Quantum scale invariance on the lattice

TL;DR

This paper introduces a non-perturbative lattice framework for quantum scale-invariant theories by replacing fixed lattice spacing with a dynamical dilaton field, enabling the study of spontaneously broken scale invariance and its relation to gravity.

Contribution

It presents a novel scheme for defining scale-invariant lattice field theories using a dynamical dilaton, advancing non-perturbative approaches to quantum scale invariance.

Findings

A method to implement scale invariance on the lattice.

Criteria for selecting phenomenologically viable theories.

Discussion on the connection between scale invariance and gravity.

Abstract

We propose a scheme leading to a non-perturbative definition of lattice field theories which are scale-invariant on the quantum level. A key idea of the construction is the replacement of the lattice spacing by a propagating dynamical field -- the dilaton. We describe how to select non-perturbatively the phenomenologically viable theories where the scale invariance is broken spontaneously. Relation to gravity is also discussed.