Emergent symmetries in the canonical tensor model

TL;DR

This paper investigates the quantum properties of the canonical tensor model (CTM), revealing that its wave function favors configurations with symmetries akin to spacetime structures, supporting the idea of spacetime emergence from quantum gravity models.

Contribution

It analyzes the symmetry properties of the CTM wave function, showing a preference for configurations with Lie-group invariances, including spacetime-like signatures, indicating potential spacetime emergence.

Findings

Wave function peaks at Lie-group invariant configurations.

Preference for spacetime-like symmetry groups such as SO(1,n).

Asymptotic behavior of the wave function is well-understood.

Abstract

The canonical tensor model (CTM) is a tensor model proposing a classically and quantum mechanically consistent model of gravity, formulated as a first-class constraint system with structural similarities to the ADM formalism of general relativity. A recent study on the formal continuum limit of the classical CTM has shown that it produces a general relativistic system. This formal continuum limit assumes the emergence of a continuous space, but ultimately continuous spaces should be obtained as preferred configurations of the quantum CTM. In this paper we study the symmetry properties of a wave function which exactly solves the quantum constraints of the CTM for general $N$. We have found that it has strong peaks at configurations invariant under some Lie-groups, as predicted by a mechanism described in our previous paper. A surprising result was the preference of configurations invariant not only under Lie-groups with positive signatures, but also with spacetime-like signatures, i.e., $SO(1,n)$. Such symmetries could characterize the global structures of spacetimes, and our results are encouraging towards showing spacetime emergence in the CTM. To verify the asymptotic convergence of the wave function we have also analyzed the asymptotic behaviour, which for the most part seems to be well under control.