  The nonlinear sigma model targeted on the coset supermanifold
$CP^{1|1}=SU(2|1)/U(1|1)$ 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 $CP^{1|1}$
indeed appears as the phase space of the strongly correlated electrons, the
canonical $CP^{1|1}$ 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 $CP^{1|1}$ NLSM. \end{abstract}
