CP1|1 nonlinear sigma model vs strong electron correlations

The nonlinear sigma model targeted on the coset supermanifold CP1|1=SU(2|1)/U(1|1) is derived in an attempt to describe the quasiclassical low-energy effective action for the doped t−J model at the SUSY point, J=2t. In spite of the fact that the supermanifold CP1|1 indeed appears as the phase space of the strongly correlated electrons, the canonical CP1|1 nonlinear sigma model (NLSM) is unable to capture the physics of strong correlations displayed by the SUSY t−J model at any finite doping. This is due to the fact that, in this regime, the doping itself cannot be self-consistently incorporated into the CP1|1 NLSM.