Duality in Quantum Hall Compressible States

It has long been known (at least since 1997) mpirically that quantum Hall plateau transitions enjoy an apparent self-dualty symmetry. The emaning of this statement is that the current-voltage (I-V) curves are non-linear and are symmetric around their liner behavior at the quantum phase transition. This behavior was first observed in dirtier samples and is now know to occur in the compressible sattes at filling fractions 1/2 and 1/4. This empirical result was interpreted by Shimshoni, Sondhi and Shahar (PRB 55, 13730 91997)) as a manifestation of a particle-vortex duality.Yet, the origin of this symmetry has been misterious and has remained unexplained until quite recently. In a very recent paper (Hart Goldman and Eduardo Fradkin, PRB 98, 165137 (2018)) Goldman and myself used the recently developed dualities of Dirac fermions (D. T. Son Phys. Rev X. 5, 031027 (2015); N. Seiberg, T. Senthil, C. Wang and E. Witten, Ann. Phys. 374, 3095 (2016)) to show that the mirror symmetry of the Jain sequences converging on 1/2n compressible states explain the observed self-duality as a property of the compressible states. Hart Goldman was the lead author of this work.