Conformal field theory description of mesoscopic phenomena in the fractional quantum Hall effect

We give a universal description of the mesoscopic effects occurring in fractional quantum Hall disks due to the Aharonov–Bohm flux threading the system. The analysis is based on the exact treatment of the flux within the conformal field theory framework and is relevant for all fractional quantum Hall states whose edge states CFTs are known. As an example we apply this scheme for the parafermion Hall states and extract the main characteristics of the lowand hightemperature asymptotic behavior of the persistent currents.