Searching for the dual of the Maxwell-Chern-Simons model minimally   coupled to dynamical U(1) charged matter
  The possibility of dual equivalence between the self-dual and the Maxwell-Chern-Simons (MCS) models when the latter is coupled to dynamical, U(1) fermionic charged matter is examined. The proper coupling in the self-dual model is then disclosed using the iterative gauge embedding approach. We found that the self-dual potential needs to couple directly to the Chern-Kernel of the source in order to establish this equivalence besides the need for a self-interaction term to render the matter sector unchanged. 
M. S. Guimar\~aes, T. Mariz, R. Menezes and C. Wotzasek