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.

Space-time symmetries are a crucial ingredient of any theoretical model in physics. Unlike internal symmetries, which may or may not be gauged and/or spontaneously broken, space-time symmetries do not admit any ambiguity: they are gauged by gravity, and any conceivable physical system (other than the vacuum) is bound to break at least some of them. Motivated by this observation, we study how to couple gravity with the Goldstone fields that non-linearly realize spontaneously broken space-time symmetries. This can be done in complete generality by weakly gauging the Poincaré symmetry group in the context of the coset construction. To illustrate the power of this method, we consider three kinds of physical systems coupled to gravity: superfluids, relativistic membranes embedded in a higher dimensional space, and rotating point-like objects. This last system is of particular importance as it can be used to model spinning astrophysical objects like neutron stars and black holes. Our approach provides a systematic and unambiguous parametrization of the degrees of freedom of these systems.

We study the scaling dimension ∆ φ n of the operator φ n where φ is the fundamental complex field of the U (1) model at the Wilson-Fisher fixed point in d = 4 − ε. Even for a perturbatively small fixed point coupling λ * , standard perturbation theory breaks down for sufficiently large λ * n. Treating λ * n as fixed for small λ * we show that ∆ φ n can be successfully computed through a semiclassical expansion around a non-trivial trajectory, resulting in We explicitly compute the first two orders in the expansion, ∆ −1 (λ * n) and ∆ 0 (λ * n). The result, when expanded at small λ * n, perfectly agrees with all available diagrammatic computations. The asymptotic at large λ * n reproduces instead the systematic large charge expansion, recently derived in CFT. Comparison with Monte Carlo simulations in d = 3 is compatible with the obvious limitations of taking ε = 1, but encouraging.

We calculate the scaling dimensions of operators with large global charge and spin in 2+1 dimensional conformal field theories. By the state-operator correspondence, these operators correspond to superfluids with vortices and can be systematically studied using effective field theory. As the spin increases from zero to the unitarity bound, the superfluid state corresponding to the lowest dimension operator passes through three distinct regimes: (1) a single phonon, (2) two vortices, and (3) multiple vortices. We also calculate correlation functions with two such operators and the Noether current.