A new class of short distance universal amplitude ratios

TL;DR

This paper introduces a new class of universal amplitude ratios based on short distance expansions near critical points, providing a tool to analyze quantum field theories even when traditional measurements are inaccessible.

Contribution

It proposes a novel class of universal amplitude ratios involving short distance correlator terms, applicable across different dimensions and perturbation regimes.

Findings

Exact predictions in two-dimensional models

Potential for perturbative calculations in three dimensions

Useful for exploring short distance properties in quantum field theories

Abstract

We propose a new class of universal amplitude ratios which involve the first terms of the short distance expansion of the correlators of a statistical model in the vicinity of a critical point. We will describe the critical system with a conformal field theory (UV fixed point) perturbed by an appropriate relevant operator. In two dimensions the exact knowledge of the UV fixed point allows for accurate predictions of the ratios and in many nontrivial integrable perturbations they can even be evaluated exactly. In three dimensional O(N) scalar systems feasible extensions of some existing results should allow to obtain perturbative expansions for the ratios. By construction these universal ratios are a perfect tool to explore the short distance properties of the underlying quantum field theory even in regimes where the correlation length and one point functions are not accessible in experiments or simulations.