= Gravitino-induced torsion
{title2=$T_{\mu\nu}{}^a=\frac{\kappa^2}{2}\bar\psi_\mu\gamma^a\psi_\nu$}
With canonical <Rarita-Schwinger field> normalization, one convention gives the displayed <torsion tensor>. Its <contorsion tensor> is $K_{\mu ab}=\kappa^2(\bar\psi_\mu\gamma_a\psi_b-\bar\psi_\mu\gamma_b\psi_a+\bar\psi_a\gamma_\mu\psi_b)/4$. The algebraic <spin connection> equation determines $\widetilde\omega=\omega(e)+K$; substituting it in the <action> produces four-<fermion> terms. This is an instance of <Einstein-Cartan theory> and is efficiently varied using the <1.5-order formalism>. A rescaled <gravitino> changes the displayed coefficient.
Back to article page
