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

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.