CFTs with broken continuous global symmetry on the moduli space require a tower of charged local operators whose scaling dimensions are asymptotically linear in the charge.
Semiclassics, Goldstone Bosons and CFT data
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abstract
Hellerman et al. (arXiv:1505.01537) have shown that in a generic CFT the spectrum of operators carrying a large U(1) charge can be analyzed semiclassically in an expansion in inverse powers of the charge. The key is the operator state correspondence by which such operators are associated with a finite density superfluid phase for the theory quantized on the cylinder. The dynamics is dominated by the corresponding Goldstone hydrodynamic mode and the derivative expansion coincides with the inverse charge expansion. We illustrate and further clarify this situation by first considering simple quantum mechanical analogues. We then systematize the approach by employing the coset construction for non-linearly realized space-time symmetries. Focussing on CFT3 we illustrate the case of higher rank and non-abelian groups and the computation of higher point functions. Three point function coefficients turn out to satisfy universal scaling laws and correlations as the charge and spin are varied.
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Numerical extraction of scaling dimensions and OPE coefficients for 32 primary operators in the O(2) Wilson-Fisher CFT via fuzzy-sphere regularization shows agreement with bootstrap predictions.
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A dissertation synthesizing universal aspects of defect dynamics in QFT through symmetry principles across defect RG flows, effective strings, and quantum gas impurities.
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Moduli Spaces in CFT: Large Charge Operators
CFTs with broken continuous global symmetry on the moduli space require a tower of charged local operators whose scaling dimensions are asymptotically linear in the charge.
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Conformal Data for the $O(2)$ Wilson-Fisher CFT in $(2+1)$-Dimensional Spacetime from Exact Diagonalization and Matrix Product States on the Fuzzy Sphere
Numerical extraction of scaling dimensions and OPE coefficients for 32 primary operators in the O(2) Wilson-Fisher CFT via fuzzy-sphere regularization shows agreement with bootstrap predictions.
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