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Selected Topics in the Large Quantum Number Expansion
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In this review we study quantum field theories and conformal field theories with global symmetries in the limit of large charge for some of the generators of the symmetry group. At low energy the sectors of the theory with large charge are described by a hybrid form of Goldstone's theorem, involving its relativistic and non-relativistic forms. The associated effective field theory in the infrared allows the computation of anomalous dimensions, and operator product expansion coefficients in a well defined expansion in inverse powers of the global charge. This applies even when the initial theory does not have a reliable semiclassical approximation. The large quantum number expansion complements, and may provide an alternative approach to the bootstrap and numerical treatments. We will present some general features of the symmetry breaking patterns and the low-energy effective actions, and a fairly large number of examples exhibiting the salient features of this method.
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Cited by 4 Pith papers
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Towers of Operators in CFTs and Convexity Bounds at Large Charge
In 3d CFTs with moduli spaces, the projected large-charge tower obeys the convexity bound α0≤0, while the leading slope α1 has no universal bound besides α1≥0.
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Trapping-potential dependence of the unitary Fermi gas at the BCS-BEC crossover
Trap-induced corrections to the unitary Fermi gas phonon spectrum and dynamic structure factor are computed in three EFT/WKB regimes, with low-energy corrections depending on trap shape and high-energy corrections set...
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Conformal Data for the O(3) Wilson-Fisher Conformal Field Theory from Fuzzy Sphere Realization of the Quantum Rotor Model
A fuzzy-sphere realization of the quantum rotor model yields scaling dimensions and OPE coefficients for the (2+1)D O(3) Wilson-Fisher CFT, benchmarked against bootstrap and large-S predictions.
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Resurgence Analysis of the Nambu-Jona-Lasinio model at large charge
For the 3d NJL model at large charge, the scaling dimension has a convergent small-q series and an asymptotic large-q series whose nonperturbative corrections are worldline-instanton terms e^{-α√q}.
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