Nonrelativistic Conformal Field Theories in the Large Charge Sector

Abstract

We study Schrödinger invariant field theories (nonrelativistic conformal field theories) in the large charge (particle number) sector. We do so by constructing the effective field theory (EFT) for a Goldstone boson of the associated $U(1)$ symmetry in a harmonic potential. This EFT can be studied semi-classically in a large charge expansion. We calculate the dimensions of the lowest lying operators, as well as correlation functions of charged operators. We find universal behavior of three point function in large charge sector. We comment on potential applications to fermions at unitarity and critical anyon systems.

arXiv comment24 pages

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• Galilean Gauge Theories from Null Reductions
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• Transition of Large $R$-Charge Operators on a Conformal Manifold
• The Shadow Formalism of Galilean CFT${}_2$
• Nonrelativistic CFTs at Large Charge: Casimir Energy and Logarithmic Enhancements
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• Applied nonrelativistic conformal field theory: scattering-length and effective-range corrections to unnuclear physics
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