Duality and modular symmetry in the quantum Hall effect from Lifshitz holography

The temperature dependence of quantum Hall conductivities is studied in the context AdS/CMT paradigm using a model with bulk theory consisting (3+1)-dimensional Einstein-Maxwell action coupled to dilaton and an axion, negative cosmological constant. We consider solution which has Lifshitz like geometry dyonic black-brane bulk. There $Sl(2,R)$ corresponding electromagnetic duality, maps between classical solutions, broken $Sl(2,Z)$ by Dirac quantisation dyons. This translates modular group on 2-dimensional transverse conductivities. infra-red then linked forms via gradient flow resulting diagrams show remarkable agreement existing experimental data both integral fractional