  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.

High Energy Physics - Theory;General Relativity and Quantum Cosmology