Advertisement

Genus-one string amplitudes from conformal field theory

  • Luis F. Alday
  • Agnese Bissi
  • Eric PerlmutterEmail author
Open Access
Regular Article - Theoretical Physics

Abstract

We explore and exploit the relation between non-planar correlators in \( \mathcal{N} \) = 4 super-Yang-Mills, and higher-genus closed string amplitudes in type IIB string theory. By conformal field theory techniques we construct the genus-one, four-point string amplitude in AdS5 × S5 in the low-energy expansion, dual to an \( \mathcal{N} \) = 4 super-Yang-Mills correlator in the ’t Hooft limit at order 1/c2 in a strong coupling expansion. In the flat space limit, this maps onto the genus-one, four-point scattering amplitude for type II closed strings in ten dimensions. Using this approach we reproduce several results obtained via string perturbation theory. We also demonstrate a novel mechanism to fix subleading terms in the flat space limit of AdS amplitudes by using string/M-theory.

Keywords

AdS-CFT Correspondence Conformal Field Theory Gauge-gravity correspondence Supersymmetric Gauge Theory 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    E. D’Hoker, D.Z. Freedman, S.D. Mathur, A. Matusis and L. Rastelli, Graviton exchange and complete four point functions in the AdS/CFT correspondence, Nucl. Phys. B 562 (1999) 353 [hep-th/9903196] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    I. Heemskerk, J. Penedones, J. Polchinski and J. Sully, Holography from Conformal Field Theory, JHEP 10 (2009) 079 [arXiv:0907.0151] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  3. [3]
    J. Penedones, Writing CFT correlation functions as AdS scattering amplitudes, JHEP 03 (2011) 025 [arXiv:1011.1485] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    L.F. Alday, A. Bissi and T. Lukowski, Lessons from crossing symmetry at large N, JHEP 06 (2015) 074 [arXiv:1410.4717] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    O. Aharony, L.F. Alday, A. Bissi and E. Perlmutter, Loops in AdS from Conformal Field Theory, JHEP 07 (2017) 036 [arXiv:1612.03891] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    L.F. Alday and A. Bissi, Loop Corrections to Supergravity on AdS 5 × S 5, Phys. Rev. Lett. 119 (2017) 171601 [arXiv:1706.02388] [INSPIRE].CrossRefGoogle Scholar
  7. [7]
    L.F. Alday, Large Spin Perturbation Theory for Conformal Field Theories, Phys. Rev. Lett. 119 (2017) 111601 [arXiv:1611.01500] [INSPIRE].CrossRefGoogle Scholar
  8. [8]
    S. Caron-Huot, Analyticity in Spin in Conformal Theories, JHEP 09 (2017) 078 [arXiv:1703.00278] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    L.F. Alday and S. Caron-Huot, Gravitational S-matrix from CFT dispersion relations, JHEP 12 (2018) 017 [arXiv:1711.02031] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    F. Aprile, J.M. Drummond, P. Heslop and H. Paul, Quantum Gravity from Conformal Field Theory, JHEP 01 (2018) 035 [arXiv:1706.02822] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    F. Aprile, J.M. Drummond, P. Heslop and H. Paul, Unmixing Supergravity, JHEP 02 (2018) 133 [arXiv:1706.08456] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    F. Aprile, J. Drummond, P. Heslop and H. Paul, Double-trace spectrum of N = 4 supersymmetric Yang-Mills theory at strong coupling, Phys. Rev. D 98 (2018) 126008 [arXiv:1802.06889] [INSPIRE].Google Scholar
  13. [13]
    L. Susskind, Holography in the flat space limit, AIP Conf. Proc. 493 (1999) 98 [hep-th/9901079] [INSPIRE].MathSciNetzbMATHGoogle Scholar
  14. [14]
    J. Polchinski, S matrices from AdS space-time, hep-th/9901076 [INSPIRE].
  15. [15]
    T. Okuda and J. Penedones, String scattering in flat space and a scaling limit of Yang-Mills correlators, Phys. Rev. D 83 (2011) 086001 [arXiv:1002.2641] [INSPIRE].Google Scholar
  16. [16]
    N. Berkovits, New higher-derivative R 4 theorems, Phys. Rev. Lett. 98 (2007) 211601 [hep-th/0609006] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    M.B. Green and J.H. Schwarz, Supersymmetrical String Theories, Phys. Lett. 109B (1982) 444 [INSPIRE].CrossRefGoogle Scholar
  18. [18]
    M.B. Green, M. Gutperle and P. Vanhove, One loop in eleven-dimensions, Phys. Lett. B 409 (1997) 177 [hep-th/9706175] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    J.G. Russo and A.A. Tseytlin, One loop four graviton amplitude in eleven-dimensional supergravity, Nucl. Phys. B 508 (1997) 245 [hep-th/9707134] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    M.B. Green and S. Sethi, Supersymmetry constraints on type IIB supergravity, Phys. Rev. D 59 (1999) 046006 [hep-th/9808061] [INSPIRE].MathSciNetGoogle Scholar
  21. [21]
    M.B. Green, H.-h. Kwon and P. Vanhove, Two loops in eleven-dimensions, Phys. Rev. D 61 (2000) 104010 [hep-th/9910055] [INSPIRE].MathSciNetGoogle Scholar
  22. [22]
    M.B. Green and P. Vanhove, The low-energy expansion of the one loop type-II superstring amplitude, Phys. Rev. D 61 (2000) 104011 [hep-th/9910056] [INSPIRE].MathSciNetGoogle Scholar
  23. [23]
    M.B. Green and P. Vanhove, Duality and higher derivative terms in M-theory, JHEP 01 (2006) 093 [hep-th/0510027] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  24. [24]
    M.B. Green, J.G. Russo and P. Vanhove, Non-renormalisation conditions in type-II string theory and maximal supergravity, JHEP 02 (2007) 099 [hep-th/0610299] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  25. [25]
    M.B. Green, J.G. Russo and P. Vanhove, Low energy expansion of the four-particle genus-one amplitude in type-II superstring theory, JHEP 02 (2008) 020 [arXiv:0801.0322] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  26. [26]
    V. Gonçalves, Four point function of \( \mathcal{N} \) = 4 stress-tensor multiplet at strong coupling, JHEP 04 (2015) 150 [arXiv:1411.1675] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  27. [27]
    M. Nirschl and H. Osborn, Superconformal Ward identities and their solution, Nucl. Phys. B 711 (2005) 409 [hep-th/0407060] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  28. [28]
    F.A. Dolan, L. Gallot and E. Sokatchev, On four-point functions of 1/2-BPS operators in general dimensions, JHEP 09 (2004) 056 [hep-th/0405180] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  29. [29]
    C. Beem, L. Rastelli and B.C. van Rees, More \( \mathcal{N} \) = 4 superconformal bootstrap, Phys. Rev. D 96 (2017) 046014 [arXiv:1612.02363] [INSPIRE].MathSciNetGoogle Scholar
  30. [30]
    G. Arutyunov and S. Frolov, Four-point functions of lowest weight chiral primary operators in N = 4 four-dimensional supersymmetric Yang-Mills theory in the supergravity approximation, Phys. Rev. D 62 (2000) 064016 [hep-th/0002170] [INSPIRE].MathSciNetGoogle Scholar
  31. [31]
    F.A. Dolan and H. Osborn, Superconformal symmetry, correlation functions and the operator product expansion, Nucl. Phys. B 629 (2002) 3 [hep-th/0112251] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  32. [32]
    L. Rastelli and X. Zhou, Mellin amplitudes for AdS 5 × S 5, Phys. Rev. Lett. 118 (2017) 091602 [arXiv:1608.06624] [INSPIRE].CrossRefGoogle Scholar
  33. [33]
    L. Rastelli and X. Zhou, How to Succeed at Holographic Correlators Without Really Trying, JHEP 04 (2018) 014 [arXiv:1710.05923] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  34. [34]
    M.S. Costa, V. Gonçalves and J. Penedones, Conformal Regge theory, JHEP 12 (2012) 091 [arXiv:1209.4355] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  35. [35]
    X.O. Camanho, J.D. Edelstein, J. Maldacena and A. Zhiboedov, Causality Constraints on Corrections to the Graviton Three-Point Coupling, JHEP 02 (2016) 020 [arXiv:1407.5597] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  36. [36]
    D. Meltzer and E. Perlmutter, Beyond a = c: gravitational couplings to matter and the stress tensor OPE, JHEP 07 (2018) 157 [arXiv:1712.04861] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  37. [37]
    N. Afkhami-Jeddi, T. Hartman, S. Kundu and A. Tajdini, Einstein gravity 3-point functions from conformal field theory, JHEP 12 (2017) 049 [arXiv:1610.09378] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  38. [38]
    M. Kulaxizi, A. Parnachev and A. Zhiboedov, Bulk Phase Shift, CFT Regge Limit and Einstein Gravity, JHEP 06 (2018) 121 [arXiv:1705.02934] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  39. [39]
    M.S. Costa, T. Hansen and J. Penedones, Bounds for OPE coefficients on the Regge trajectory, JHEP 10 (2017) 197 [arXiv:1707.07689] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  40. [40]
    M. Gary, S.B. Giddings and J. Penedones, Local bulk S-matrix elements and CFT singularities, Phys. Rev. D 80 (2009) 085005 [arXiv:0903.4437] [INSPIRE].Google Scholar
  41. [41]
    J. Maldacena, D. Simmons-Duffin and A. Zhiboedov, Looking for a bulk point, JHEP 01 (2017) 013 [arXiv:1509.03612] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  42. [42]
    S. Caron-Huot and A.-K. Trinh, All tree-level correlators in AdS 5 × S 5 supergravity: hidden ten-dimensional conformal symmetry, JHEP 01 (2019) 196 [arXiv:1809.09173] [INSPIRE].CrossRefzbMATHGoogle Scholar
  43. [43]
    D. Simmons-Duffin, D. Stanford and E. Witten, A spacetime derivation of the Lorentzian OPE inversion formula, JHEP 07 (2018) 085 [arXiv:1711.03816] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  44. [44]
    J. Liu, E. Perlmutter, V. Rosenhaus and D. Simmons-Duffin, d-dimensional SYK, AdS Loops and 6j Symbols, JHEP 03 (2019) 052 [arXiv:1808.00612] [INSPIRE].
  45. [45]
    M.A. Virasoro, Alternative constructions of crossing-symmetric amplitudes with Regge behavior, Phys. Rev. 177 (1969) 2309 [INSPIRE].CrossRefGoogle Scholar
  46. [46]
    L.F. Alday and A. Bissi, Unitarity and positivity constraints for CFT at large central charge, JHEP 07 (2017) 044 [arXiv:1606.09593] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  47. [47]
    E. D’Hoker and D.H. Phong, Two-loop superstrings VI: Non-renormalization theorems and the 4-point function, Nucl. Phys. B 715 (2005) 3 [hep-th/0501197] [INSPIRE].CrossRefzbMATHGoogle Scholar
  48. [48]
    H. Gomez and C.R. Mafra, The closed-string 3-loop amplitude and S-duality, JHEP 10 (2013) 217 [arXiv:1308.6567] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  49. [49]
    E. D’Hoker, M.B. Green and P. Vanhove, On the modular structure of the genus-one Type II superstring low energy expansion, JHEP 08 (2015) 041 [arXiv:1502.06698] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  50. [50]
    E. D’Hoker, M.B. Green and B. Pioline, Higher genus modular graph functions, string invariants and their exact asymptotics, Commun. Math. Phys. 366 (2019) 927 [arXiv:1712.06135] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  51. [51]
    S.M. Chester and E. Perlmutter, M-Theory Reconstruction from (2,0) CFT and the Chiral Algebra Conjecture, JHEP 08 (2018) 116 [arXiv:1805.00892] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  52. [52]
    S.M. Chester, S.S. Pufu and X. Yin, The M-theory S-matrix From ABJM: Beyond 11D Supergravity, JHEP 08 (2018) 115 [arXiv:1804.00949] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  53. [53]
    E. D’Hoker, M. Gutperle and D.H. Phong, Two-loop superstrings and S-duality, Nucl. Phys. B 722 (2005) 81 [hep-th/0503180] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  54. [54]
    M.B. Green, J.H. Schwarz and E. Witten, Superstring theory. Vol. 2: Loop amplitudes, anomalies and phenomenology, Cambridge University Press, (1988), [ https://doi.org/10.1017/CBO9781139248570].

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Mathematical InstituteUniversity of OxfordOxfordU.K.
  2. 2.Department of Physics and AstronomyUppsala UniversityUppsalaSweden
  3. 3.Walter Burke Institute for Theoretical PhysicsCaltechPasadenaU.S.A.

Personalised recommendations