Nonrelativistic conformal field theories

TL;DR

This paper explores nonrelativistic conformal field theories by analyzing Schr"odinger algebra representations, establishing a correspondence with few-body quantum systems, and calculating energies of fermions and anyons near specific dimensions.

Contribution

It introduces a novel correspondence between primary operators in nonrelativistic CFTs and eigenstates of few-body systems, enabling analytical energy computations.

Findings

Computed fermion energies at unitarity near two and four dimensions.

Calculated energies of anyons near bosonic and fermionic limits.

Established a link between operator representations and quantum eigenstates.

Abstract

We study representations of the Schr\"odinger algebra in terms of operators in nonrelativistic conformal field theories. We prove a correspondence between primary operators and eigenstates of few-body systems in a harmonic potential. Using the correspondence we compute analytically the energy of fermions at unitarity in a harmonic potential near two and four spatial dimensions. We also compute the energy of anyons in a harmonic potential near the bosonic and fermionic limits.