gravity and gauge theory, arXiv:1703.05448.
  3. T. He, P. Mitra, A. P. Porfyriadis, and A. Strominger, New symmetries of massless QED, J. High Energy Phys. 10 (2014) 112.
  4. S. Pasterski and S.-H. Shao, Conformal basis for flat space amplitudes, Phys. Rev. D 96, 065022 (2017).
  5. L. Donnay, A. Fiorucci, Y. Herfray, and R. Ruzziconi, Carrollian perspective on celestial holography, Phys. Rev. Lett. 129, 071602 (2022).
  6. A. Bagchi, S. Banerjee, R. Basu, and S. Dutta, Scattering amplitudes: Celestial and Carrollian, Phys. Rev. Lett. 128, 241601 (2022).
  7. L. Donnay, A. Fiorucci, Y. Herfray, and R. Ruzziconi, Bridging Carrollian and celestial holography, Phys. Rev. D 107, 126027 (2023).
  8. T. He, V. Lysov, P. Mitra, and A. Strominger, BMS supertranslations and Weinberg’s soft graviton theorem, J. High Energy Phys. 05 (2015) 151.
  9. A. Strominger and A. Zhiboedov, Gravitational memory, BMS supertranslations and soft theorems, J. High Energy Phys. 01 (2016) 086.
  10. S. W. Hawking, M. J. Perry, and A. Strominger, Soft hair on black holes, Phys. Rev. Lett. 116, 231301 (2016).
  11. S. Pasterski, S.-H. Shao, and A. Strominger, Flat space amplitudes and conformal symmetry of the celestial sphere, Phys. Rev. D 96, 065026 (2017).
  12. W.-B. Liu and J. Long, Symmetry group at future null infinity: Scalar theory, Phys. Rev. D 107, 126002 (2023).
  13. W.-B. Liu and J. Long, Symmetry group at future null infinity II: Vector theory, J. High Energy Phys. 07 (2023) 152.
  14. W.-B. Liu and J. Long, Symmetry group at future null infinity III: Gravitational theory, J. High Energy Phys. 10 (2023) 117.
  15. W.-B. Liu, J. Long, and X.-H. Zhou, Quantum flux operators in higher spin theories, arXiv:2311.11361.
  16. A. Li, W.-B. Liu, J. Long, and R.-Z. Yu, Quantum flux operators for Carrollian diffeomorphism in general dimensions, J. High Energy Phys. 11 (2023) 140.
  17. J. M. Lévy-Leblond, Une nouvelle limite non-relativiste du groupe de Poincaré, Ann. Inst. H Poincaré 3, 1 (1965).
  18. N. Gupta, On an analogue of the galilei group, Nuovo Cimento Della Societa Italiana Di Fisica A-nuclei Particles and Fields 44, 512 (1966).
  19. M. Henneaux, Geometry of zero signature space-times, Bull. Soc. Math. Belg. 31, 47 (1979).
  20. L. Ciambelli, C. Marteau, A. C. Petkou, P. M. Petropoulos, and K. Siampos, Covariant Galilean versus Carrollian hydrodynamics from relativistic fluids, Classical Quantum Gravity 35, 165001 (2018).
  21. L. Ciambelli, R. G. Leigh, C. Marteau, and P. M. Petropoulos, Carroll structures, null geometry and conformal isometries, Phys. Rev. D 100, 046010 (2019).
  22. L. Donnay and C. Marteau, Carrollian physics at the black hole horizon, Classical Quantum Gravity 36, 165002 (2019).
  23. H. Bondi, M. G. J. van der Burg, and A. W. K. Metzner, Gravitational waves in general relativity. 7. Waves from axisymmetric isolated systems, Proc. R. Soc. A 269, 21 (1962).
  24. R. K. Sachs, Gravitational waves in general relativity. 8. Waves in asymptotically flat space-times, Proc. R. Soc. A 270, 103 (1962).
  25. R. Sachs, Asymptotic symmetries in gravitational theory, Phys. Rev. 128, 2851 (1962).
  26. G. Barnich and C. Troessaert, Aspects of the BMS/CFT correspondence, J. High Energy Phys. 05 (2010) 062.
  27. G. Barnich and C. Troessaert, BMS charge algebra, J. High Energy Phys. 12 (2011) 105.
  28. M. Campiglia and A. Laddha, Asymptotic symmetries and subleading soft graviton theorem, Phys. Rev. D 90, 124028 (2014).
  29. M. Campiglia and A. Laddha, New symmetries for the gravitational S-matrix, J. High Energy Phys. 04 (2015) 076.
  30. M. Campiglia and A. Laddha, Asymptotic symmetries of QED and Weinberg’s soft photon theorem, J. High Energy Phys. 07 (2015) 115.
  31. M. Campiglia and J. Peraza, Generalized BMS charge algebra, Phys. Rev. D 101, 104039 (2020).
  32. C. Duval, G. W. Gibbons, and P. A. Horvathy, Conformal Carroll groups and BMS symmetry, Classical Quantum Gravity 31, 092001 (2014).
  33. C. Duval, G. W. Gibbons, and P. A. Horvathy, Conformal Carroll groups, J. Phys. A 47, 335204 (2014).
  34. G. Satishchandran and R. M. Wald, Asymptotic behavior of massless fields and the memory effect, Phys. Rev. D 99, 084007 (2019).
  35. X. Bekaert and B. Oblak, Massless scalars and higher-spin BMS in any dimension, J. High Energy Phys. 11 (2022) 022.
  36. A. Ashtekar and M. Streubel, Symplectic geometry of radiative modes and conserved quantities at null infinity, Proc. R. Soc. A 376, 585 (1981).
  37. A. Ashtekar, Asymptotic quantization of the gravitational field, Phys. Rev. Lett. 46, 573 (1981).
  38. R. M. Wald, Black hole entropy is the Noether charge, Phys. Rev. D 48, R3427 (1993).
  39. V. Iyer and R. M. Wald, Some properties of Noether charge and a proposal for dynamical black hole entropy, Phys. Rev. D 50, 846 (1994).
  40. 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).
  41. G. Compère, R. Oliveri, and A. Seraj, The Poincaré and BMS flux-balance laws with application to binary systems, J. High Energy Phys. 10 (2020) 116.
  42. G. Compère, A. Fiorucci, and R. Ruzziconi, Superboost transitions, refraction memory and super-Lorentz charge algebra, J. High Energy Phys. 11 (2018) 200; 04 (2020) 172(E).
  43. G. Compère, A. Fiorucci, and R. Ruzziconi, The Λ−BMS4 charge algebra, J. High Energy Phys. 10 (2020) 205.
  44. L. Donnay, K. Nguyen, and R. Ruzziconi, Loop-corrected subleading soft theorem and the celestial stress tensor, J. High Energy Phys. 09 (2022) 063.
  45. E. E. Flanagan and D. A. Nichols, Conserved charges of the extended Bondi-Metzner-Sachs algebra, Phys. Rev. D 95, 044002 (2017).
  46. S. W. Hawking, Zeta function regularization of path integrals in curved spacetime, Commun. Math. Phys. 55, 133 (1977).
  47. E. Elizalde, S. D. Odintsov, A. Romeo, A. A. Bytsenko, and S. Zerbini, Zeta Regularization Techniques with Applications (World Scientific Publishing, Singapore, 1994).
  48. I. Polterovich, Heat invariants of Riemannian manifolds, Isr. J. Math. 119, 239 (2000).
  49. D. V. Vassilevich, Heat kernel expansion: User’s manual, Phys. Rep. 388, 279 (2003).
  50. D. Birmingham, Conformal anomaly in spherical spacetimes, Phys. Rev. D 36, 3037 (1987).
  51. P. A. M. Dirac, Quantised singularities in the electromagnetic field, Proc. R. Soc. A 133, 60 (1931).
  52. S. Deser and C. Teitelboim, Duality transformations of Abelian and non-Abelian gauge fields, Phys. Rev. D 13, 1592 (1976).
  53. K. Y. Bliokh, A. Y. Bekshaev, and F. Nori, Dual electromagnetism: Helicity, spin, momentum, and angular momentum, New J. Phys. 15, 033026 (2013).
  54. Y. Hamada, M.-S. Seo, and G. Shiu, Electromagnetic duality and the electric memory effect, J. High Energy Phys. 02 (2018) 046.
  55. V. Hosseinzadeh, A. Seraj, and M. M. Sheikh-Jabbari, Soft charges and electric-magnetic duality, J. High Energy Phys. 08 (2018) 102.
  56. A. Seraj and B. Oblak, Precession caused by gravitational waves, Phys. Rev. Lett. 129, 061101 (2022).
  57. M. Henneaux and C. Teitelboim, Duality in linearized gravity, Phys. Rev. D 71, 024018 (2005).
  58. B. Julia, J. Levie, and S. Ray, Gravitational duality near de Sitter space, J. High Energy Phys. 11 (2005) 025.
  59. C. W. Bunster, S. Cnockaert, M. Henneaux, and R. Portugues, Monopoles for gravitation and for higher spin fields, Phys. Rev. D 73, 105014 (2006).
  60. S. Ramaswamy and A. Sen, Dualmass in general relativity, J. Math. Phys. (N.Y.) 22, 2612 (1981).
  61. A. Strominger, Magnetic corrections to the soft photon theorem, Phys. Rev. Lett. 116, 031602 (2016).
  62. L. Freidel and D. Pranzetti, Electromagnetic duality and central charge, Phys. Rev. D 98, 116008 (2018).
  63. H. Godazgar, M. Godazgar, and C. N. Pope, Subleading BMS charges and fake news near null infinity, J. High Energy Phys. 01 (2019) 143.
  64. H. Godazgar, M. Godazgar, and C. N. Pope, New dual gravitational charges, Phys. Rev. D 99, 024013 (2019).
  65. H. Godazgar, M. Godazgar, and C. N. Pope, Tower of subleading dual BMS charges, J. High Energy Phys. 03 (2019) 057.
  66. E. T. Newman and T. W. J. Unti, Behavior of asymptotically flat empty spaces, J. Math. Phys. (N.Y.) 3, 891 (1962).
  67. G. Barnich and P.-H. Lambert, A note on the Newman-Unti group and the BMS charge algebra in terms of Newman-Penrose coefficients, Adv. Theor. Math. Phys. 2012, 197385 (2012).
  68. P. Kravchuk and D. Simmons-Duffin, Light-ray operators in conformal field theory, J. High Energy Phys. 11 (2018) 102.
  69. C. Córdova and S.-H. Shao, Light-ray operators and the BMS algebra, Phys. Rev. D 98, 125015 (2018).
  70. G. P. Korchemsky, E. Sokatchev, and A. Zhiboedov, Generalizing event shapes: In search of lost collider time, J. High Energy Phys. 08 (2022) 188.
  71. G. P. Korchemsky and A. Zhiboedov, On the light-ray algebra in conformal field theories, J. High Energy Phys. 02 (2022) 140.

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Phys. Rev. D 109, L061901– Published 5 March, 2024
  • Received 12 July 2023
  • Accepted 18 January 2024
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