Holographic Formulation of Quantum Supergravity

TL;DR

This paper reformulates ${ m extbf{N}}=1$ supergravity with a cosmological constant as a constrained topological field theory based on the supergroup $Osp(1|4)$, extending it to include boundaries and constructing a boundary theory with supersymmetric Chern-Simons theory.

Contribution

It introduces a holographic formulation of quantum supergravity using a supergroup-based topological field theory and boundary conditions leading to a supersymmetric Chern-Simons boundary theory.

Findings

Boundary states satisfy the Bekenstein bound.

Boundary theory constructed from supersymmetric Chern-Simons on punctured sphere.

Consistent boundary conditions induce a supersymmetric boundary theory.

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.