Scale invariant Euclidean field theory in any dimension

TL;DR

This paper introduces a novel class of scale-invariant Euclidean quantum field theories in arbitrary dimensions, constructed via projections of scalar fields interacting with scale-invariant random metrics, including Gaussian and non-Gaussian models.

Contribution

It presents a new method to generate scale-invariant Euclidean field theories in any dimension through projections of scalar fields coupled with scale-invariant random metrics.

Findings

Constructed scale-invariant models in various dimensions.

Demonstrated projection method for non-Gaussian models.

Extended scale invariance to lower-dimensional subspaces.

Abstract

We discuss D-dimensional scalar field interacting with a scale invariant random metric which is either a Gaussian field or a square of a Gaussian field. The metric depends on d-dimensional coordinates (where d is less than D). By a projection to a lower dimensional subspace we obtain a scale invariant non-Gaussian model of Euclidean quantum field theory in D-d or d dimensions.