Direct Experimental Test of Conformal Invariance via Grazing Scattering: A Proposal for X-ray and Neutron Experiments

TL;DR

This paper proposes a novel experimental approach using grazing scattering to directly test conformal invariance in critical phenomena, which has not been verified before.

Contribution

It introduces a method to verify conformal invariance through X-ray or neutron scattering experiments analyzing two-point correlation functions near boundaries.

Findings

Differential constraints on scattering cross-section derived from conformal Ward identities

Feasibility of experimental verification with existing techniques like binary alloys

First direct experimental test of conformal invariance in critical phenomena

Abstract

We propose a test of conformal invariance in critical phenomena based on the study of a two-point correlation function in the presence of a boundary. This two-point function can be studied using X-ray or neutron scattering in the conditions of total reflection (so-called grazing scattering). The conformal Ward identity in momentum space is here expressed as a differential constraint on the scattering cross-section, as a function of the momentum transfer and the scattering angle. Experimental verification, using e.g. binary alloys, appears well within the existing techniques. This would be the first direct experimental test of conformal invariance in critical phenomena, a symmetry widely assumed but never directly verified.