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Coupling Fields to 3D Quantum Gravity via Chern-Simons Theory.

Alejandra Castro1, Ioana Coman2, Jackson R Fliss1

  • 1Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom.

Physical Review Letters
|November 13, 2023
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Summary
This summary is machine-generated.

We introduce a novel mechanism coupling matter fields to 3D quantum gravity using Wilson spools. This approach works for positive or negative cosmological constants and reproduces key results for black holes.

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Area of Science:

  • Theoretical physics
  • Quantum gravity
  • High-energy physics

Background:

  • Three-dimensional gravity offers a simplified model for studying quantum gravity phenomena.
  • The Chern-Simons formulation provides a powerful framework for non-perturbative quantum gravity.
  • Understanding matter-gravity coupling is crucial for developing a complete theory of quantum gravity.

Purpose of the Study:

  • To propose a new mechanism for coupling matter fields to three-dimensional quantum gravity.
  • To develop a formalism applicable to both positive and negative cosmological constants.
  • To investigate the role of Wilson spools in quantum gravity calculations.

Main Methods:

  • Utilizing the Chern-Simons formulation of three-dimensional gravity.
  • Employing a collection of Wilson loops, termed a Wilson spool, winding around background paths.
  • Analyzing the one-loop determinant of a free massive scalar field.

Main Results:

  • The proposed mechanism successfully couples matter fields to 3D quantum gravity.
  • The Wilson spool formalism reproduces the one-loop determinant for scalar fields on rotating black holes in Anti-de Sitter space (AdS_{3}) and Euclidean de Sitter space (dS_{3}) in the limit of vanishing Newton's constant (G_{N}→0).
  • A method for incorporating quantum metric fluctuations is described.

Conclusions:

  • The Wilson spool offers a viable approach to studying quantum gravity with matter fields.
  • The formalism is versatile, accommodating different cosmological constants and spacetime geometries.
  • Future work can extend this to include quantum metric fluctuations for a more complete picture.