Quantum gravity as a Fermi liquid

Details Quantum gravity as a Fermi liquid Quantum gravity as a Fermi liquid

2008-07-01

arxiv.org/abs/0807.0225v2

Found.Phys.38:1148-1184,2008

Physics

High Energy Physics

High Energy Physics - Theory

45 pages, 1 figure; v2: discussion improved, version accepted by Found. Phys

Scientific paper

10.1007/s10701-008-9257-6

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.

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