= Anti-de Sitter Killing-spinor connection
{c}
{title2=$\mathcal D_\mu=\nabla_\mu+\gamma_\mu/(2a)$}
For constant sectional curvature $-1/a^2$, spin curvature is $[\nabla_\mu,\nabla_\nu]=-\gamma_{\mu\nu}/(2a^2)$. The added Clifford term in $\mathcal D$ has the opposite commutator, making $\mathcal D$ flat. On a simply connected region, parallel transport of any initial spinor is path independent and constructs solutions of $\mathcal D\epsilon=0$. Thus <Anti-de Sitter spacetime> and its universal cover admit the associated <Killing spinors> locally and, with appropriate global spin data, globally.
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