Logarithmic corrections to $\mathcal{N}\ge 2$ black hole entropy

We revisit the computation of logarithmic corrections to black holes with $\mathcal{N}\ge 2$ supersymmetry. We employ an on-shell method that takes advantage of the symmetries in the ${\mathrm{AdS}}_2\times S^2$ near horizon geometry. For bulk modes interactions are incorporated through the spectrum of chiral primaries that we derive afresh. The spectrum of boundary states is computed explicitly by analyzing gauge variations. Elementary heat kernels in four and two dimensions then give the logarithmic corrections to the black hole entropy. Our computation represents a streamlined and simplified derivation that agrees with the results recently found by A. Sen.