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We identify all symmetry superalgebras $\mathfrak{g}$ of near horizongeometries of black holes with a Killing horizon, assuming the solution issmooth and that the spatial cross section of the event horizon is compactwithout boundary. This includes all warped AdS$_2$ backgrounds with the mostgeneral allowed fluxes in 10- and 11-dimensional supergravities. If the indexof a particular Dirac operator vanishes, we find that the even symmetrysubalgebra decomposes as $\mathfrak{g}_0=\mathfrak{sl}(2,\mathbb{R})\oplus\mathfrak{t}_0$, where $\mathfrak{t}_0/\mathfrak{c}$ is the Lie algebra of agroup that acts transitively and effectively on spheres, and $\mathfrak{c}$ isthe center of $\mathfrak{g}$. If the Dirac operator index does not vanish, thenthe symmetry superalgebra is nilpotent with one even generator. We alsodemonstrate that there are no near horizon geometries, and also therefore nowarped AdS$_2$ backgrounds, in 10- and 11-dimensions that preserve more than 16supersymmetries.

All superalgebras for warped AdS$_2$ and black hole near horizon geometries