= Kappa symmetry projector
{title2=$P_\pm=(1\pm\Gamma_\kappa)/2$}
With $\Gamma_\kappa^2=1$, the two complementary <linear projections> select its two eigenspaces. A bosonic brane preserves a background <Killing spinor> precisely when its target-space supersymmetry variation can be compensated by <kappa symmetry>, giving $\Gamma_\kappa\epsilon=\epsilon$. This condition must hold at every worldvolume point; several branes require a common solution. The full superspace construction is described in https://arxiv.org/abs/hep-th/9803209[Superspace Geometry for Supermembrane Backgrounds].
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