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Effective field theory for chaotic CFTs

Haehl, Felix M., Rozali, Moshe·2018·Journal of High Energy Physics
DOI 10.1007/jhep10(2018)118
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Abstract

We derive an effective field theory for general chaotic two-dimensional conformal field theories with a large central charge. The theory is a specific and calculable instance of a more general framework recently proposed in [1]. We discuss the gauge symmetries of the model and how they relate to the Lyapunov behaviour of certain correlators. We calculate the out-of-time-ordered correlators diagnosing quantum chaos, as well as certain more fine-grained higher-point generalizations, using our Lorentzian effective field theory. We comment on potential future applications of the effective theory to real-time thermal physics and conformal field theory.

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Figures

Figure 1 Contours in the complex ω -plane, defining the retarded, advanced, and Keldysh (symmetric) correlation functions, respectively. The contour C K = C R -C A . The red crosses denote the poles of the integrand at ω ∈ {-i, 0 ± iε, i } , where ε > 0 is a small regulator that enforces consistent boundary conditions.
Figure 1 Contours in the complex ω -plane, defining the retarded, advanced, and Keldysh (symmetric) correlation functions, respectively. The contour C K = C R -C A . The red crosses denote the poles of the integrand at ω ∈ {-i, 0 ± iε, i } , where ε > 0 is a small regulator that enforces consistent boundary conditions.CC-BY · From the PDF
Figure 2 We choose the k -OTO contour in the complex time plane to be such that all legs are equally separated by ϕ in the imaginary direction. We often set either ϕ = π k (equal separations) or ϕ = δ ≪ 1 (small separation limit). The legs of the contour are labelled by indices α, β, . . . = 1 , . . . , 2 k .
Figure 2 We choose the k -OTO contour in the complex time plane to be such that all legs are equally separated by ϕ in the imaginary direction. We often set either ϕ = π k (equal separations) or ϕ = δ ≪ 1 (small separation limit). The legs of the contour are labelled by indices α, β, . . . = 1 , . . . , 2 k .CC-BY · From the PDF
Figure 3 Illustration of the 4- and 6-point out-of-time-ordered correlators that we consider.
Figure 3 Illustration of the 4- and 6-point out-of-time-ordered correlators that we consider.CC-BY · From the PDF
Figure 4 Illustration of the arrangement of operators in our 2 k -point observable F 2 k , for the case k = 5. It provides a generalization of the familiar 4-point OTOC, which has the property that the associated time of exponential growth (which we call as k -scrambling time t ( k ) ∗ ) is maximal: t ( k ) ∗ = ( k -1) log c . The red solid lines indicate bilocal operators B ( h, ¯ h ) . The red wiggly lines schematically indicate the (maximally braided) propagation of the scrambling mode ϵ .
Figure 4 Illustration of the arrangement of operators in our 2 k -point observable F 2 k , for the case k = 5. It provides a generalization of the familiar 4-point OTOC, which has the property that the associated time of exponential growth (which we call as k -scrambling time t ( k ) ∗ ) is maximal: t ( k ) ∗ = ( k -1) log c . The red solid lines indicate bilocal operators B ( h, ¯ h ) . The red wiggly lines schematically indicate the (maximally braided) propagation of the scrambling mode ϵ .CC-BY · From the PDF

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Citations

Cites

Research works printed but not linked: 45

  1. M. Blake, H. Lee and H. Liu, A quantum hydrodynamical description for scrambling and many-body chaos, arXiv:1801.00010 [INSPIRE]. · arXiv
  2. J. Maldacena, S.H. Shenker and D. Stanford, A bound on chaos, JHEP 08 (2016) 106 [arXiv:1503.01409] [INSPIRE]. · DOI
  3. A.I. Larkin and Y.N. Ovchinnikov, Quasiclassical method in the theory of superconductivity, Sov. Phys. JETP 28 (1969) 1200.
  4. S.H. Shenker and D. Stanford, Black holes and the butterfly effect, JHEP 03 (2014) 067 [arXiv:1306.0622] [INSPIRE]. · DOI · Paper page
  5. S.H. Shenker and D. Stanford, Multiple Shocks, JHEP 12 (2014) 046 [arXiv:1312.3296] [INSPIRE]. · DOI
  6. S. Leichenauer, Disrupting Entanglement of Black Holes, Phys. Rev. D 90 (2014) 046009 [arXiv:1405.7365] [INSPIRE]. · arXiv
  7. Y. Gu, X.-L. Qi and D. Stanford, Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models, JHEP 05 (2017) 125 [arXiv:1609.07832] [INSPIRE]. · DOI
  8. A.A. Patel and S. Sachdev, Quantum chaos on a critical Fermi surface, Proc. Nat. Acad. Sci. 114 (2017) 1844 [arXiv:1611.00003] [INSPIRE]. · DOI
  9. B. Swingle and D. Chowdhury, Slow scrambling in disordered quantum systems, Phys. Rev. B 95 (2017) 060201 [arXiv:1608.03280] [INSPIRE]. · DOI
  10. M. Blake, Universal Charge Diffusion and the Butterfly Effect in Holographic Theories, Phys. Rev. Lett. 117 (2016) 091601 [arXiv:1603.08510] [INSPIRE]. · DOI
  11. M. Blake and A. Donos, Diffusion and Chaos from near AdS 2 horizons, JHEP 02 (2017) 013 [arXiv:1611.09380] [INSPIRE]. · DOI
  12. M. Blake, Universal Diffusion in Incoherent Black Holes, Phys. Rev. D 94 (2016) 086014 [arXiv:1604.01754] [INSPIRE]. · arXiv
  13. M. Blake, R.A. Davison and S. Sachdev, Thermal diffusivity and chaos in metals without quasiparticles, Phys. Rev. D 96 (2017) 106008 [arXiv:1705.07896] [INSPIRE]. · arXiv
  14. R.A. Davison, W. Fu, A. Georges, Y. Gu, K. Jensen and S. Sachdev, Thermoelectric transport in disordered metals without quasiparticles: The Sachdev-Ye-Kitaev models and holography, Phys. Rev. B 95 (2017) 155131 [arXiv:1612.00849] [INSPIRE]. · DOI
  15. J. Maldacena and D. Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev. D 94 (2016) 106002 [arXiv:1604.07818] [INSPIRE]. · arXiv
  16. A. Kitaev and S.J. Suh, The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual, JHEP 05 (2018) 183 [arXiv:1711.08467] [INSPIRE]. · DOI · Paper page
  17. J. Engelsöy, T.G. Mertens and H. Verlinde, An investigation of AdS 2 backreaction and holography, JHEP 07 (2016) 139 [arXiv:1606.03438] [INSPIRE]. · DOI · Paper page
  18. G. Turiaci and H. Verlinde, Towards a 2d QFT Analog of the SYK Model, JHEP 10 (2017) 167 [arXiv:1701.00528] [INSPIRE]. · DOI
  19. S. Grozdanov, K. Schalm and V. Scopelliti, Black hole scrambling from hydrodynamics, Phys. Rev. Lett. 120 (2018) 231601 [arXiv:1710.00921] [INSPIRE]. · DOI · Paper page
  20. D.A. Roberts and D. Stanford, Two-dimensional conformal field theory and the butterfly effect, Phys. Rev. Lett. 115 (2015) 131603 [arXiv:1412.5123] [INSPIRE]. · DOI
  21. G. Turiaci and H. Verlinde, On CFT and Quantum Chaos, JHEP 12 (2016) 110 [arXiv:1603.03020] [INSPIRE]. · DOI
  22. F.M. Haehl and M. Rozali, Fine Grained Chaos in AdS 2 Gravity, Phys. Rev. Lett. 120 (2018) 121601 [arXiv:1712.04963] [INSPIRE]. · DOI
  23. J. Cotler and K. Jensen, A theory of reparameterizations for AdS 3 gravity, arXiv:1808.03263 [INSPIRE]. · arXiv
  24. E. Perlmutter, Bounding the Space of Holographic CFTs with Chaos, JHEP 10 (2016) 069 [arXiv:1602.08272] [INSPIRE]. · DOI
  25. D. Nickel and D.T. Son, Deconstructing holographic liquids, New J. Phys. 13 (2011) 075010 [arXiv:1009.3094] [INSPIRE]. · DOI
  26. S. Dubovsky, L. Hui, A. Nicolis and D.T. Son, Effective field theory for hydrodynamics: thermodynamics and the derivative expansion, Phys. Rev. D 85 (2012) 085029 [arXiv:1107.0731] [INSPIRE]. · arXiv
  27. S. Dubovsky, L. Hui and A. Nicolis, Effective field theory for hydrodynamics: Wess-Zumino term and anomalies in two spacetime dimensions, Phys. Rev. D 89 (2014) 045016 [arXiv:1107.0732] [INSPIRE]. · arXiv
  28. F.M. Haehl, R. Loganayagam and M. Rangamani, Adiabatic hydrodynamics: The eightfold way to dissipation, JHEP 05 (2015) 060 [arXiv:1502.00636] [INSPIRE]. · DOI
  29. F.M. Haehl, R. Loganayagam and M. Rangamani, Effective actions for anomalous hydrodynamics, JHEP 03 (2014) 034 [arXiv:1312.0610] [INSPIRE]. · DOI
  30. J. Maldacena, D. Stanford and Z. Yang, Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space, PTEP 2016 (2016) 12C104 [arXiv:1606.01857] [INSPIRE]. · DOI · Paper page
  31. A. Almheiri and J. Polchinski, Models of AdS 2 backreaction and holography, JHEP 11 (2015) 014 [arXiv:1402.6334] [INSPIRE]. · DOI · Paper page
  32. S. Weinberg, The quantum theory of fields. Vol. 2: Modern applications, Cambridge University Press, (2013).
  33. A.M. Polyakov, Quantum Gravity in Two-Dimensions, Mod. Phys. Lett. A 2 (1987) 893 [INSPIRE]. · DOI
  34. D. Simmons-Duffin, Projectors, Shadows and Conformal Blocks, JHEP 04 (2014) 146 [arXiv:1204.3894] [INSPIRE]. · DOI
  35. V. Iyer and R.M. Wald, Some properties of Noether charge and a proposal for dynamical black hole entropy, Phys. Rev. D 50 (1994) 846 [gr-qc/9403028] [INSPIRE]. · DOI · Paper page
  36. F.M. Haehl, R. Loganayagam and M. Rangamani, The eightfold way to dissipation, Phys. Rev. Lett. 114 (2015) 201601 [arXiv:1412.1090] [INSPIRE]. · DOI
  37. F.M. Haehl, R. Loganayagam and M. Rangamani, The Fluid Manifesto: Emergent symmetries, hydrodynamics and black holes, JHEP 01 (2016) 184 [arXiv:1510.02494] [INSPIRE]. · DOI
  38. F.M. Haehl, R. Loganayagam, P. Narayan and M. Rangamani, Classification of out-of-time-order correlators, arXiv:1701.02820 [INSPIRE]. · arXiv
  39. F.M. Haehl, R. Loganayagam, P. Narayan, A.A. Nizami and M. Rangamani, Thermal out-of-time-order correlators, KMS relations and spectral functions, JHEP 12 (2017) 154 [arXiv:1706.08956] [INSPIRE]. · DOI
  40. N. Yunger Halpern, B. Swingle and J. Dressel, Quasiprobability behind the out-of-time-ordered correlator, Phys. Rev. A 97 (2018) 042105 [arXiv:1704.01971] [INSPIRE]. · DOI
  41. Y.-H. Qi, Y. Seo, S.-J. Sin and G. Song, Schwarzian correction to quantum correlation in SYK model, arXiv:1804.06164 [INSPIRE]. · arXiv
  42. H.T. Lam, T.G. Mertens, G.J. Turiaci and H. Verlinde, Shockwave S-matrix from Schwarzian Quantum Mechanics, arXiv:1804.09834 [INSPIRE]. · arXiv
  43. F.A. Smirnov and A.B. Zamolodchikov, On space of integrable quantum field theories, Nucl. Phys. B 915 (2017) 363 [arXiv:1608.05499] [INSPIRE]. · DOI · Paper page
  44. A. Cavaglià, S. Negro, I.M. Szécsényi and R. Tateo, $$ T\overline{T} $$ -deformed 2D Quantum Field Theories, JHEP 10 (2016) 112 [arXiv:1608.05534] [INSPIRE]. · DOI
  45. H. Osborn and A.C. Petkou, Implications of conformal invariance in field theories for general dimensions, Annals Phys. 231 (1994) 311 [hep-th/9307010] [INSPIRE]. · DOI

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Metadata

Authors
Haehl, F. M., & Rozali, M.
Venue
Journal of High Energy Physics
Publisher
Springer Science and Business Media LLC
Published
2018-10
Volume
2018
Issue
10
ISSN
1029-8479
DOI
10.1007/jhep10(2018)118
Cited by
96
References
3
Language
en
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