  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.
