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Matrix models and deformations of JT gravity.

Edward Witten1

  • 1Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540, USA.

Proceedings. Mathematical, Physical, and Engineering Sciences
|January 7, 2021
PubMed
Summary
This summary is machine-generated.

A deformation of Jackiw-Teitelboim (JT) gravity is shown to be dual to a matrix model. The study determines the density of eigenvalues for this dual matrix model, finding a simple result under specific conditions.

Keywords:
JT gravitymatrix modelsquantum gravity

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Area of Science:

  • Theoretical Physics
  • Quantum Gravity
  • String Theory

Background:

  • Jackiw-Teitelboim (JT) gravity is a 2D theory.
  • JT gravity has been found to be dual to a matrix model.
  • Matrix models represent random ensembles of quantum systems.

Purpose of the Study:

  • To investigate a deformation of JT gravity.
  • To establish its duality with a matrix model.
  • To determine the eigenvalue density of the dual matrix model.

Main Methods:

  • Deforming the bulk action of JT gravity.
  • Defining a specific path integral procedure for the deformed theory.
  • Calculating the density of eigenvalues for the resulting matrix model.

Main Results:

  • The deformed JT gravity is demonstrated to be dual to a matrix model.
  • The eigenvalue density of the dual matrix model was determined.
  • A simple eigenvalue density occurs when W(0)=0, otherwise it is complex.

Conclusions:

  • The duality between deformed JT gravity and matrix models is established.
  • The eigenvalue density provides insight into the quantum properties of the system.
  • The condition W(0)=0 simplifies the spectral properties of the dual matrix model.