The semi-classical saddles in three-dimensional gravity via holography and mini-superspace approach - INSPIRE

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The semi-classical saddles in three-dimensional gravity via holography and mini-superspace approach

Apr 16, 2024

47 pages

Published in:

JHEP 07 (2024) 283

Published: Jul 31, 2024

e-Print:

2404.10277 [hep-th]

DOI:

10.1007/JHEP07(2024)283

Report number:

YITP-24-50

View in:

ADS Abstract Service

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Abstract: (Springer)

We determine the complex geometries dual to the semi-classical saddles in three-dimensional gravity with positive or negative cosmological constant. We examine the semi-classical saddles in Liouville field theory and interpret them in terms of gravity theory. For this, we describe the gravity theory by Chern-Simons theory and classify the possible saddles based on the homotopy group argument. We further realize the semi-classical saddles using the mini-superspace model of quantum gravity and explicitly determine the integral contour. In the case of positive cosmological constant, we recovered the geometry used for no-boundary proposal of Hartle and Hawking. In the case of negative cosmological constant, the geometry can be identified with Euclidean anti-de Sitter space attached with imaginary radius spheres. The geometry should be unphysical and several arguments on this issue are provided. Partial results were already presented in our earlier letter, and more detailed derivations and explanations on the results are given along with additional results. In particular, we reproduce the classical Liouville action from the Chern-Simons formulation of dual gravity theory.

Note:

47 pages, 6 figures

Conformal and W Symmetry
Gauge-Gravity Correspondence
Models of Quantum Gravity
dimension: 3
cosmological constant: negative
geometry: complex
gravitation: duality
field theory: Liouville
space: anti-de Sitter
geometry: duality

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