algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)
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From Maldacena-Stanford 16:
Studies of holography have been hampered by the lack of a simple solvable model that can capture features of Einstein gravity. The simplest model, which is a single matrix quantum mechanics, does not appear to lead to black holes. $\mathcal{N} = 4$ super Yang Mills at strong ’t Hooft coupling certainly leads to black holes, and exact results are known at large N for many anomalous dimensions and some vacuum correlation functions, but at finite temperature the theory is difficult to study.
A system that reproduces some of the dynamics of black holes should be interacting, but we might hope for a model with interactions that are simple enough that it is still reasonable solvable.
Kitaev has proposed to study a quantum mechanical model of $N$ Majorana fermions interacting with random interactions (Kitaev 15). It is a simple variant of a model introduced by Sachdev and Ye (Sachdev-Ye 93), which was first discussed in relation to holography in (Sachdev 10).
From Maldacena 18:
The SYK model gives us a glimpse into the interior of an extremal black hole… That’s the feature of SYK that I find most interesting… It is a feature this model has, that I think no other model has
Let $\mathcal{J}_{ijkl}$ be random variables with expectation values $E[\mathcal{J}_{ijkl}]=0$ and $E[\mathcal{J}_{ijkl}^2]=\frac{6J^2}{N^3}$.
The Lagrangian density definign the SYK model is this:
Review includes
Subir Sachdev, The SYK model, talk at Aspen Center for Physics, 2018 (pdf)
Vladimir Rosenhaus, An introduction to the SYK model, Journal of Physics A: Mathematical and Theoretical, Volume 52, Number 32 (arrXiv:1807.03334, doi:10.1088/1751-8121/ab2ce1)
The model is due to
Subir Sachdev, Jinwu Ye, Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet, Phys. Rev. Lett. 70:3339, 1993 (arXiv:cond-mat/9212030)
Alexei Kitaev, A simple model of quantum holography, Talks at KITP, April 7, 2015 and May 27, 2015. (part I, part II)
with further discussion in
Further developments in
See also
Discussion in view of AdS-CFT duality, specifically AdS-CFT in condensed matter physics, includes:
Subir Sachdev, Holographic metals and the fractionalized Fermi liquid, Phys.Rev.Lett.105:151602, 2010 (arXiv:1006.3794)
Juan Maldacena, Toy models for black holes II, talk at PiTP 2018 From QBits to spacetime (recording)
Relation to black holes in string theory and random matrix theory:
Last revised on July 23, 2019 at 15:25:33. See the history of this page for a list of all contributions to it.