I thought there was the Fermionic String Action (Dirac Action) given by:$$S = \frac{{iT}}{{{c_0}}}\int_{}^{} {\sqrt { - \det {h_{\alpha \beta }}} {h_{\alpha \beta }}\psi _ - ^\mu \left( {\frac{{\partial \psi _ + ^\nu }}{{\partial \tau }} - \frac{{\partial \psi _ + ^\nu }}{{\partial \sigma }}} \right){g_{\mu \nu }}{\rm{d}}\sigma {\rm{ d}}\tau } $$