Horizon constraints on holographic Green’s functions

Journal Article · 31 December 2019 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/jhep01(2020)077 · OSTI ID:1802384

Blake, Mike ^[1]; Davison, Richard A. ^[2]; Vegh, David ^[3]

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1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Center for Theoretical Physics; Bristol Univ. (United Kingdom). School of Mathematics; OSTI
2. Univ. of Cambridge (United Kingdom). Dept. of Applied Mathematics and Theoretical Physics; Heriot-Watt Univ., Edinburgh, Scotland (United Kingdom). Maxwell Inst. for Mathematical Sciences. Dept. of Mathematics
3. Queen Mary Univ. of London (United Kingdom). School of Physics and Astronomy. Centre for Research in String Theory

We explore a new class of general properties of thermal holographic Green’s functions that can be deduced from the near-horizon behaviour of classical perturbations in asymptotically anti-de Sitter spacetimes. We show that at negative imaginary Matsubara frequencies and appropriate complex values of the wavenumber the retarded Green’s functions of generic operators are not uniquely defined, due to the lack of a unique ingoing solution for the bulk perturbations. From a boundary perspective these ‘pole-skipping’ points correspond to locations in the complex frequency and momentum planes at which a line of poles of the retarded Green’s function intersects with a line of zeroes. As a consequence the dispersion relations of collective modes in the boundary theory at energy scales ω ~ T are directly constrained by the bulk dynamics near the black-brane horizon. For the case of conserved U(1) current and energy-momentum tensor operators we give examples where the dispersion relations of hydrodynamic modes pass through a succession of poleskipping points as real wavenumber is increased. We discuss implications of our results for transport, hydrodynamics and quantum chaos in holographic systems.

• Research Organization: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
• Sponsoring Organization: USDOE Office of Science (SC)
• Grant/Contract Number: SC0012567
• OSTI ID: 1802384
• Journal Information: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 1 Vol. 2020; ISSN 1029-8479
• Publisher: Springer BerlinCopyright Statement
• Country of Publication: United States
• Language: English