Particle-Hole Duality in the Lowest Landau Level
  We derive a number of exact relations between response functions of holomorphic, chiral fractional quantum Hall states and their particle-hole (PH) conjugates. These exact relations allow one to calculate the Hall conductivity, Hall viscosity, various Berry phases, and the static structure factor of PH-conjugate states from the corresponding properties of the original states. These relations establish a precise duality between chiral quantum Hall states and their PH-conjugates. The key ingredient in the proof of the relations is a generalization of Girvin's construction of PH-conjugate states to inhomogeneous magnetic field and curvature. Finally, we make several non-trivial checks of the relations, including for the Jain states and their PH-conjugates. 
Dung Xuan Nguyen, Tankut Can, Andrey Gromov
cond-mat.str-el cond-mat.mes-hall hep-th