Advertisement

Perturbative four-point functions in planar \( \mathcal{N}=4 \) SYM From hexagonalization

  • Frank Coronado
Open Access
Regular Article - Theoretical Physics
  • 15 Downloads

Abstract

We use hexagonalization to compute four-point correlation functions of long BPS operators with special R-charge polarizations. We perform the computation at weak coupling and show that at any loop order our correlators can be expressed in terms of single value polylogarithms with uniform and maximal transcendentality. As a check of our computation we extract nine-loop OPE data and compare it against sum rules of (squared) structures constants of non-protected exchanged operators described by hundreds of Bethe solutions.

Keywords

Bethe Ansatz Conformal Field Theory Integrable Field Theories 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]
    L.F. Alday and A. Bissi, Higher-spin correlators, JHEP 10 (2013) 202 [arXiv:1305.4604] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    J. Maldacena, D. Simmons-Duffin and A. Zhiboedov, Looking for a bulk point, JHEP 01 (2017) 013 [arXiv:1509.03612] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    M.S. Costa, V. Goncalves and J. Penedones, Conformal Regge theory, JHEP 12 (2012) 091 [arXiv:1209.4355] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    B. Basso, S. Komatsu and P. Vieira, Structure constants and integrable bootstrap in planar N = 4 SYM theory, arXiv:1505.06745 [INSPIRE].
  5. [5]
    T. Fleury and S. Komatsu, Hexagonalization of correlation functions, JHEP 01 (2017) 130 [arXiv:1611.05577] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    P. Vieira and T. Wang, Tailoring non-compact spin chains, JHEP 10 (2014) 035 [arXiv:1311.6404] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    B. Basso, F. Coronado, S. Komatsu, H.T. Lam, P. Vieira and D.-l. Zhong, Asymptotic four point functions, arXiv:1701.04462 [INSPIRE].
  8. [8]
    T. Fleury and S. Komatsu, Hexagonalization of correlation functions II: two-particle contributions, JHEP 02 (2018) 177 [arXiv:1711.05327] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    B. Eden and A. Sfondrini, Tessellating cushions: four-point functions in N = 4 SYM, JHEP 10 (2017) 098 [arXiv:1611.05436] [INSPIRE].
  10. [10]
    C. Marboe and D. Volin, Fast analytic solver of rational Bethe equations, J. Phys. A 50 (2017) 204002 [arXiv:1608.06504] [INSPIRE].
  11. [11]
    C. Marboe and D. Volin, The full spectrum of AdS 5 /CFT 4 I: representation theory and one-loop Q-system, J. Phys. A 51 (2018) 165401 [arXiv:1701.03704] [INSPIRE].
  12. [12]
    N. Beisert, The SU(2|2) dynamic S-matrix, Adv. Theor. Math. Phys. 12 (2008) 945 [hep-th/0511082] [INSPIRE].
  13. [13]
    G. Arutyunov, M. de Leeuw and A. Torrielli, The bound state S-matrix for AdS 5 × S 5 superstring, Nucl. Phys. B 819 (2009) 319 [arXiv:0902.0183] [INSPIRE].
  14. [14]
    R.I. Nepomechie and F. Ravanini, Completeness of the Bethe ansatz solution of the open XXZ chain with nondiagonal boundary terms, J. Phys. A 36 (2003) 11391 [hep-th/0307095] [INSPIRE].
  15. [15]
    G. Albertini, S. Dasmahapatra and B.M. McCoy, Spectrum and completeness of the integrable three state Potts model: a finite size study, Int. J. Mod. Phys. A 07 (1992) 1.Google Scholar
  16. [16]
    N. Beisert and M. Staudacher, Long-range PSU(2, 2|4) Bethe ansätze for gauge theory and strings, Nucl. Phys. B 727 (2005) 1 [hep-th/0504190] [INSPIRE].
  17. [17]
    B. Basso and L.J. Dixon, Gluing ladder Feynman diagrams into fishnets, Phys. Rev. Lett. 119 (2017) 071601 [arXiv:1705.03545] [INSPIRE].
  18. [18]
    N. Beisert, Review of AdS/CFT integrability, chapter VI.1: superconformal symmetry, Lett. Math. Phys. 99 (2012) 529 [arXiv:1012.4004] [INSPIRE].
  19. [19]
    B. Eden, Y. Jiang, D. le Plat and A. Sfondrini, Colour-dressed hexagon tessellations for correlation functions and non-planar corrections, JHEP 02 (2018) 170 [arXiv:1710.10212] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    T. Bargheer, J. Caetano, T. Fleury, S. Komatsu and P. Vieira, Handling handles: nonplanar integrability in N = 4 supersymmetric Yang-Mills theory, Phys. Rev. Lett. 121 (2018) 231602 [arXiv:1711.05326] [INSPIRE].
  21. [21]
    T. Bargheer, J. Caetano, T. Fleury, S. Komatsu and P. Vieira, Handling handles. Part II: stratification and data analysis, JHEP 11 (2018) 095 [arXiv:1809.09145] [INSPIRE].
  22. [22]
    M. Hogervorst and S. Rychkov, Radial coordinates for conformal blocks, Phys. Rev. D 87 (2013) 106004 [arXiv:1303.1111] [INSPIRE].
  23. [23]
    D. Chicherin, J. Drummond, P. Heslop and E. Sokatchev, All three-loop four-point correlators of half-BPS operators in planar N = 4 SYM, JHEP 08 (2016) 053 [arXiv:1512.02926] [INSPIRE].
  24. [24]
    D. Chicherin, A. Georgoudis, V. Gonçalves and R. Pereira, All five-loop planar four-point functions of half-BPS operators in N = 4 SYM, JHEP 11 (2018) 069 [arXiv:1809.00551] [INSPIRE].
  25. [25]
    J.L. Bourjaily, P. Heslop and V.-V. Tran, Amplitudes and correlators to ten loops using simple, graphical bootstraps, JHEP 11 (2016) 125 [arXiv:1609.00007] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  26. [26]
    P. Vieira, Mathematica notebook at the Nordita Integrability School, https://www.nordita.org/~zarembo/Nordita2014/program.html, (2014).
  27. [27]
    N. Beisert and B.I. Zwiebel, On symmetry enhancement in the PSU(1, 1|2) sector of N = 4 SYM, JHEP 10 (2007) 031 [arXiv:0707.1031] [INSPIRE].
  28. [28]
    D.J. Broadhurst and A.I. Davydychev, Exponential suppression with four legs and an infinity of loops, Nucl. Phys. Proc. Suppl. 205-206 (2010) 326 [arXiv:1007.0237] [INSPIRE].
  29. [29]
    S. Caron-Huot, L.J. Dixon, M. von Hippel, A.J. McLeod and G. Papathanasiou, The double pentaladder integral to all orders, JHEP 07 (2018) 170 [arXiv:1806.01361] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  30. [30]
    N.I. Usyukina and A.I. Davydychev, Exact results for three and four point ladder diagrams with an arbitrary number of rungs, Phys. Lett. B 305 (1993) 136 [INSPIRE].
  31. [31]
    L. Rastelli and X. Zhou, How to succeed at holographic correlators without really trying, JHEP 04 (2018) 014 [arXiv:1710.05923] [INSPIRE].
  32. [32]
    L. Rastelli and X. Zhou, Mellin amplitudes for AdS 5 × S 5, Phys. Rev. Lett. 118 (2017) 091602 [arXiv:1608.06624] [INSPIRE].
  33. [33]
    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].
  34. [34]
    F. Aprile, J.M. Drummond, P. Heslop and H. Paul, Quantum gravity from conformal field theory, JHEP 01 (2018) 035 [arXiv:1706.02822] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  35. [35]
    V. Gonçalves, Four point function of N = 4 stress-tensor multiplet at strong coupling, JHEP 04 (2015) 150 [arXiv:1411.1675] [INSPIRE].
  36. [36]
    L.F. Alday, A. Bissi and E. Perlmutter, Genus-one string amplitudes from conformal field theory, arXiv:1809.10670 [INSPIRE].
  37. [37]
    F. Coronado, Bootstrapping the simplest correlator in planar N = 4 SYM at all loops, arXiv:1811.03282 [INSPIRE].
  38. [38]
    T. Bargheer, F. Coronado and P. Vieira, Large cyclic operators I combinatorics and non-planar resummations, to appear.Google Scholar
  39. [39]
    T. Bargheer, F. Coronado, V. Gonçalves and P. Vieira, Large cyclic operators II, work in progress.Google Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Perimeter Institute for Theoretical PhysicsWaterlooCanada
  2. 2.Department of Physics and Astronomy & Guelph-Waterloo Physics InstituteUniversity of WaterlooWaterlooCanada
  3. 3.ICTP South American Institute for Fundamental ResearchSão PauloBrazil

Personalised recommendations