= Spin connection
{title2=$\omega_{\mu AB}$}
{wiki}
In an <orthonormal frame>, the spin connection is the Lorentz connection acting on spinors. With $\gamma^{AB}=\tfrac12[\gamma^A,\gamma^B]$, its <covariant derivative> is $\nabla_\mu\psi=\partial_\mu\psi+\tfrac14\omega_{\mu AB}\gamma^{AB}\psi$. The metric connection determines $\omega$ when torsion conditions are specified. A <zweibein> gives its two-dimensional form; omitting it on a curved worldsheet generally destroys covariance.
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