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 c5 , we show that for large enough deformations the RG flows approach an intermediate scaling regime with approximate conformal invariance governed by AdS c5 . 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 2 B /(2πT), with E(T) → 0.5 as T → 0.
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References
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].
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].
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].
A. Donos, J.P. Gauntlett and O. Sosa-Rodriguez, Anisotropic plasmas from axion and dilaton deformations, JHEP 11 (2016) 002 [arXiv:1608.02970] [INSPIRE].
G.T. Horowitz, J.E. Santos and D. Tong, Optical conductivity with holographic lattices, JHEP 07 (2012) 168 [arXiv:1204.0519] [INSPIRE].
T. Azeyanagi, W. Li and T. Takayanagi, On string theory duals of Lifshitz-like fixed points, JHEP 06 (2009) 084 [arXiv:0905.0688] [INSPIRE].
A. Donos and J.P. Gauntlett, Holographic Q-lattices, JHEP 04 (2014) 040 [arXiv:1311.3292] [INSPIRE].
S. Harrison, S. Kachru and H. Wang, Resolving Lifshitz horizons, JHEP 02 (2014) 085 [arXiv:1202.6635] [INSPIRE].
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].
J. Bhattacharya, S. Cremonini and A. Sinkovics, On the IR completion of geometries with hyperscaling violation, JHEP 02 (2013) 147 [arXiv:1208.1752] [INSPIRE].
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].
N. Kundu, P. Narayan, N. Sircar and S.P. Trivedi, Entangled dilaton dyons, JHEP 03 (2013) 155 [arXiv:1208.2008] [INSPIRE].
A. Donos, J.P. Gauntlett and C. Pantelidou, Semi-local quantum criticality in string/M-theory, JHEP 03 (2013) 103 [arXiv:1212.1462] [INSPIRE].
J. Bhattacharya, S. Cremonini and B. Goutéraux, Intermediate scalings in holographic RG flows and conductivities, JHEP 02 (2015) 035 [arXiv:1409.4797] [INSPIRE].
H. Casini and M. Huerta, A c-theorem for the entanglement entropy, J. Phys. A 40 (2007) 7031 [cond-mat/0610375] [INSPIRE].
T. Nishioka, S. Ryu and T. Takayanagi, Holographic entanglement entropy: an overview, J. Phys. A 42 (2009) 504008 [arXiv:0905.0932] [INSPIRE].
R.C. Myers and A. Singh, Comments on holographic entanglement entropy and RG flows, JHEP 04 (2012) 122 [arXiv:1202.2068] [INSPIRE].
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].
S.S. Gubser, Curvature singularities: the good, the bad and the naked, Adv. Theor. Math. Phys. 4 (2000) 679 [hep-th/0002160] [INSPIRE].
A. Donos and S.A. Hartnoll, Interaction-driven localization in holography, Nature Phys. 9 (2013) 649 [arXiv:1212.2998] [INSPIRE].
A. Donos and J.P. Gauntlett, Novel metals and insulators from holography, JHEP 06 (2014) 007 [arXiv:1401.5077] [INSPIRE].
B. Goutéraux, Charge transport in holography with momentum dissipation, JHEP 04 (2014) 181 [arXiv:1401.5436] [INSPIRE].
A. Donos, B. Goutéraux and E. Kiritsis, Holographic metals and insulators with helical symmetry, JHEP 09 (2014) 038 [arXiv:1406.6351] [INSPIRE].
S.A. Hartnoll, Theory of universal incoherent metallic transport, Nature Phys. 11 (2015) 54 [arXiv:1405.3651] [INSPIRE].
M. Blake, Universal charge diffusion and the butterfly effect in holographic theories, Phys. Rev. Lett. 117 (2016) 091601 [arXiv:1603.08510] [INSPIRE].
M. Blake, Universal diffusion in incoherent black holes, Phys. Rev. D 94 (2016) 086014 [arXiv:1604.01754] [INSPIRE].
A. Lucas and J. Steinberg, Charge diffusion and the butterfly effect in striped holographic matter, JHEP 10 (2016) 143 [arXiv:1608.03286] [INSPIRE].
Y. Ling, P. Liu and J.-P. Wu, Holographic butterfly effect at quantum critical points, JHEP 10 (2017) 025 [arXiv:1610.02669] [INSPIRE].
M. Blake and A. Donos, Diffusion and chaos from near AdS 2 horizons, JHEP 02 (2017) 013 [arXiv:1611.09380] [INSPIRE].
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].
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].
S.-F. Wu, B. Wang, X.-H. Ge and Y. Tian, Collective diffusion and strange-metal transport, arXiv:1702.08803 [INSPIRE].
K.-Y. Kim and C. Niu, Diffusion and butterfly velocity at finite density, JHEP 06 (2017) 030 [arXiv:1704.00947] [INSPIRE].
M. Baggioli and W.-J. Li, Diffusivities bounds and chaos in holographic Horndeski theories, JHEP 07 (2017) 055 [arXiv:1705.01766] [INSPIRE].
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].
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].
D. Giataganas, U. Gürsoy and J.F. Pedraza, Strongly-coupled anisotropic gauge theories and holography, arXiv:1708.05691 [INSPIRE].
S. Grozdanov, K. Schalm and V. Scopelliti, Black hole scrambling from hydrodynamics, arXiv:1710.00921 [INSPIRE].
A. Lucas, Constraints on hydrodynamics from many-body quantum chaos, arXiv:1710.01005 [INSPIRE].
S.H. Shenker and D. Stanford, Black holes and the butterfly effect, JHEP 03 (2014) 067 [arXiv:1306.0622] [INSPIRE].
J. Maldacena, S.H. Shenker and D. Stanford, A bound on chaos, JHEP 08 (2016) 106 [arXiv:1503.01409] [INSPIRE].
K. Sfetsos, On gravitational shock waves in curved space-times, Nucl. Phys. B 436 (1995) 721 [hep-th/9408169] [INSPIRE].
I.R. Klebanov and E. Witten, AdS/CFT correspondence and symmetry breaking, Nucl. Phys. B 556 (1999) 89 [hep-th/9905104] [INSPIRE].
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].
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
S. Ryu and T. Takayanagi, Aspects of holographic entanglement entropy, JHEP 08 (2006) 045 [hep-th/0605073] [INSPIRE].
T. Albash and C.V. Johnson, Holographic entanglement entropy and renormalization group flow, JHEP 02 (2012) 095 [arXiv:1110.1074] [INSPIRE].
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].
A. Donos and J.P. Gauntlett, Thermoelectric DC conductivities from black hole horizons, JHEP 11 (2014) 081 [arXiv:1406.4742] [INSPIRE].
A. Donos, J.P. Gauntlett and V. Ziogas, Diffusion in inhomogeneous media, Phys. Rev. D 96 (2017) 125003 [arXiv:1708.05412] [INSPIRE].
A. Donos, J.P. Gauntlett and V. Ziogas, Diffusion for holographic lattices, JHEP 03 (2018) 056 [arXiv:1710.04221] [INSPIRE].
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Donos, A., Gauntlett, J.P., Rosen, C. et al. Boomerang RG flows with intermediate conformal invariance. J. High Energ. Phys. 2018, 17 (2018). https://doi.org/10.1007/JHEP04(2018)017
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DOI: https://doi.org/10.1007/JHEP04(2018)017