Backgrounds from Tensor Models: A Proposal

TL;DR

This paper proposes a novel connection between tensor models and classical Euclidean gravity by using Schur invariants, enabling the emergence of spacetime features and locality from tensor theory.

Contribution

It introduces a new approach using Schur invariants to relate tensor models to classical spacetime, addressing the gap in understanding quantum gravity.

Findings

Classical spacetime features are identified on the tensor side.

Locality emerges through Ward identities and Young diagram corners.

A connection between tensor models and Euclidean gravity is established.

Abstract

Although tensor models are serious candidates for a theory of quantum gravity, a connection with classical spacetimes have been elusive so far. This paper aims to fill this gap by proposing a neat connection between tensor theory and Euclidean gravity at the classical level. The main departure from the usual approach is the use of Schur invariants (instead of monomial invariants) as manifold partners. Classical spacetime features can be identified naturally on the tensor side in this new setup. A notion of locality is shown to emerge through Ward identities, where proximity between spacetime points translates into vicinity between Young diagram corners.