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Einstein Rings in Holography

Koji Hashimoto, Shunichiro Kinoshita, and Keiju Murata
Phys. Rev. Lett. 123, 031602 – Published 19 July 2019
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Abstract

Clarifying conditions for the existence of a gravitational picture for a given quantum field theory (QFT) is one of the fundamental problems in the AdS/CFT correspondence. We propose a direct way to demonstrate the existence of the dual black holes: imaging an Einstein ring. We consider a response function of the thermal QFT on a two-dimensional sphere under a time-periodic localized source. The dual gravity picture, if it exists, is a black hole in an asymptotic global AdS4 and a bulk probe field with a localized source on the AdS boundary. The response function corresponds to the asymptotic data of the bulk field propagating in the black hole spacetime. We find a formula that converts the response function to the image of the dual black hole: The view of the sky of the AdS bulk from a point on the boundary. Using the formula, we demonstrate that, for a thermal state dual to the SchwarzschildAdS4 spacetime, the Einstein ring is constructed from the response function. The evaluated Einstein radius is found to be determined by the total energy of the dual QFT. Our theoretical proposal opens a door to gravitational phenomena on strongly correlated materials.

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  • Received 17 December 2018
  • Revised 15 April 2019

DOI:https://doi.org/10.1103/PhysRevLett.123.031602

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Particles & Fields

Authors & Affiliations

Koji Hashimoto1, Shunichiro Kinoshita2, and Keiju Murata1,3

  • 1Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan
  • 2Department of Physics, Chuo University, Tokyo 112-8551, Japan
  • 3Department of Physics, College of Humanities and Sciences, Nihon University, Tokyo 156-8550, Japan

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Issue

Vol. 123, Iss. 3 — 19 July 2019

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