Holographic Formulation of Quantum Supergravity

TL;DR

This paper develops a holographic formulation of ${\cal N}=1$ supergravity with a finite cosmological constant by recasting the theory as a constrained topological ${\rm BF}$ model based on ${\rm Osp(1|4)}$ and extending it to spacetimes with timelike boundaries. The boundary dynamics are shown to be governed by a supersymmetric ${\rm Osp(1|2)\oplus Osp(1|2)}$ Chern-Simons theory on the boundary, with a boundary Hilbert space built from punctured-sphere conformal blocks that realize a finite-dimensional, Bekenstein-bounded spectrum via a boundary area operator. Quantization proceeds through supersymmetric spin networks and (q-deformed) boundary Chern-Simons states, yielding a discrete area spectrum and a physically finite boundary state space whose dimension scales as $\exp(cA/(G\hbar))$. The results generalize holographic ideas from quantum GR to ${\cal N}=1$ supergravity, offering groundwork for AdS/CFT-type dualities and horizon physics in a background-independent, non-perturbative framework.

Abstract

We show that ${\cal N}=1$ supergravity with a cosmological constant can be expressed as constrained topological field theory based on the supergroup $Osp(1|4)$. The theory is then extended to include timelike boundaries with finite spatial area. Consistent boundary conditions are found which induce a boundary theory based on a supersymmetric Chern-Simons theory. The boundary state space is constructed from states of the boundary supersymmetric Chern-Simons theory on the punctured two sphere and naturally satisfies the Bekenstein bound, where area is measured by the area operator of quantum supergravity.