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Constraints on a fine-grained AdS/CFT correspondence

Mirah Gary* and Steven B. Giddings†

  • Department of Physics, University of California, Santa Barbara, California 93106, USA

  • *mgary@alumni.physics.ucsb.edu
  • †giddings@physics.ucsb.edu
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Phys. Rev. D 94, 065017 – Published 14 September, 2016

DOI: https://doi.org/10.1103/PhysRevD.94.065017

Abstract

For a boundary conformal field theory to give a good approximation to the bulk flat-space S-matrix, a number of conditions need to be satisfied: some of those are investigated here. In particular, one would like to identify an appropriate set of approximate asymptotic scattering states, constructed purely via boundary data. We overview, elaborate, and simplify obstacles encountered with existing proposals for these. Those corresponding to normalizable wave functions undergo multiple interactions; we contrast this situation with that needed for a flat-space Lehmann-Symanzik-Zimmermann treatment. Non-normalizable wave functions can have spurious interactions, due either to power-law tails of wave packets or to their non-normalizable behavior, which obscure S-matrix amplitudes we wish to extract, although in the latter case we show that such gravitational interactions can be finite, as a result of gravitational redshift. We outline an illustrative construction of arbitrary normalizable wave packets from boundary data that also yields such spurious interactions. Another set of nontrivial questions regard the form of unitarity relations for the bulk S-matrix, and in particular its normalization and multiparticle cuts. These combined constraints, together with those found earlier on a boundary singularity structure needed for bulk momentum conservation and other physical/analytic properties, are a nontrivial collection of obstacles to surmount if a fine-grained S-matrix, as opposed to a coarse-grained construction, is to be defined purely from boundary data.

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References (35)

  1. J. M. Maldacena, The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2, 231 (1998); Int. J. Theor. Phys. 38, 1113 (1999); arXiv:hep-th/9711200.
  2. J. Polchinski, Emergent spacetime from AdS/CFT, talk at the workshop Harmony of Scattering Amplitudes, KITP, 2011 (2011)http://online.itp.ucsb.edu/online/qcdscat11/polchinski/.
  3. J. Polchinski, S-matrices from AdS spacetime, arXiv:hep-th/9901076.
  4. L. Susskind, Holography in the flat space limit, arXiv:hep-th/9901079.
  5. S. B. Giddings, Flat-space scattering and bulk locality in the AdS/CFT correspondence, Phys. Rev. D 61, 106008 (2000); arXiv:hep-th/9907129.
  6. M. Gary, S. B. Giddings, and J. Penedones, Local bulk S-matrix elements and CFT singularities, Phys. Rev. D 80, 085005 (2009); arXiv:0903.4437.
  7. M. Gary and S. B. Giddings, The flat space S-matrix from the AdS/CFT correspondence?, Phys. Rev. D 80, 046008 (2009); arXiv:0904.3544.
  8. I. Heemskerk, J. Penedones, J. Polchinski, and J. Sully, Holography from conformal field theory, J. High Energy Phys. 10 (2009) 079; arXiv:0907.0151.
  9. A. L. Fitzpatrick, E. Katz, D. Poland, and D. Simmons-Duffin, Effective conformal theory and the flat-space limit of AdS, J. High Energy Phys. 07 (2011) 023; arXiv:1007.2412.
  10. A. L. Fitzpatrick and J. Kaplan, Scattering states in AdS/CFT, arXiv:1104.2597.
  11. S. B. Giddings, Is string theory a theory of quantum gravity?, Found. Phys. 43, 115 (2013); arXiv:1105.6359.
  12. S. B. Giddings, Nonlocality versus complementarity: A conservative approach to the information problem, Classical Quantum Gravity 28, 025002 (2011); arXiv:0911.3395.
  13. S. Coleman, Acausality, in Erice 1969, Ettore Majorana School On Subnuclear Phenomena (Academic Press, New York 1970), pp. 282–327.
  14. S. B. Giddings and R. A. Porto, The gravitational S-matrix, Phys. Rev. D 81, 025002 (2010); arXiv:0908.0004.
  15. S. B. Giddings, The gravitational S-matrix: Erice lectures, Subnuclear series 48, 93 (2013); arXiv:1105.2036.
  16. E. D’Hoker, D. Z. Freedman, S. D. Mathur, A. Matusis, and L. Rastelli, Graviton and gauge boson propagators in AdS(d+1), Nucl. Phys. B562, 330 (1999); arXiv:hepth/9902042.
  17. S. S. Gubser, I. R. Klebanov, and A. M. Polyakov, Gauge theory correlators from non-critical string theory, Phys. Lett. B 428, 105 (1998); arXiv:hep-th/9802109.
  18. E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2, 253 (1998); arXiv:hep-th/9802150.
  19. S. B. Giddings, The Boundary S Matrix and the AdS to CFT Dictionary, Phys. Rev. Lett. 83, 2707 (1999); arXiv:hep-th/9903048.
  20. C. P. Burgess and C. A. Lutken, Propagators and effective potentials in anti-de Sitter space, Phys. Lett. 153B, 137 (1985).
  21. V. Balasubramanian, P. Kraus, and A. E. Lawrence, Bulk versus boundary dynamics in anti-de Sitter space-time, Phys. Rev. D 59, 046003 (1999); C. P. Burgess and C. A. LutkenarXiv:hep-th/9805171.
  22. M. Reed and B. Simon, Methods of Mathematical Physics, Scattering Theory Vol. 3 (Academic, New York, 1979).
  23. S. B. Giddings and M. Srednicki, High-energy gravitational scattering and black hole resonances, Phys. Rev. D 77, 085025 (2008); V. Balasubramanian, P. Kraus, and A. E. LawrencearXiv:0711.5012.
  24. C. Fefferman and R. Graham, Conformal invariants, in Élie Cartan et les Mathématiques d’Aujourdui, Astérisque, 95 (Lyon, 1985).
  25. T. Andrade and D. Marolf, AdS/CFT beyond the unitarity bound, J. High Energy Phys. 01 (2012) 049; arXiv:1105.6337.
  26. S. Raju, Generalized Recursion Relations for Correlators in the Gauge-Gravity Correspondence, Phys. Rev. Lett. 106, 091601 (2011); arXiv:1011.0780.
  27. A. L. Fitzpatrick, J. Kaplan, J. Penedones, S. Raju, and B. C. van Rees, A natural language for AdS/CFT correlators, J. High Energy Phys. 11 (2011) 095; arXiv:1107.1499.
  28. J. Penedones, talk at Strings 2015, https://strings2015.icts.res.in/speakerProfile.php?sId=45.
  29. A. L. Fitzpatrick and J. Kaplan, Analyticity and the holographic S-matrix, J. High Energy Phys. 10 (2012) 127; arXiv:1111.6972.
  30. A. L. Fitzpatrick and J. Kaplan, Unitarity and the holographic S-matrix, J. High Energy Phys. 10 (2012) 032; arXiv:1112.4845.
  31. D. Christodoulou and S. Klainerman, The Global Nonlinear Stability of the Minkowski Space (Princeton University Press, Princeton, NJ, 1993).
  32. M. T. Anderson, On the uniqueness and global dynamics of AdS spacetimes, Classical Quantum Gravity 23, 6935 (2006); arXiv:hep-th/0605293.
  33. P. Bizon and A. Rostworowski, On Weakly Turbulent Instability of Anti-de Sitter space, Phys. Rev. Lett. 107, 031102 (2011); arXiv:1104.3702.
  34. O. J. C. Dias, G. T. Horowitz, and J. E. Santos, Gravitational turbulent instability of anti-de Sitter space, arXiv:1109.1825.
  35. J. Polchinski, comment on talk by E. Silverstein at the workshop Black Holes, Complementarity, Fuzz, or Fire, KITP, UCSB, 2013 (2013) http://online.kitp.ucsb.edu/online/fuzzorfire_m13/silverstein/.

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Phys. Rev. D 94, 065017– Published 14 September, 2016
  • Received 25 August 2011
Article part of CHORUS

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