Mutual-Chern-Simons effective theory of doped antiferromagnets
  A mutual-Chern-Simons Lagrangian is derived as a minimal field theory description of the phase-string model for doped antiferromagnets. Such an effective Lagrangian is shown to retain the full symmetries of parity, time-reversal, and global SU(2) spin rotation, in contrast to conventional Chern-Simons theories where first two symmetries are usually broken. Two ordered phases, i.e., antiferromagnetic and superconducting states, are found at low temperatures as characterized by dual Meissner effects and dual flux quantization conditions due to the mutual-Chern-Simons gauge structure. A dual confinement in charge/spin degrees of freedom occurs such that no true spin-charge separation is present in these ordered phases, but the spin-charge separation/deconfinement serves as a driving force in the unconventional phase transitions of these ordered states to disordered states. 
Su-Peng Kou, Xiao-Liang Qi, and Zheng-Yu Weng