The light-ray OPE and conformal colliders

Abstract

We derive a nonperturbative, convergent operator product expansion (OPE) for null-integrated operators on the same null plane in a CFT. The objects appearing in the expansion are light-ray operators, whose matrix elements can be computed by the generalized Lorentzian inversion formula. For example, a product of average null energy (ANEC) operators has an expansion in the light-ray operators that appear in the stress-tensor OPE. An important application is to collider event shapes. The light-ray OPE gives a nonperturbative expansion for event shapes in special functions that we call celestial blocks. As an example, we apply the celestial block expansion to energy-energy correlators in \( \mathcal{N} \) = 4 Super Yang-Mills theory. Using known OPE data, we find perfect agreement with previous results both at weak and strong coupling, and make new predictions at weak coupling through 4 loops (NNNLO).

A preprint version of the article is available at ArXiv.

References

  1. [1]

    M. Koloğlu, P. Kravchuk, D. Simmons-Duffin and A. Zhiboedov, Shocks, Superconvergence, and a Stringy Equivalence Principle, JHEP 11 (2020) 096 [arXiv:1904.05905] [INSPIRE].

    ADS  Article  Google Scholar 

  2. [2]

    C.L. Basham, L.S. Brown, S.D. Ellis and S.T. Love, Electron - Positron Annihilation Energy Pattern in Quantum Chromodynamics: Asymptotically Free Perturbation Theory, Phys. Rev. D 17 (1978) 2298 [INSPIRE].

    ADS  Article  Google Scholar 

  3. [3]

    C.L. Basham, L.S. Brown, S.D. Ellis and S.T. Love, Energy Correlations in electron-Positron Annihilation in Quantum Chromodynamics: Asymptotically Free Perturbation Theory, Phys. Rev. D 19 (1979) 2018 [INSPIRE].

    ADS  Article  Google Scholar 

  4. [4]

    C. Basham, L.S. Brown, S.D. Ellis and S.T. Love, Energy Correlations in electron - Positron Annihilation: Testing QCD, Phys. Rev. Lett. 41 (1978) 1585 [INSPIRE].

    ADS  Article  Google Scholar 

  5. [5]

    D.M. Hofman and J. Maldacena, Conformal collider physics: Energy and charge correlations, JHEP 05 (2008) 012 [arXiv:0803.1467] [INSPIRE].

    ADS  Article  Google Scholar 

  6. [6]

    A.V. Belitsky, S. Hohenegger, G.P. Korchemsky, E. Sokatchev and A. Zhiboedov, From correlation functions to event shapes, Nucl. Phys. B 884 (2014) 305 [arXiv:1309.0769] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  7. [7]

    T. Faulkner, R.G. Leigh, O. Parrikar and H. Wang, Modular Hamiltonians for Deformed Half-Spaces and the Averaged Null Energy Condition, JHEP 09 (2016) 038 [arXiv:1605.08072] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  8. [8]

    H. Casini, E. Teste and G. Torroba, Modular Hamiltonians on the null plane and the Markov property of the vacuum state, J. Phys. A 50 (2017) 364001 [arXiv:1703.10656] [INSPIRE].

    MathSciNet  MATH  Article  Google Scholar 

  9. [9]

    F. Ceyhan and T. Faulkner, Recovering the QNEC from the ANEC, Commun. Math. Phys. 377 (2020) 999 [arXiv:1812.04683] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  10. [10]

    C. Córdova and S.-H. Shao, Light-ray Operators and the BMS Algebra, Phys. Rev. D 98 (2018) 125015 [arXiv:1810.05706] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  11. [11]

    D.M. Hofman, Higher Derivative Gravity, Causality and Positivity of Energy in a UV complete QFT, Nucl. Phys. B 823 (2009) 174 [arXiv:0907.1625] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  12. [12]

    T. Hartman, S. Kundu and A. Tajdini, Averaged Null Energy Condition from Causality, JHEP 07 (2017) 066 [arXiv:1610.05308] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  13. [13]

    S.D. Chowdhury, J.R. David and S. Prakash, Constraints on parity violating conformal field theories in d = 3, JHEP 11 (2017) 171 [arXiv:1707.03007] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  14. [14]

    C. Cordova and K. Diab, Universal Bounds on Operator Dimensions from the Average Null Energy Condition, JHEP 02 (2018) 131 [arXiv:1712.01089] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  15. [15]

    C. Cordova, J. Maldacena and G.J. Turiaci, Bounds on OPE Coefficients from Interference Effects in the Conformal Collider, JHEP 11 (2017) 032 [arXiv:1710.03199] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  16. [16]

    L.V. Delacrétaz, T. Hartman, S.A. Hartnoll and A. Lewkowycz, Thermalization, Viscosity and the Averaged Null Energy Condition, JHEP 10 (2018) 028 [arXiv:1805.04194] [INSPIRE].

    ADS  MATH  Article  Google Scholar 

  17. [17]

    D. Meltzer, Higher Spin ANEC and the Space of CFTs, JHEP 07 (2019) 001 [arXiv:1811.01913] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  18. [18]

    A. Belin, D.M. Hofman and G. Mathys, Einstein gravity from ANEC correlators, JHEP 08 (2019) 032 [arXiv:1904.05892] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  19. [19]

    S. Ferrara, A.F. Grillo and R. Gatto, Tensor representations of conformal algebra and conformally covariant operator product expansion, Annals Phys. 76 (1973) 161 [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  20. [20]

    A.M. Polyakov, Nonhamiltonian approach to conformal quantum field theory, Zh. Eksp. Teor. Fiz. 66 (1974) 23 [INSPIRE].

    Google Scholar 

  21. [21]

    J. Polchinski, String theory. Vol. 1: An introduction to the bosonic string, Cambridge Monographs on Mathematical Physics. Cambridge University Press, 12, 2007, 10.1017/CBO9780511816079 [INSPIRE].

  22. [22]

    G. Mack, Convergence of Operator Product Expansions on the Vacuum in Conformal Invariant Quantum Field Theory, Commun. Math. Phys. 53 (1977) 155 [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  23. [23]

    P. Kravchuk and D. Simmons-Duffin, Light-ray operators in conformal field theory, JHEP 11 (2018) 102 [arXiv:1805.00098] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  24. [24]

    S. Caron-Huot, Analyticity in Spin in Conformal Theories, JHEP 09 (2017) 078 [arXiv:1703.00278] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  25. [25]

    C.H. Chang, M. Koloğlu, P. Kravchuk, D. Simmons-Duffin and A. Zhiboedov, Transverse spin in the light-ray OPE, to appear.

  26. [26]

    P. Kravchuk and D. Simmons-Duffin, Counting Conformal Correlators, JHEP 02 (2018) 096 [arXiv:1612.08987] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  27. [27]

    D.M. McAvity and H. Osborn, Conformal field theories near a boundary in general dimensions, Nucl. Phys. B 455 (1995) 522 [cond-mat/9505127] [INSPIRE].

  28. [28]

    P. Liendo, L. Rastelli and B.C. van Rees, The Bootstrap Program for Boundary CFTd, JHEP 07 (2013) 113 [arXiv:1210.4258] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  29. [29]

    A.V. Belitsky, S. Hohenegger, G.P. Korchemsky and E. Sokatchev, N = 4 superconformal Ward identities for correlation functions, Nucl. Phys. B 904 (2016) 176 [arXiv:1409.2502] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  30. [30]

    G.P. Korchemsky and E. Sokatchev, Four-point correlation function of stress-energy tensors in \( \mathcal{N} \) = 4 superconformal theories, JHEP 12 (2015) 133 [arXiv:1504.07904] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  31. [31]

    G.P. Korchemsky, Energy correlations in the end-point region, JHEP 01 (2020) 008 [arXiv:1905.01444] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  32. [32]

    L.J. Dixon, I. Moult and H.X. Zhu, Collinear limit of the energy-energy correlator, Phys. Rev. D 100 (2019) 014009 [SLAC-PUB-17427] [arXiv:1905.01310] [INSPIRE].

  33. [33]

    L.F. Alday, B. Eden, G.P. Korchemsky, J. Maldacena and E. Sokatchev, From correlation functions to Wilson loops, JHEP 09 (2011) 123 [arXiv:1007.3243] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  34. [34]

    A.V. Belitsky, S. Hohenegger, G.P. Korchemsky, E. Sokatchev and A. Zhiboedov, Energy-Energy Correlations in N = 4 Supersymmetric Yang-Mills Theory, Phys. Rev. Lett. 112 (2014) 071601 [arXiv:1311.6800] [INSPIRE].

    ADS  MATH  Article  Google Scholar 

  35. [35]

    J.M. Henn, E. Sokatchev, K. Yan and A. Zhiboedov, Energy-energy correlation in N = 4 super Yang-Mills theory at next-to-next-to-leading order, Phys. Rev. D 100 (2019) 036010 [arXiv:1903.05314] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  36. [36]

    P.A.M. Dirac, Wave equations in conformal space, Annals Math. 37 (1936) 429 [INSPIRE].

    MathSciNet  MATH  Article  Google Scholar 

  37. [37]

    G. Mack and A. Salam, Finite component field representations of the conformal group, Annals Phys. 53 (1969) 174 [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  38. [38]

    D.G. Boulware, L.S. Brown and R.D. Peccei, Deep-inelastic electroproduction and conformal symmetry, Phys. Rev. D 2 (1970) 293 [INSPIRE].

    ADS  Article  Google Scholar 

  39. [39]

    S. Ferrara, P. Gatto and A.F. Grilla, Conformal algebra in space-time and operator product expansion, Springer Tracts Mod. Phys. 67 (1973) 1 [INSPIRE].

    ADS  Article  Google Scholar 

  40. [40]

    L. Cornalba, M.S. Costa and J. Penedones, Deep Inelastic Scattering in Conformal QCD, JHEP 03 (2010) 133 [arXiv:0911.0043] [INSPIRE].

    ADS  MATH  Article  Google Scholar 

  41. [41]

    S. Weinberg, Six-dimensional Methods for Four-dimensional Conformal Field Theories, Phys. Rev. D 82 (2010) 045031 [arXiv:1006.3480] [INSPIRE].

    ADS  Article  Google Scholar 

  42. [42]

    M.S. Costa, J. Penedones, D. Poland and S. Rychkov, Spinning Conformal Correlators, JHEP 11 (2011) 071 [arXiv:1107.3554] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  43. [43]

    G. Mack, All unitary ray representations of the conformal group SU(2, 2) with positive energy, Commun. Math. Phys. 55 (1977) 1 [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  44. [44]

    Event Horizon Telescope collaboration, First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole, Astrophys. J. 875 (2019) L1 [arXiv:1906.11238] [INSPIRE].

  45. [45]

    A.V. Belitsky, S. Hohenegger, G.P. Korchemsky, E. Sokatchev and A. Zhiboedov, Event shapes in \( \mathcal{N} \) = 4 super-Yang-Mills theory, Nucl. Phys. B 884 (2014) 206 [arXiv:1309.1424] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  46. [46]

    V.K. Dobrev, G. Mack, V.B. Petkova, S.G. Petrova and I.T. Todorov, Harmonic Analysis on the n-Dimensional Lorentz Group and Its Application to Conformal Quantum Field Theory, Lect. Notes Phys. 63 (1977) 1.

    MATH  Article  Google Scholar 

  47. [47]

    A. Fitzpatrick and J. Kaplan, Unitarity and the Holographic S-matrix, JHEP 10 (2012) 032 [arXiv:1112.4845] [INSPIRE].

    ADS  MATH  Article  Google Scholar 

  48. [48]

    D. Karateev, P. Kravchuk and D. Simmons-Duffin, Harmonic Analysis and Mean Field Theory, JHEP 10 (2019) 217 [arXiv:1809.05111] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  49. [49]

    A. Dymarsky, F. Kos, P. Kravchuk, D. Poland and D. Simmons-Duffin, The 3d Stress-Tensor Bootstrap, JHEP 02 (2018) 164 [arXiv:1708.05718] [INSPIRE].

    ADS  MATH  Article  Google Scholar 

  50. [50]

    D. Pappadopulo, S. Rychkov, J. Espin and R. Rattazzi, OPE Convergence in Conformal Field Theory, Phys. Rev. D 86 (2012) 105043 [arXiv:1208.6449] [INSPIRE].

    ADS  Article  Google Scholar 

  51. [51]

    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].

  52. [52]

    A. Gadde, Conformal constraints on defects, JHEP 01 (2020) 038 [arXiv:1602.06354] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  53. [53]

    L. Cornalba, Eikonal methods in AdS/CFT: Regge theory and multi-reggeon exchange, arXiv:0710.5480 [INSPIRE].

  54. [54]

    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].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  55. [55]

    F.A. Dolan and H. Osborn, Conformal four point functions and the operator product expansion, Nucl. Phys. B 599 (2001) 459 [hep-th/0011040] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  56. [56]

    F.A. Dolan and H. Osborn, Conformal partial waves and the operator product expansion, Nucl. Phys. B 678 (2004) 491 [hep-th/0309180] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  57. [57]

    J. Maldacena and D. Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev. D 94 (2016) 106002 [arXiv:1604.07818] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  58. [58]

    B. Eden, P.S. Howe and P.C. West, Nilpotent invariants in N = 4 SYM, Phys. Lett. B 463 (1999) 19 [hep-th/9905085] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  59. [59]

    P.S. Howe, C. Schubert, E. Sokatchev and P.C. West, Explicit construction of nilpotent covariants in N = 4 SYM, Nucl. Phys. B 571 (2000) 71 [hep-th/9910011] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  60. [60]

    J. Drummond, C. Duhr, B. Eden, P. Heslop, J. Pennington and V.A. Smirnov, Leading singularities and off-shell conformal integrals, JHEP 08 (2013) 133 [arXiv:1303.6909] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  61. [61]

    B. Eden, P. Heslop, G.P. Korchemsky and E. Sokatchev, Hidden symmetry of four-point correlation functions and amplitudes in N = 4 SYM, Nucl. Phys. B 862 (2012) 193 [arXiv:1108.3557] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  62. [62]

    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].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  63. [63]

    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].

    ADS  MathSciNet  Article  Google Scholar 

  64. [64]

    L.F. Alday and S. Caron-Huot, Gravitational S-matrix from CFT dispersion relations, JHEP 12 (2018) 017 [arXiv:1711.02031] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  65. [65]

    J. Henriksson and T. Lukowski, Perturbative Four-Point Functions from the Analytic Conformal Bootstrap, JHEP 02 (2018) 123 [arXiv:1710.06242] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  66. [66]

    B. Eden, C. Schubert and E. Sokatchev, Three loop four point correlator in N = 4 SYM, Phys. Lett. B 482 (2000) 309 [hep-th/0003096] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  67. [67]

    M. Bianchi, S. Kovacs, G. Rossi and Y.S. Stanev, Anomalous dimensions in N = 4 SYM theory at order g4, Nucl. Phys. B 584 (2000) 216 [hep-th/0003203] [INSPIRE].

    ADS  MATH  Article  Google Scholar 

  68. [68]

    F.A. Dolan and H. Osborn, Conformal partial wave expansions for N = 4 chiral four point functions, Annals Phys. 321 (2006) 581 [hep-th/0412335] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  69. [69]

    A.V. Kotikov and V.N. Velizhanin, Analytic continuation of the Mellin moments of deep inelastic structure functions, hep-ph/0501274 [INSPIRE].

  70. [70]

    N. Gromov, V. Kazakov, S. Leurent and D. Volin, Quantum Spectral Curve for Planar \( \mathcal{N} \) = 4 Super-Yang-Mills Theory, Phys. Rev. Lett. 112 (2014) 011602 [arXiv:1305.1939] [INSPIRE].

    ADS  Article  Google Scholar 

  71. [71]

    N. Gromov, F. Levkovich-Maslyuk, G. Sizov and S. Valatka, Quantum spectral curve at work: from small spin to strong coupling in \( \mathcal{N} \) = 4 SYM, JHEP 07 (2014) 156 [arXiv:1402.0871] [INSPIRE].

    ADS  Article  Google Scholar 

  72. [72]

    B. Eden, P. Heslop, G.P. Korchemsky and E. Sokatchev, Constructing the correlation function of four stress-tensor multiplets and the four-particle amplitude in N = 4 SYM, Nucl. Phys. B 862 (2012) 450 [arXiv:1201.5329] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  73. [73]

    B. Eden, Three-loop universal structure constants in N = 4 SUSY Yang-Mills theory, arXiv:1207.3112 [INSPIRE].

  74. [74]

    L.F. Alday and A. Bissi, Higher-spin correlators, JHEP 10 (2013) 202 [arXiv:1305.4604] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  75. [75]

    A.V. Kotikov, L.N. Lipatov, A. Rej, M. Staudacher and V.N. Velizhanin, Dressing and wrapping, J. Stat. Mech. 0710 (2007) P10003 [arXiv:0704.3586] [INSPIRE].

    MATH  Article  Google Scholar 

  76. [76]

    Z. Bajnok, R.A. Janik and T. Lukowski, Four loop twist two, BFKL, wrapping and strings, Nucl. Phys. B 816 (2009) 376 [arXiv:0811.4448] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  77. [77]

    D. Maître, HPL, a mathematica implementation of the harmonic polylogarithms, Comput. Phys. Commun. 174 (2006) 222 [hep-ph/0507152] [INSPIRE].

  78. [78]

    N. Gromov, F. Levkovich-Maslyuk and G. Sizov, Pomeron Eigenvalue at Three Loops in \( \mathcal{N} \) = 4 Supersymmetric Yang-Mills Theory, Phys. Rev. Lett. 115 (2015) 251601 [arXiv:1507.04010] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  79. [79]

    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].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  80. [80]

    J.C. Collins and D.E. Soper, Back-To-Back Jets in QCD, Nucl. Phys. B 193 (1981) 381 [Erratum ibid. 213 (1983) 545] [INSPIRE].

  81. [81]

    G. Arutyunov and S. Frolov, Four point functions of lowest weight CPOs in N = 4 SYM(4) in supergravity approximation, Phys. Rev. D 62 (2000) 064016 [hep-th/0002170] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  82. [82]

    F. Aprile, J.M. Drummond, P. Heslop and H. Paul, Quantum Gravity from Conformal Field Theory, JHEP 01 (2018) 035 [arXiv:1706.02822] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  83. [83]

    F. Aprile, J.M. Drummond, P. Heslop and H. Paul, Loop corrections for Kaluza-Klein AdS amplitudes, JHEP 05 (2018) 056 [arXiv:1711.03903] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  84. [84]

    L.F. Alday and A. Bissi, Loop Corrections to Supergravity on AdS5 × S5, Phys. Rev. Lett. 119 (2017) 171601 [arXiv:1706.02388] [INSPIRE].

    ADS  Article  Google Scholar 

  85. [85]

    R. Rattazzi, V.S. Rychkov, E. Tonni and A. Vichi, Bounding scalar operator dimensions in 4D CFT, JHEP 12 (2008) 031 [arXiv:0807.0004] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  86. [86]

    S. El-Showk, M.F. Paulos, D. Poland, S. Rychkov, D. Simmons-Duffin and A. Vichi, Solving the 3D Ising Model with the Conformal Bootstrap, Phys. Rev. D 86 (2012) 025022 [arXiv:1203.6064] [INSPIRE].

    ADS  MATH  Article  Google Scholar 

  87. [87]

    D. Poland, S. Rychkov and A. Vichi, The Conformal Bootstrap: Theory, Numerical Techniques, and Applications, Rev. Mod. Phys. 91 (2019) 015002 [arXiv:1805.04405] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  88. [88]

    D. Karateev, P. Kravchuk and D. Simmons-Duffin, Weight Shifting Operators and Conformal Blocks, JHEP 02 (2018) 081 [arXiv:1706.07813] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  89. [89]

    L.F. Alday, D. Gaiotto, J. Maldacena, A. Sever and P. Vieira, An Operator Product Expansion for Polygonal null Wilson Loops, JHEP 04 (2011) 088 [arXiv:1006.2788] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  90. [90]

    B. Basso, A. Sever and P. Vieira, Spacetime and Flux Tube S-Matrices at Finite Coupling for N = 4 Supersymmetric Yang-Mills Theory, Phys. Rev. Lett. 111 (2013) 091602 [arXiv:1303.1396] [INSPIRE].

    ADS  Article  Google Scholar 

  91. [91]

    B. Basso, A. Sever and P. Vieira, Space-time S-matrix and Flux tube S-matrix II. Extracting and Matching Data, JHEP 01 (2014) 008 [arXiv:1306.2058] [INSPIRE].

  92. [92]

    B. Basso, A. Sever and P. Vieira, Space-time S-matrix and Flux-tube S-matrix III. The two-particle contributions, JHEP 08 (2014) 085 [arXiv:1402.3307] [INSPIRE].

  93. [93]

    B. Basso, A. Sever and P. Vieira, Collinear Limit of Scattering Amplitudes at Strong Coupling, Phys. Rev. Lett. 113 (2014) 261604 [arXiv:1405.6350] [INSPIRE].

    ADS  Article  Google Scholar 

  94. [94]

    B. Basso, A. Sever and P. Vieira, Space-time S-matrix and Flux-tube S-matrix IV. Gluons and Fusion, JHEP 09 (2014) 149 [arXiv:1407.1736] [INSPIRE].

  95. [95]

    S. Pasterski, S.-H. Shao and A. Strominger, Flat Space Amplitudes and Conformal Symmetry of the Celestial Sphere, Phys. Rev. D 96 (2017) 065026 [arXiv:1701.00049] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  96. [96]

    S. Pasterski and S.-H. Shao, Conformal basis for flat space amplitudes, Phys. Rev. D 96 (2017) 065022 [arXiv:1705.01027] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  97. [97]

    K. Konishi, A. Ukawa and G. Veneziano, Jet Calculus: A Simple Algorithm for Resolving QCD Jets, Nucl. Phys. B 157 (1979) 45 [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  98. [98]

    L.J. Dixon, M.-X. Luo, V. Shtabovenko, T.-Z. Yang and H.X. Zhu, Analytical Computation of Energy-Energy Correlation at Next-to-Leading Order in QCD, Phys. Rev. Lett. 120 (2018) 102001 [arXiv:1801.03219] [INSPIRE].

    ADS  Article  Google Scholar 

  99. [99]

    M.-X. Luo, V. Shtabovenko, T.-Z. Yang and H.X. Zhu, Analytic Next-To-Leading Order Calculation of Energy-Energy Correlation in Gluon-Initiated Higgs Decays, JHEP 06 (2019) 037 [arXiv:1903.07277] [INSPIRE].

    ADS  Article  Google Scholar 

  100. [100]

    L.J. Dixon, J.M. Drummond and J.M. Henn, Bootstrapping the three-loop hexagon, JHEP 11 (2011) 023 [arXiv:1108.4461] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  101. [101]

    L.J. Dixon, J.M. Drummond, M. von Hippel and J. Pennington, Hexagon functions and the three-loop remainder function, JHEP 12 (2013) 049 [arXiv:1308.2276] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  102. [102]

    L.J. Dixon and M. von Hippel, Bootstrapping an NMHV amplitude through three loops, JHEP 10 (2014) 065 [arXiv:1408.1505] [INSPIRE].

    ADS  Article  Google Scholar 

  103. [103]

    J.M. Drummond, G. Papathanasiou and M. Spradlin, A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon, JHEP 03 (2015) 072 [arXiv:1412.3763] [INSPIRE].

    ADS  Article  Google Scholar 

  104. [104]

    L.J. Dixon, J.M. Drummond, C. Duhr, M. von Hippel and J. Pennington, Bootstrapping six-gluon scattering in planar N = 4 super-Yang-Mills theory, PoS LL2014 (2014) 077 [arXiv:1407.4724] [INSPIRE].

  105. [105]

    J. Golden and M. Spradlin, A Cluster Bootstrap for Two-Loop MHV Amplitudes, JHEP 02 (2015) 002 [arXiv:1411.3289] [INSPIRE].

    ADS  Article  Google Scholar 

  106. [106]

    S. Caron-Huot, L.J. Dixon, A. McLeod and M. von Hippel, Bootstrapping a Five-Loop Amplitude Using Steinmann Relations, Phys. Rev. Lett. 117 (2016) 241601 [arXiv:1609.00669] [INSPIRE].

    ADS  Article  Google Scholar 

  107. [107]

    S. Caron-Huot, L.J. Dixon, F. Dulat, M. von Hippel, A.J. McLeod and G. Papathanasiou, Six-Gluon amplitudes in planar \( \mathcal{N} \) = 4 super-Yang-Mills theory at six and seven loops, JHEP 08 (2019) 016 [arXiv:1903.10890] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  108. [108]

    V. Gonçalves, Four point function of \( \mathcal{N} \) = 4 stress-tensor multiplet at strong coupling, JHEP 04 (2015) 150 [arXiv:1411.1675] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  109. [109]

    R. Bousso, Z. Fisher, S. Leichenauer and A.C. Wall, Quantum focusing conjecture, Phys. Rev. D 93 (2016) 064044 [arXiv:1506.02669] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  110. [110]

    R. Bousso, Z. Fisher, J. Koeller, S. Leichenauer and A.C. Wall, Proof of the Quantum Null Energy Condition, Phys. Rev. D 93 (2016) 024017 [arXiv:1509.02542] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  111. [111]

    S. Balakrishnan, T. Faulkner, Z.U. Khandker and H. Wang, A General Proof of the Quantum Null Energy Condition, JHEP 09 (2019) 020 [arXiv:1706.09432] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  112. [112]

    A. Strominger, Lectures on the Infrared Structure of Gravity and Gauge Theory, arXiv:1703.05448 [INSPIRE].

  113. [113]

    A. Strominger, On BMS Invariance of Gravitational Scattering, JHEP 07 (2014) 152 [arXiv:1312.2229] [INSPIRE].

    ADS  MATH  Article  Google Scholar 

  114. [114]

    T. He, V. Lysov, P. Mitra and A. Strominger, BMS supertranslations and Weinberg’s soft graviton theorem, JHEP 05 (2015) 151 [arXiv:1401.7026] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  115. [115]

    A. Strominger and A. Zhiboedov, Gravitational Memory, BMS Supertranslations and Soft Theorems, JHEP 01 (2016) 086 [arXiv:1411.5745] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  116. [116]

    P. Kravchuk, Casimir recursion relations for general conformal blocks, JHEP 02 (2018) 011 [arXiv:1709.05347] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  117. [117]

    M.S. Costa and T. Hansen, Conformal correlators of mixed-symmetry tensors, JHEP 02 (2015) 151 [arXiv:1411.7351] [INSPIRE].

    ADS  MathSciNet  MATH  Article  Google Scholar 

  118. [118]

    L. Freyhult, Review of AdS/CFT Integrability, Chapter III.4: Twist States and the cusp Anomalous Dimension, Lett. Math. Phys. 99 (2012) 255 [arXiv:1012.3993] [INSPIRE].

  119. [119]

    R.H. Boels, T. Huber and G. Yang, Four-Loop Nonplanar Cusp Anomalous Dimension in N = 4 Supersymmetric Yang-Mills Theory, Phys. Rev. Lett. 119 (2017) 201601 [arXiv:1705.03444] [INSPIRE].

    ADS  Article  Google Scholar 

  120. [120]

    R.H. Boels, T. Huber and G. Yang, The nonplanar cusp and collinear anomalous dimension at four loops in \( \mathcal{N} \) = 4 SYM theory, PoS RADCOR2017 (2017) 042 [arXiv:1712.07563] [INSPIRE].

  121. [121]

    J.M. Henn, T. Peraro, M. Stahlhofen and P. Wasser, Matter dependence of the four-loop cusp anomalous dimension, Phys. Rev. Lett. 122 (2019) 201602 [arXiv:1901.03693] [INSPIRE].

    ADS  Article  Google Scholar 

  122. [122]

    N. Beisert, B. Eden and M. Staudacher, Transcendentality and Crossing, J. Stat. Mech. 0701 (2007) P01021 [hep-th/0610251] [INSPIRE].

    MATH  Google Scholar 

  123. [123]

    L. Freyhult, A. Rej and M. Staudacher, A Generalized Scaling Function for AdS/CFT, J. Stat. Mech. 0807 (2008) P07015 [arXiv:0712.2743] [INSPIRE].

    MathSciNet  Google Scholar 

  124. [124]

    L.J. Dixon, The Principle of Maximal Transcendentality and the Four-Loop Collinear Anomalous Dimension, JHEP 01 (2018) 075 [arXiv:1712.07274] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Murat Koloğlu.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

ArXiv ePrint: 1905.01311

Rights and permissions

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.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Koloğlu, M., Kravchuk, P., Simmons-Duffin, D. et al. The light-ray OPE and conformal colliders. J. High Energ. Phys. 2021, 128 (2021). https://doi.org/10.1007/JHEP01(2021)128

Download citation

Keywords

  • Conformal and W Symmetry
  • Conformal Field Theory
  • Field Theories in Higher Dimensions