Abstract
We investigate a new property of retarded Green’s functions using AdS/CFT. The Green's functions are not unique at special points in complex momentum space. This arises because there is no unique incoming mode at the horizon and is similar to the “pole skipping” phenomenon in holographic chaos. Our examples include the bulk scalar field, the bulk Maxwell vector and scalar modes, and the shear mode of gravitational perturbations. In these examples, the special points are always located at 𝜔★ = –i(2πT) with appropriate values of complex wave number.
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References
J.M. Maldacena, The Large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys.38 (1999) 1113 [hep-th/9711200] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys.2 (1998) 253 [hep-th/9802150] [INSPIRE].
E. Witten, Anti-de Sitter space, thermal phase transition and confinement in gauge theories, Adv. Theor. Math. Phys.2 (1998) 505 [hep-th/9803131] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett .B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
J. Casalderrey-Solana, H. Liu, D. Mateos, K. Rajagopal and U.A. Wiedemann, Gauge/String Duality, Hot QCD and Heavy Ion Collisions, arXiv:1101.0618 [INSPIRE].
M. Natsuume, AdS/CFT Duality User Guide, Lect. Notes Phys.903 (2015) pp.1 [arXiv:1409.3575] [INSPIRE].
M. Ammon and J. Erdmenger, Gauge/gravity duality: Foundations and applications, Cambridge University Press, Cambridge U.K. (2015).
J. Zaanen, Y.W. Sun, Y. Liu and K. Schalm, Holographic Duality in Condensed Matter Physics, Cambridge University Press, Cambridge U.K. (2015).
S.A. Hartnoll, A. Lucas and S. Sachdev, Holographic quantum matter, arXiv:1612.07324 [INSPIRE].
S.H. Shenker and D. Stanford, Black holes and the butterfly effect, JHEP03 (2014) 067 [arXiv:1306.0622] [INSPIRE].
D.A. Roberts, D. Stanford and L. Susskind, Localized shocks, JHEP03 (2015) 051 [arXiv:1409.8180] [INSPIRE].
S.H. Shenker and D. Stanford, Stringy effects in scrambling, JHEP05 (2015) 132 [arXiv:1412.6087] [INSPIRE].
J. Maldacena, S.H. Shenker and D. Stanford, A bound on chaos, JHEP08 (2016) 106 [arXiv:1503.01409] [INSPIRE].
S. Grozdanov, K. Schalm and V. Scopelliti, Black hole scrambling from hydrodynamics, Phys. Rev. Lett.120 (2018) 231601 [arXiv:1710.00921] [INSPIRE].
M. Blake, R.A. Davison, S. Grozdanov and H. Liu, Many-body chaos and energy dynamics in holography, JHEP10 (2018) 035 [arXiv:1809.01169] [INSPIRE].
P.K. Kovtun and A.O. Starinets, Quasinormal modes and holography, Phys. Rev.D 72 (2005) 086009 [hep-th/0506184] [INSPIRE].
H. Kodama and A. Ishibashi, A Master equation for gravitational perturbations of maximally symmetric black holes in higher dimensions, Frog. Theor. Phys.110 (2003) 701 [hep-th/0305147] [INSPIRE].
M. Natsuume and T. Okamura, Holographic chaos, pole-skipping and regularity, arXiv:1905.12014 [INSPIRE].
S. Grozdanov, P.K. Kovtun, A.O. Starinets and P. Tadić, The complex life of hydrodynamic modes, JHEP11 (2019) 097 [arXiv:1904.12862] [INSPIRE].
M. Blake, R.A. Davison and D. Vegh, Horizon constraints on holographic Green’s functions, arXiv:1904.12883 [INSPIRE].
C.P. Herzog, P. Kovtun, S. Sachdev and D.T. Son, Quantum critical transport, duality and M-theory, Phys. Rev.D 75 (2007) 085020 [hep-th/0701036] [INSPIRE].
M. Natsuume and T. Okamura, Pole-skipping with finite-coupling corrections, Phys. Rev.D 100 (2019) 126012 [arXiv:1909.09168] [INSPIRE].
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ArXiv ePrint: 1905.12015
Makoto Natsuume also at Department of Particle and Nuclear Physics, SOKENDAI (The Graduate University for Advanced Studies), 1-1 Oho, Tsukuba, Ibaraki, 305-0801, Japan; Department of Physics Engineering, Mie University, Tsu, 514-8507, Japan.
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Natsuume, M., Okamura, T. Nonuniqueness of Green’s functions at special points. J. High Energ. Phys. 2019, 139 (2019). https://doi.org/10.1007/JHEP12(2019)139
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DOI: https://doi.org/10.1007/JHEP12(2019)139