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Boomerang RG flows with intermediate conformal invariance

  • Aristomenis Donos
  • Jerome P. Gauntlett
  • Christopher Rosen
  • Omar Sosa-Rodriguez
Open Access
Regular Article - Theoretical Physics
  • 59 Downloads

Abstract

For a class of D = 5 holographic models we construct boomerang RG flow solutions that start in the UV at an AdS5 vacuum and end up at the same vacuum in the IR. The RG flows are driven by deformations by relevant operators that explicitly break translation invariance. For specific models, such that they admit another AdS5 solution, AdS 5 c , we show that for large enough deformations the RG flows approach an intermediate scaling regime with approximate conformal invariance governed by AdS 5 c . For these flows we calculate the holographic entanglement entropy and the entropic c-function for the RG flows. The latter is not monotonic, but it does encapsulate the degrees of freedom in each scaling region. For a different set of models, we find boomerang RG flows with intermediate scaling governed by an AdS2 × ℝ3 solution which breaks translation invariance. Furthermore, for large enough deformations these models have interesting and novel thermal insulating ground states for which the entropy vanishes as the temperature goes to zero, but not as a power-law. Remarkably, the thermal diffusivity and the butterfly velocity for these new insulating ground states are related via D = Ev B 2 /(2πT), with E(T) → 0.5 as T → 0.

Keywords

AdS-CFT Correspondence Gauge-gravity correspondence 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]
    A. Donos, J.P. Gauntlett, C. Rosen and O. Sosa-Rodriguez, Boomerang RG flows in M-theory with intermediate scaling, JHEP 07 (2017) 128 [arXiv:1705.03000] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    P. Chesler, A. Lucas and S. Sachdev, Conformal field theories in a periodic potential: results from holography and field theory, Phys. Rev. D 89 (2014) 026005 [arXiv:1308.0329] [INSPIRE].ADSGoogle Scholar
  3. [3]
    A. Donos, J.P. Gauntlett and C. Pantelidou, Conformal field theories in d = 4 with a helical twist, Phys. Rev. D 91 (2015) 066003 [arXiv:1412.3446] [INSPIRE].ADSMathSciNetGoogle Scholar
  4. [4]
    A. Donos, J.P. Gauntlett and O. Sosa-Rodriguez, Anisotropic plasmas from axion and dilaton deformations, JHEP 11 (2016) 002 [arXiv:1608.02970] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  5. [5]
    G.T. Horowitz, J.E. Santos and D. Tong, Optical conductivity with holographic lattices, JHEP 07 (2012) 168 [arXiv:1204.0519] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  6. [6]
    T. Azeyanagi, W. Li and T. Takayanagi, On string theory duals of Lifshitz-like fixed points, JHEP 06 (2009) 084 [arXiv:0905.0688] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  7. [7]
    A. Donos and J.P. Gauntlett, Holographic Q-lattices, JHEP 04 (2014) 040 [arXiv:1311.3292] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    S. Harrison, S. Kachru and H. Wang, Resolving Lifshitz horizons, JHEP 02 (2014) 085 [arXiv:1202.6635] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    N. Bao, X. Dong, S. Harrison and E. Silverstein, The benefits of stress: resolution of the Lifshitz singularity, Phys. Rev. D 86 (2012) 106008 [arXiv:1207.0171] [INSPIRE].ADSGoogle Scholar
  10. [10]
    J. Bhattacharya, S. Cremonini and A. Sinkovics, On the IR completion of geometries with hyperscaling violation, JHEP 02 (2013) 147 [arXiv:1208.1752] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    S. Jain, N. Kundu, K. Sen, A. Sinha and S.P. Trivedi, A strongly coupled anisotropic fluid from dilaton driven holography, JHEP 01 (2015) 005 [arXiv:1406.4874] [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    N. Kundu, P. Narayan, N. Sircar and S.P. Trivedi, Entangled dilaton dyons, JHEP 03 (2013) 155 [arXiv:1208.2008] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    A. Donos, J.P. Gauntlett and C. Pantelidou, Semi-local quantum criticality in string/M-theory, JHEP 03 (2013) 103 [arXiv:1212.1462] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    J. Bhattacharya, S. Cremonini and B. Goutéraux, Intermediate scalings in holographic RG flows and conductivities, JHEP 02 (2015) 035 [arXiv:1409.4797] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  15. [15]
    H. Casini and M. Huerta, A c-theorem for the entanglement entropy, J. Phys. A 40 (2007) 7031 [cond-mat/0610375] [INSPIRE].
  16. [16]
    T. Nishioka, S. Ryu and T. Takayanagi, Holographic entanglement entropy: an overview, J. Phys. A 42 (2009) 504008 [arXiv:0905.0932] [INSPIRE].MathSciNetzbMATHGoogle Scholar
  17. [17]
    R.C. Myers and A. Singh, Comments on holographic entanglement entropy and RG flows, JHEP 04 (2012) 122 [arXiv:1202.2068] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    H. Liu and M. Mezei, A refinement of entanglement entropy and the number of degrees of freedom, JHEP 04 (2013) 162 [arXiv:1202.2070] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    S.S. Gubser, Curvature singularities: the good, the bad and the naked, Adv. Theor. Math. Phys. 4 (2000) 679 [hep-th/0002160] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    A. Donos and S.A. Hartnoll, Interaction-driven localization in holography, Nature Phys. 9 (2013) 649 [arXiv:1212.2998] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    A. Donos and J.P. Gauntlett, Novel metals and insulators from holography, JHEP 06 (2014) 007 [arXiv:1401.5077] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    B. Goutéraux, Charge transport in holography with momentum dissipation, JHEP 04 (2014) 181 [arXiv:1401.5436] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    A. Donos, B. Goutéraux and E. Kiritsis, Holographic metals and insulators with helical symmetry, JHEP 09 (2014) 038 [arXiv:1406.6351] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    S.A. Hartnoll, Theory of universal incoherent metallic transport, Nature Phys. 11 (2015) 54 [arXiv:1405.3651] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    M. Blake, Universal charge diffusion and the butterfly effect in holographic theories, Phys. Rev. Lett. 117 (2016) 091601 [arXiv:1603.08510] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    M. Blake, Universal diffusion in incoherent black holes, Phys. Rev. D 94 (2016) 086014 [arXiv:1604.01754] [INSPIRE].ADSMathSciNetGoogle Scholar
  27. [27]
    A. Lucas and J. Steinberg, Charge diffusion and the butterfly effect in striped holographic matter, JHEP 10 (2016) 143 [arXiv:1608.03286] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  28. [28]
    Y. Ling, P. Liu and J.-P. Wu, Holographic butterfly effect at quantum critical points, JHEP 10 (2017) 025 [arXiv:1610.02669] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  29. [29]
    M. Blake and A. Donos, Diffusion and chaos from near AdS 2 horizons, JHEP 02 (2017) 013 [arXiv:1611.09380] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  30. [30]
    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].ADSCrossRefGoogle Scholar
  31. [31]
    M. Baggioli, B. Goutéraux, E. Kiritsis and W.-J. Li, Higher derivative corrections to incoherent metallic transport in holography, JHEP 03 (2017) 170 [arXiv:1612.05500] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  32. [32]
    S.-F. Wu, B. Wang, X.-H. Ge and Y. Tian, Collective diffusion and strange-metal transport, arXiv:1702.08803 [INSPIRE].
  33. [33]
    K.-Y. Kim and C. Niu, Diffusion and butterfly velocity at finite density, JHEP 06 (2017) 030 [arXiv:1704.00947] [INSPIRE].MathSciNetzbMATHGoogle Scholar
  34. [34]
    M. Baggioli and W.-J. Li, Diffusivities bounds and chaos in holographic Horndeski theories, JHEP 07 (2017) 055 [arXiv:1705.01766] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  35. [35]
    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].ADSGoogle Scholar
  36. [36]
    S.-F. Wu, B. Wang, X.-H. Ge and Y. Tian, Holographic RG flow of thermo-electric transports with momentum dissipation, arXiv:1706.00718 [INSPIRE].
  37. [37]
    D. Giataganas, U. Gürsoy and J.F. Pedraza, Strongly-coupled anisotropic gauge theories and holography, arXiv:1708.05691 [INSPIRE].
  38. [38]
    S. Grozdanov, K. Schalm and V. Scopelliti, Black hole scrambling from hydrodynamics, arXiv:1710.00921 [INSPIRE].
  39. [39]
    A. Lucas, Constraints on hydrodynamics from many-body quantum chaos, arXiv:1710.01005 [INSPIRE].
  40. [40]
    S.H. Shenker and D. Stanford, Black holes and the butterfly effect, JHEP 03 (2014) 067 [arXiv:1306.0622] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  41. [41]
    J. Maldacena, S.H. Shenker and D. Stanford, A bound on chaos, JHEP 08 (2016) 106 [arXiv:1503.01409] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  42. [42]
    K. Sfetsos, On gravitational shock waves in curved space-times, Nucl. Phys. B 436 (1995) 721 [hep-th/9408169] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  43. [43]
    I.R. Klebanov and E. Witten, AdS/CFT correspondence and symmetry breaking, Nucl. Phys. B 556 (1999) 89 [hep-th/9905104] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  44. [44]
    S.S. Gubser, S.S. Pufu and F.D. Rocha, Quantum critical superconductors in string theory and M-theory, Phys. Lett. B 683 (2010) 201 [arXiv:0908.0011] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  45. [45]
    S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  46. [46]
    S. Ryu and T. Takayanagi, Aspects of holographic entanglement entropy, JHEP 08 (2006) 045 [hep-th/0605073] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  47. [47]
    T. Albash and C.V. Johnson, Holographic entanglement entropy and renormalization group flow, JHEP 02 (2012) 095 [arXiv:1110.1074] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  48. [48]
    A. Donos and J.P. Gauntlett, Navier-Stokes equations on black hole horizons and DC thermoelectric conductivity, Phys. Rev. D 92 (2015) 121901 [arXiv:1506.01360] [INSPIRE].ADSGoogle Scholar
  49. [49]
    A. Donos and J.P. Gauntlett, Thermoelectric DC conductivities from black hole horizons, JHEP 11 (2014) 081 [arXiv:1406.4742] [INSPIRE].ADSCrossRefGoogle Scholar
  50. [50]
    A. Donos, J.P. Gauntlett and V. Ziogas, Diffusion in inhomogeneous media, Phys. Rev. D 96 (2017) 125003 [arXiv:1708.05412] [INSPIRE].ADSGoogle Scholar
  51. [51]
    A. Donos, J.P. Gauntlett and V. Ziogas, Diffusion for holographic lattices, JHEP 03 (2018) 056 [arXiv:1710.04221] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  • Aristomenis Donos
    • 1
  • Jerome P. Gauntlett
    • 2
  • Christopher Rosen
    • 2
  • Omar Sosa-Rodriguez
    • 1
  1. 1.Centre for Particle Theory and Department of Mathematical SciencesDurham UniversityDurhamU.K.
  2. 2.Blackett LaboratoryImperial CollegeLondonU.K.

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