Einstein Rings in Holography.

Area of Science:

• Theoretical Physics
• Quantum Field Theory
• AdS/CFT Correspondence

Background:

• The AdS/CFT correspondence is a key framework for understanding quantum field theories (QFTs) and quantum gravity.
• A fundamental challenge is to identify conditions under which a QFT has a dual gravitational description, particularly involving black holes.

Purpose of the Study:

• To propose a direct method for demonstrating the existence of dual black hole solutions in the AdS/CFT correspondence.
• To establish a connection between observable QFT quantities and geometric features of the dual spacetime.

Main Methods:

• Consider a thermal quantum field theory on a 2D sphere subjected to a time-periodic localized source.
• Analyze the response function of this QFT.
• Develop a formula to convert the QFT response function into an image of the dual black hole spacetime, representing the 'view of the sky' from the boundary.

Main Results:

• A formula is derived that maps the QFT response function to the asymptotic data of a bulk field in the dual black hole spacetime.
• It is demonstrated that an Einstein ring, a gravitational lensing phenomenon, can be constructed from the response function for a thermal state dual to Schwarzschild-AdS4 spacetime.
• The Einstein radius is found to be directly determined by the total energy of the dual QFT.

Conclusions:

• The proposed method provides a direct observational signature for the existence of gravitational duals in AdS/CFT.
• This work bridges the gap between QFT observables and spacetime geometry, enabling the study of gravitational phenomena in strongly correlated systems.