Chiral loop quantum supergravity and black hole entropy

Recent work has shown that local supersymmetry on a spacetime boundary in $\mathcal{N}$-extended AdS supergravity in chiral variables implies coupling to a boundary $\mathrm{O}\mathrm{S}\mathrm{p}(\mathcal{N}\mathrm{\mid }2{)}_{\mathbb{C}}$ super Chern-Simons theory. We propose a way to calculate the entropy $S$ for the boundary, in the supersymmetric version of loop quantum gravity, for the minimal case $\mathcal{N}=1$. We calculate the dimensions of the quantum state spaces of $\mathrm{U}\mathrm{O}\mathrm{S}\mathrm{p}(1\mathrm{\mid }2)$ super Chern-Simons theory with punctures, and analytically continue, for fixed quantum super area of the surface, to $\mathrm{O}\mathrm{S}\mathrm{p}(1\mathrm{\mid }2{)}_{\mathbb{C}}$. We find $S=a_H\mathrm{/}4$ for large areas and determine the subleading correction.