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Emergent Sasaki-Einstein geometry and AdS/CFT.

Robert J Berman¹, Tristan C Collins², Daniel Persson³

¹Department of Mathematical Sciences, Chalmers University of Technology, Gothenburg, Sweden. robertb@chalmers.se.

Nature Communications

|January 19, 2022

Summary

This summary is machine-generated.

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This study demonstrates how classical spacetime geometry emerges from quantum states in gauge theories using the gauge/gravity correspondence. Researchers derived approximations for the Sasaki-Einstein metric from a canonical quantum state, simplifying calculations via tropicalization.

Area of Science:

Theoretical Physics
Quantum Gravity
String Theory

Background:

Explaining classical spacetime emergence from quantum gravity is a fundamental challenge.
The gauge/gravity correspondence offers a holographic framework to address this problem.
This correspondence links supergravity in Anti-deSitter space to conformal field theories on its boundary.

Purpose of the Study:

To confirm that classical spacetime geometry emerges from quantum states in the dual gauge theory.
To derive approximations of the Sasaki-Einstein metric from a canonical quantum state.

Main Methods:

Utilizing the gauge/gravity correspondence (AdS/CFT correspondence).
Deriving an explicit integral formula involving a canonical quantum state.
Applying tropicalization for computational simplification in specific gauge theories.

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Main Results:

Confirmation that classical geometry emerges from quantum states.
Obtained approximations to the Sasaki-Einstein metric.
Demonstrated computational simplification through tropicalization for toric quiver gauge theories.

Conclusions:

The study provides concrete evidence for the emergence of classical geometry from quantum states within the gauge/gravity framework.
The derived methods offer a pathway to study quantum gravity phenomena through gauge theory computations.
Tropicalization presents an efficient method for calculations in specific holographic contexts.