# Einstein Rings in Holography

## TL;DR

This paper proposes a method to visualize dual black holes in AdS/CFT by imaging Einstein rings from the response functions of thermal quantum field theories, linking gravitational phenomena to strongly correlated materials.

## Contribution

It introduces a formula converting QFT response functions into images of dual black holes, demonstrating Einstein rings in the holographic context for the first time.

## Key findings

- Einstein rings can be constructed from QFT response functions.
- The Einstein radius relates to the total energy of the dual QFT.
- The method links gravitational phenomena to strongly correlated materials.

## 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 AdS$_4$ 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 Schwarzschild-AdS$_4$ 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.