Conformal field theories (CFTs) describe many experimentally relevant quantum critical phase transitions, such as the ones in the 2+1D Ising and XY models.
These theories are strongly interacting as they don't have (quasi)particle excitations. I'll discuss dynamical properties of CFTs in 2+1D at finite temperature. As an example I'll treat correlators involving conserved currents, in particular the conductivity. At frequencies much greater than the temperature, ω >> T, the ω dependence of the conductivity can be computed from the operator product expansion (OPE) between the currents and operators which acquire a non-zero expectation at T > 0. Such results are found to be in excellent agreement with our quantum Monte Carlo studies of the O(2) Wilson-Fisher CFT. I'll use these large-ω properties to construct an effective AdS/CFT holographic representation of the CFT: this allows us to extrapolate to the challenging regime of small frequencies. I'll also prove sum rules obeyed by the conductivity in these strongly interacting systems. Extensions to other observables and universality classes will be discussed.
* WK, Sørensen, Sachdev, Nat. Phys. 10, 2014 [arXiv:1309.2941] ;  Katz, Sachdev, Sørensen, WK, Phys. Rev. B 90, 2014 [arXiv:1409.3841].