PoS - Proceedings of Science
Volume 406 - Corfu Summer Institute 2021 "School and Workshops on Elementary Particle Physics and Gravity" (CORFU2021) - Workshop on Quantum Geometry, Field Theory and Gravity
Emergence of classical spacetimes in canonical tensor model
N. Sasakura
Full text: pdf
Published on: November 23, 2022
Abstract
We study the wave function of a tensor model in the canonical formalism by Hamiltonian Monte Carlo method
for Lie group symmetric or nearby values for the argument of the wave function,
and show that there emerge Lie-group symmetric semi-classical spacetimes.
More precisely, we consider some $SO(n+1)\ (n=1,2,3)$ symmetric values for the tensor argument of the wave function, and
show that there emerge discrete $n$-dimensional spheres.
A key fact is that there exist two phases, the classical phase and the quantum phase, depending
on the values of the argument of the wave function,
and emergence of classical spaces above occur in the former phase,
while fluctuations of configurations are too large for such emergence in the latter phase.
The transition between the two phases has similarity with the Gross-Witten-Wadia transition, or that between the one-cut
and the two-cut solutions in the matrix model.
Based on the results, we give some speculations on how spacetimes evolve in the tensor model.
DOI: https://doi.org/10.22323/1.406.0264
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