David Pirtskhalava (EPFL)
Superfluids and CFT data
It has been recently observed by Hellerman et al. (arXiv 1505.01537) that in certain CFTs with global U(1) symmetry, the spectrum of operators carrying a large internal charge can be studied semiclassically. The key is the operator-state correspondence thanks to which these operators are associated with a (weakly-coupled) finite density superfluid phase of the theory, quantized on a cylinder. In this talk, starting off with simple quantum-mechanical examples, I will systematize the approach, invoking the Callan-Coleman-Wess-Zumino (CCWZ) construction for non-linearly realized space-time symmetries. The latter has the advantage of being easily generalized to higher rank and non-abelian groups. I will then illustrate how to use the approach to access CFT data beyond scaling dimensions, showing that three-point functions of large charge operators satisfy universal scaling laws as their charges are varied.