Alexander Altland, Boris Post, Julian Sonner, Jeremy van der Heijden, Erik Verlinde
SciPost Phys. 15, 064 (2023) ·
published 16 August 2023

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We present a quantitative and fully nonperturbative description of the ergodic phase of quantum chaos in the setting of twodimensional gravity. To this end we describe the doubly nonperturbative completion of semiclassical 2D gravity in terms of its associated universe field theory. The guiding principle of our analysis is a flavormatrix theory (fMT) description of the ergodic phase of holographic gravity, which exhibits $\mathrm{U}(nn)$ causal symmetry breaking and restoration. JT gravity and its 2Dgravity cousins alone do not realize an action principle with causal symmetry, however we demonstrate that their universe field theory, the KodairaSpencer (KS) theory of gravity, does. After directly deriving the fMT from braneantibrane correlators in KS theory, we show that causal symmetry breaking and restoration can be understood geometrically in terms of different (topological) Dbrane vacua. We interpret our results in terms of an openclosed string duality between holomorphic ChernSimons theory and its closedstring equivalent, the KS theory of gravity. Emphasis will be put on relating these geometric principles to the characteristic spectral correlations of the quantum ergodic phase.
SciPost Phys. 2, 016 (2017) ·
published 16 May 2017

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Recent theoretical progress indicates that spacetime and gravity emerge together from the entanglement structure of an underlying microscopic theory. These ideas are best understood in Antide Sitter space, where they rely on the area law for entanglement entropy. The extension to de Sitter space requires taking into account the entropy and temperature associated with the cosmological horizon. Using insights from string theory, black hole physics and quantum information theory we argue that the positive dark energy leads to a thermal volume law contribution to the entropy that overtakes the area law precisely at the cosmological horizon. Due to the competition between area and volume law entanglement the microscopic de Sitter states do not thermalise at subHubble scales: they exhibit memory effects in the form of an entropy displacement caused by matter. The emergent laws of gravity contain an additional 'dark' gravitational force describing the 'elastic' response due to the entropy displacement. We derive an estimate of the strength of this extra force in terms of the baryonic mass, Newton's constant and the Hubble acceleration scale $a_0$ =$cH_0$, and provide evidence for the fact that this additional 'dark gravity force' explains the observed phenomena in galaxies and clusters currently attributed to dark matter.
Prof. Verlinde: "I would like to thank the refe..."
in Submissions  report on Emergent Gravity and the Dark Universe