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.

We construct supergravity backgrounds for the integrable η-deformations of the AdS 2 ×S 2 ×T 6 and AdS 5 ×S 5 superstring sigma models. The η-deformation is governed by an R-matrix that solves the non-split modified classical Yang-Baxter equation on the superisometry algebra of the model. Such R-matrices include those of Drinfel'd-Jimbo type, which are constructed from a Dynkin diagram and the associated Cartan-Weyl basis. Drinfel'd-Jimbo R-matrices associated with inequivalent bases will typically lead to different deformed backgrounds. For the two models under consideration we find that the unimodularity condition, implying that there is no Weyl anomaly, is satisfied if and only if all the simple roots are fermionic. For AdS 2 × S 2 × T 6 we construct backgrounds corresponding to the three Dynkin diagrams. When all the simple roots are fermionic we find a supergravity background previously obtained by directly solving the supergravity equations. For AdS 5 × S 5 we construct a supergravity background corresponding to the Dynkin diagram with all fermionic simple roots. arXiv:1811.07841v4 [hep-th]

For supercosets with isometry group of the formĜ ×Ĝ, the η-deformation can be generalised to a two-parameter integrable deformation with independent q-deformations of the two copies. We study its kappa-symmetry and write down a formula for the Ramond-Ramond fluxes. We then focus onĜ = PSU(1, 1|2) and construct two supergravity backgrounds for the two-parameter integrable deformation of the AdS 3 × S 3 × T 4 superstring, as well as explore their limits. We also construct backgrounds that are solutions of the weaker generalised supergravity equations of motion and compare them to the literature.