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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.

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.