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Area of Science:

  • Mathematical Physics
  • Quantum Field Theory
  • String Theory

Background:

  • Random Matrix Theory (RMT) is crucial in quantum mechanics and statistical physics.
  • Two-dimensional conformal field theories (CFTs) possess unique symmetries.
  • Existing RMT lacks direct compatibility with CFT symmetries.

Purpose of the Study:

  • To define a nonperturbative Random Matrix Theory in 2D (RMT2) compatible with CFT symmetries.
  • To establish a method for lifting RMT spectral correlations to RMT2.
  • To explore applications of RMT2 in quantum gravity, specifically AdS3 gravity.

Main Methods:

  • Developed a nonperturbative definition of RMT2.
  • Utilized Mellin space representation of RMT.
  • Employed SL(2,Z) spectral decomposition for lifting RMT to 2D.
  • Calculated RMT2 lift of GUE Airy model correlations.

Main Results:

  • A general prescription for modular-invariant lift of RMT spectral correlations to RMT2.
  • RMT2 correlators reduce to original RMT correlators in a near-extremal limit.
  • Demonstrated explicit RMT2 lift for GUE Airy model two-point correlations.

Conclusions:

  • Proposed RMT2 as the framework for semiclassical amplitudes of off-shell n-boundary torus wormholes in AdS3 pure gravity.
  • Identified a matching gravity calculation for the three-boundary case.
  • RMT2 provides a powerful tool for studying quantum gravity phenomena.