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Analytic bootstrap for boundary CFT

  • Agnese Bissi
  • Tobias Hansen
  • Alexander Söderberg
Open Access
Regular Article - Theoretical Physics
  • 32 Downloads

Abstract

We propose a method to analytically solve the bootstrap equation for two point functions in boundary CFT. We consider the analytic structure of the correlator in Lorentzian signature and in particular the discontinuity of bulk and boundary conformal blocks to extract CFT data. As an application, the correlator 〈ϕϕ〉 in ϕ4 theory at the Wilson-Fisher fixed point is computed to order ϵ2 in the ϵ expansion.

Keywords

Conformal Field Theory Boundary Quantum Field Theory Renormalization Group 

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, Large Spin Perturbation Theory for Conformal Field Theories, Phys. Rev. Lett. 119 (2017) 111601 [arXiv:1611.01500] [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    S. Caron-Huot, Analyticity in Spin in Conformal Theories, JHEP 09 (2017) 078 [arXiv:1703.00278] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    M. Billò, V. Gonçalves, E. Lauria and M. Meineri, Defects in conformal field theory, JHEP 04 (2016) 091 [arXiv:1601.02883] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  4. [4]
    A. Gadde, Conformal constraints on defects, arXiv:1602.06354 [INSPIRE].
  5. [5]
    P. Liendo and C. Meneghelli, Bootstrap equations for \( \mathcal{N} \) = 4 SYM with defects, JHEP 01 (2017) 122 [arXiv:1608.05126] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    M. de Leeuw, A.C. Ipsen, C. Kristjansen, K.E. Vardinghus and M. Wilhelm, Two-point functions in AdS/dCFT and the boundary conformal bootstrap equations, JHEP 08 (2017) 020 [arXiv:1705.03898] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    L. Rastelli and X. Zhou, The Mellin Formalism for Boundary CFT d, JHEP 10 (2017) 146 [arXiv:1705.05362] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  8. [8]
    A. Söderberg, Anomalous Dimensions in the WF O(N) Model with a Monodromy Line Defect, JHEP 03 (2018) 058 [arXiv:1706.02414] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    C.P. Herzog and K.-W. Huang, Boundary Conformal Field Theory and a Boundary Central Charge, JHEP 10 (2017) 189 [arXiv:1707.06224] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    A. Karch and Y. Sato, Boundary Holographic Witten Diagrams, JHEP 09 (2017) 121 [arXiv:1708.01328] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    M. Fukuda, N. Kobayashi and T. Nishioka, Operator product expansion for conformal defects, JHEP 01 (2018) 013 [arXiv:1710.11165] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    Y. Sato, More on Boundary Holographic Witten Diagrams, Phys. Rev. D 97 (2018) 026005 [arXiv:1711.02138] [INSPIRE].ADSGoogle Scholar
  13. [13]
    E. Lauria, M. Meineri and E. Trevisani, Radial coordinates for defect CFTs, JHEP 11 (2018) 148 [arXiv:1712.07668] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  14. [14]
    M. Lemos, P. Liendo, M. Meineri and S. Sarkar, Universality at large transverse spin in defect CFT, JHEP 09 (2018) 091 [arXiv:1712.08185] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  15. [15]
    V. Goncalves and G. Itsios, A note on defect Mellin amplitudes, arXiv:1803.06721 [INSPIRE].
  16. [16]
    V. Prochazka, The Conformal Anomaly in bCFT from Momentum Space Perspective, JHEP 10 (2018) 170 [arXiv:1804.01974] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  17. [17]
    L. Bianchi, M. Lemos and M. Meineri, Line Defects and Radiation in \( \mathcal{N} \) = 2 Conformal Theories, Phys. Rev. Lett. 121 (2018) 141601 [arXiv:1805.04111] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    N. Kobayashi and T. Nishioka, Spinning conformal defects, JHEP 09 (2018) 134 [arXiv:1805.05967] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  19. [19]
    A. Karch and Y. Sato, Conformal Manifolds with Boundaries or Defects, JHEP 07 (2018) 156 [arXiv:1805.10427] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    S. Guha and B. Nagaraj, Correlators of Mixed Symmetry Operators in Defect CFTs, JHEP 10 (2018) 198 [arXiv:1805.12341] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  21. [21]
    M. Isachenkov, P. Liendo, Y. Linke and V. Schomerus, Calogero-Sutherland Approach to Defect Blocks, JHEP 10 (2018) 204 [arXiv:1806.09703] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  22. [22]
    P. Liendo, C. Meneghelli and V. Mitev, Bootstrapping the half-BPS line defect, JHEP 10 (2018) 077 [arXiv:1806.01862] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  23. [23]
    E. Lauria, M. Meineri and E. Trevisani, Spinning operators and defects in conformal field theory, arXiv:1807.02522 [INSPIRE].
  24. [24]
    P. Liendo, L. Rastelli and B.C. van Rees, The Bootstrap Program for Boundary CFT d, JHEP 07 (2013) 113 [arXiv:1210.4258] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  25. [25]
    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].
  26. [26]
    T. Hartman, S. Jain and S. Kundu, Causality Constraints in Conformal Field Theory, JHEP 05 (2016) 099 [arXiv:1509.00014] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    K.G. Wilson, Quantum field theory models in less than four-dimensions, Phys. Rev. D 7 (1973) 2911 [INSPIRE].ADSGoogle Scholar
  28. [28]
    S. Rychkov and Z.M. Tan, The ϵ-expansion from conformal field theory, J. Phys. A 48 (2015) 29FT01 [arXiv:1505.00963] [INSPIRE].
  29. [29]
    F. Gliozzi, A.L. Guerrieri, A.C. Petkou and C. Wen, The analytic structure of conformal blocks and the generalized Wilson-Fisher fixed points, JHEP 04 (2017) 056 [arXiv:1702.03938] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  30. [30]
    J.S. Reeve, Renormalisation group calculation of the critical exponents of the special transition in semi-infinite systems, Phys. Lett. A 81 (1981) 237.ADSCrossRefGoogle Scholar
  31. [31]
    J.S. Reeve and A.J. Guttmann, Critical behavior of the n-vector model with a free surface, Phys. Rev. Lett. 45 (1980) 1581.ADSCrossRefGoogle Scholar
  32. [32]
    H.W. Diehl and S. Dietrich, Field-theoretical approach to static critical phenomena in semi-infinite systems, Z. Phys. B 42 (1981) 65 [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    I. Heemskerk, J. Penedones, J. Polchinski and J. Sully, Holography from Conformal Field Theory, JHEP 10 (2009) 079 [arXiv:0907.0151] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  34. [34]
    K. Lang and W. Rühl, The Critical O(N) σ-model at dimensions 2 < d < 4: Fusion coefficients and anomalous dimensions, Nucl. Phys. B 400 (1993) 597 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  35. [35]
    D. Gaiotto, Domain Walls for Two-Dimensional Renormalization Group Flows, JHEP 12 (2012) 103 [arXiv:1201.0767] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  36. [36]
    F. Gliozzi, P. Liendo, M. Meineri and A. Rago, Boundary and Interface CFTs from the Conformal Bootstrap, JHEP 05 (2015) 036 [arXiv:1502.07217] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  37. [37]
    C. Melby-Thompson and C. Schmidt-Colinet, Double Trace Interfaces, JHEP 11 (2017) 110 [arXiv:1707.03418] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  38. [38]
    T. Huber and D. Maître, HypExp: A Mathematica package for expanding hypergeometric functions around integer-valued parameters, Comput. Phys. Commun. 175 (2006) 122 [hep-ph/0507094] [INSPIRE].

Copyright information

© The Author(s) 2019

Authors and Affiliations

  • Agnese Bissi
    • 1
  • Tobias Hansen
    • 1
  • Alexander Söderberg
    • 1
  1. 1.Department of Physics and AstronomyUppsala UniversityUppsalaSweden

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