Droplet-Edge Operators in Nonrelativistic Conformal Field Theories

Abstract

We consider the large-charge expansion of the charged ground state of a Schrodinger-invariant, nonrelativistic conformal field theory in a harmonic trap, in general dimension d. In the existing literature, the energy in the trap has been computed to next-to-leading order (NLO) at large charge Q, which comes from the classical contribution of two higher-derivative terms in the effective field theory. In this note, we explain the structure of operators localized at the edge of the droplet, where the density drops to zero. We list all operators contributing to the ground-state energy with nonnegative powers of Q in the large-Q expansion. As a test, we use dimensional regularization to reproduce the calculation of the NLO ground state energy by Kravec and Pal , and we recover the same universal coefficient for the logarithmic term as in that work. We refine the derivation by presenting a systematic operator analysis of the possible edge counterterms, showing that different choices of cutoff procedures must yield the same renormalized result up to an enumerable list of Wilson coefficients for conformally invariant local counterterms at the droplet edge. We also demonstrate the existence of a previously unnoticed edge contribution to the ground-state operator dimension of order Q^{{2\over 3} - {1\over d}} in d spatial dimensions. Finally, we show there is no bulk or edge counterterm scaling as Q^0 in two spatial dimensions, which establishes the universality of the order Q^0 term in large-Q expansion of the lowest charged operator dimension in d=2.

49 pages, LaTeX

References in corpus (9)

• General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas
• Nonrelativistic conformal field theories
• The Epsilon Expansion Meets Semiclassics
• Corrections to Nambu-Goto energy levels from the effective string action
• Feynman diagrams and the large charge expansion in $3-\epsilon$ dimensions
• A note on the large charge expansion in 4d CFT
• Charging the Conformal Window
• Transition of Large $R$-Charge Operators on a Conformal Manifold
• On the quantization of folded strings in non-critical dimensions

Cited by in corpus (5)

• Galilean Gauge Theories from Null Reductions
• Five-Dimensional Non-Lorentzian Conformal Field Theories and their Relation to Six-Dimensions
• Nonrelativistic CFTs at Large Charge: Casimir Energy and Logarithmic Enhancements
• Near-Schrödinger dynamics at large charge
• On the exponentially small corrections to $\mathcal{N}=2$ superconformal correlators at large R-charge