Advertisement

Quantum fishchain in AdS5

  • Nikolay Gromov
  • Amit SeverEmail author
Open Access
Regular Article - Theoretical Physics

Abstract

In our previous paper we derived the holographic dual of the planar fishnet CFT in four dimensions. The dual model becomes classical in the strongly coupled regime of the CFT and takes the form of an integrable chain of particles in five dimensions. Here we study the theory at the quantum level. By applying the canonical quantization procedure with constraints, we show that the model describes a quantum chain of particles propagating in AdS5. We prove the duality at the full quantum level in the \( \mathfrak{u} \) (1) sector and reproduce exactly the spectrum for the cases when it is known analytically.

Keywords

AdS-CFT Correspondence Integrable Field Theories 1/N Expansion Conformal Field 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]
    Ö. Gürdoğan and V. Kazakov, New Integrable 4D Quantum Field Theories from Strongly Deformed Planar \( \mathcal{N} \) = 4 Supersymmetric Yang-Mills Theory, Phys. Rev. Lett.117 (2016) 201602 [arXiv:1512.06704] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  2. [2]
    A.B. Zamolodchikov, ’Fishnetdiagrams as a completely integrable system, Phys. Lett.97B (1980) 63 [INSPIRE].
  3. [3]
    D. Grabner, N. Gromov, V. Kazakov and G. Korchemsky, Strongly γ-Deformed N = 4 Supersymmetric Yang-Mills Theory as an Integrable Conformal Field Theory, Phys. Rev. Lett.120 (2018) 111601 [arXiv:1711.04786] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  4. [4]
    N. Gromov, V. Kazakov, G. Korchemsky, S. Negro and G. Sizov, Integrability of Conformal Fishnet Theory, JHEP01 (2018) 095 [arXiv:1706.04167] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  5. [5]
    N. Gromov, V. Kazakov and G. Korchemsky, Exact Correlation Functions in Conformal Fishnet Theory, JHEP08 (2019) 123 [arXiv:1808.02688] [INSPIRE].ADSCrossRefGoogle Scholar
  6. [6]
    J.K. Erickson, G.W. Semenoff, R.J. Szabo and K. Zarembo, Static potential in N = 4 supersymmetric Yang-Mills theory, Phys. Rev.D 61 (2000) 105006 [hep-th/9911088] [INSPIRE].
  7. [7]
    D. Correa, J. Henn, J. Maldacena and A. Sever, The cusp anomalous dimension at three loops and beyond, JHEP05 (2012) 098 [arXiv:1203.1019] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  8. [8]
    N. Gromov and A. Sever, Derivation of the Holographic Dual of a Planar Conformal Field Theory in 4D, Phys. Rev. Lett.123 (2019) 081602 [arXiv:1903.10508] [INSPIRE].
  9. [9]
    N. Gromov and A. Sever, The Holographic Dual of Strongly γ-deformed N = 4 SYM Theory: Derivation, Generalization, Integrability and Discrete Reparametrization Symmetry, arXiv:1908.10379 [INSPIRE].
  10. [10]
    J. Fokken, C. Sieg and M. Wilhelm, Non-conformality of γ i-deformed N = 4 SYM theory, J. Phys.A 47 (2014) 455401 [arXiv:1308.4420] [INSPIRE].
  11. [11]
    R. Couvreur, J.L. Jacobsen and H. Saleur, Entanglement in nonunitary quantum critical spin chains, Phys. Rev. Lett.119 (2017) 040601 [arXiv:1611.08506] [INSPIRE].
  12. [12]
    H.B. Nielsen and P. Olesen, A Parton view on dual amplitudes, Phys. Lett.32B (1970) 203 [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    P.A.M. Dirac, Wave equations in conformal space, Annals Math.37 (1936) 429.MathSciNetCrossRefGoogle Scholar
  14. [14]
    A. Cavaglià, D. Grabner, N. Gromov and A. Sever, to appear.Google Scholar
  15. [15]
    V. Kazakov and E. Olivucci, Biscalar Integrable Conformal Field Theories in Any Dimension, Phys. Rev. Lett.121 (2018) 131601 [arXiv:1801.09844] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  16. [16]
    D. Simmons-Duffin, Projectors, Shadows and Conformal Blocks, JHEP04 (2014) 146 [arXiv:1204.3894] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  17. [17]
    O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large N field theories, string theory and gravity, Phys. Rept.323 (2000) 183 [hep-th/9905111] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  18. [18]
    L.D. Faddeev, How algebraic Bethe ansatz works for integrable model, in Relativistic gravitation and gravitational radiation. Proceedings, School of Physics, Les Houches, France, 26 September-6 October 1995, pp. 149-219 (1996) [hep-th/9605187] [INSPIRE].
  19. [19]
    O. Lipan, P.B. Wiegmann and A. Zabrodin, Fusion rules for quantum transfer matrices as a dynamical system on Grassmann manifolds, Mod. Phys. Lett.A 12 (1997) 1369 [solv-int/9704015] [INSPIRE].
  20. [20]
    A. Pittelli and M. Preti, Integrable Fishnet from γ-Deformed \( \mathcal{N} \) = 2 Quivers, arXiv:1906.03680 [INSPIRE].
  21. [21]
    B. Basso, S. Komatsu and P. Vieira, Structure Constants and Integrable Bootstrap in Planar N = 4 SYM Theory,arXiv:1505.06745[INSPIRE].
  22. [22]
    B. Basso, J. Caetano and T. Fleury, Hexagons and Correlators in the Fishnet Theory, arXiv:1812.09794 [INSPIRE].
  23. [23]
    D. Bykov and K. Zarembo, Ladders for Wilson Loops Beyond Leading Order, JHEP09 (2012)057 [arXiv:1206.7117] [INSPIRE].
  24. [24]
    J. Caetano, Ö. Gürdoğan and V. Kazakov, Chiral limit of \( \mathcal{N} \) = 4 SYM and ABJM and integrable Feynman graphs, JHEP03 (2018) 077 [arXiv:1612.05895] [INSPIRE].
  25. [25]
    V. Kazakov, E. Olivucci and M. Preti, Generalized fishnets and exact four-point correlators in chiral CFT 4, JHEP06 (2019) 078 [arXiv:1901.00011] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    J. Maldacena and D. Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev.D 94 (2016) 106002 [arXiv:1604.07818] [INSPIRE].
  27. [27]
    B. Basso and D.-l. Zhong, Continuum limit of fishnet graphs and AdS σ-model, JHEP01 (2019)002 [arXiv:1806.04105] [INSPIRE].
  28. [28]
    N. Berkovits, Sketching a Proof of the Maldacena Conjecture at Small Radius, JHEP06 (2019) 111 [arXiv:1903.08264] [INSPIRE].

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Mathematics DepartmentKing’s College LondonLondonU.K.
  2. 2.St. Petersburg INPSt. PetersburgRussia
  3. 3.School of Physics and AstronomyTel Aviv UniversityRamat AvivIsrael
  4. 4.CERN, Theoretical Physics DepartmentGeneva 23Switzerland

Personalised recommendations