Nonrelativistic conformal field theories

Abstract

We study representations of the Schrödinger 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.

26 pages, 9 figures; added a comment on the convergence of epsilon expansions

References in corpus (1)

• Short Range Scaling Laws of Quantum Gases With Contact Interactions

Cited by in corpus (7)

• Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry
• Gravity duals for non-relativistic CFTs
• Renormalization of Lorentz violating theories
• Remark on quantum mechanics with conformal Galilean symmetry
• Null Melvin Twist to Sakai-Sugimoto model
• Renormalization group analysis of resonantly interacting anyons
• The fate of conformal symmetry in the non-linear Schrödinger theory