Quantum gravity as a Fermi liquid

TL;DR

This paper reformulates loop quantum gravity with a cosmological constant as a Fermi-liquid theory, linking quantum geometry, wormholes, and superconductivity to address the cosmological constant problem.

Contribution

It introduces a novel Fermi-liquid framework for loop quantum gravity, connecting topological sectors, fermionic excitations, and superconductivity analogies to quantum geometry.

Findings

Chern-Simons state reduces to fermionic sector with nonlocal interactions.

Cooper pairs correspond to wormhole correlations at the de Sitter horizon.

Quantum measurements are described as excitations of a Fermi sea.

Abstract

We present a reformulation of loop quantum gravity with a cosmological constant and no matter as a Fermi-liquid theory. When the topological sector is deformed and large gauge symmetry is broken, we show that the Chern-Simons state reduces to Jacobson's degenerate sector describing 1+1 dimensional propagating fermions with nonlocal interactions. The Hamiltonian admits a dual description which we realize in the simple BCS model of superconductivity. On one hand, Cooper pairs are interpreted as wormhole correlations at the de Sitter horizon; their number yields the de Sitter entropy. On the other hand, BCS is mapped into a deformed conformal field theory reproducing the structure of quantum spin networks. When area measurements are performed, Cooper-pair insertions are activated on those edges of the spin network intersecting the given area, thus providing a description of quantum measurements in terms of excitations of a Fermi sea to superconducting levels. The cosmological constant problem is naturally addressed as a nonperturbative mass-gap effect of the true Fermi-liquid vacuum.