Chiral loop quantum supergravity and black hole entropy

TL;DR

This paper extends loop quantum gravity to supersymmetric settings with boundary super Chern-Simons theory, providing a method to compute black hole entropy that aligns with the Bekenstein-Hawking formula and explores quantum corrections.

Contribution

It introduces a supersymmetric approach to black hole entropy calculation within loop quantum gravity using boundary super Chern-Simons theory for the minimal =1 case.

Findings

Derived the dimension of super Chern-Simons state spaces with punctures.

Performed analytic continuation to complex super gauge groups.

Confirmed the entropy matches the Bekenstein-Hawking area law for large areas.

Abstract

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 $\mathrm{OSp}(\mathcal{N}|2)_{\mathbb{C}}$ 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 $\mathrm{UOSp}(1|2)$ super Chern-Simons theory with punctures, and analytically continue, for fixed quantum super area of the surface, to $\mathrm{OSp}(1|2)_{\mathbb{C}}$. We find $S = a_H/4$ for large areas and determine the subleading correction.