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SITP IT from Qubit: Subregions and a bulk area law entanglement in the emergent geometry of matrix quantum mechanics

Alex Frenkel

Event Details:

Friday, October 15, 2021
2:00pm - 3:00pm PDT
In the 1990s, Matrix quantum mechanics (MQM) models were conjectured to be nonperturbative definitions of M theory or String theory in the large N limit [1]. These are realizations of D+1 dimensional emergent geometry from a 0+1 quantum mechanical system, with the geometry being noncommutative at finite N [2,3]. Crucially, these MQM models come with a U(N) gauge symmetry which contains both a local U(p) and area preserving diffeomorphisms of the emergent spacetime in the large N limit [4].
 
Since then, there has been much work in understanding the role of gauge symmetry in entanglement. The presence of gauge symmetry leads to a non-factorizability in the Hilbert space, and defining entanglement requires boundary degrees of freedom that have the gauge group as their target space to be introduced on the geometric subregions of interest [5]. Focusing on a simpler two matrix model with an effective Chern-Simons description in the large N limit [4,6], I will describe how these boundary degrees of freedom emerge from the matrix model and suggest the presence of nonlocal degrees of freedom in the emergent geometry. Like in Chern-Simons, these boundary degrees of freedom are crucial for recovering the area-law entanglement and a term that resembles a topological entanglement entropy.
 
Some References:
[2] Steinacker Noncommutative Geometry and Matrix Models - https://arxiv.org/abs/1109.5521
[3] Han and Hartnoll Deep Quantum Geometry of Matrices - https://arxiv.org/abs/1906.08781
[4] Susskind noncommutative chern simons - https://arxiv.org/abs/hep-th/0101029
[5] Donnelly Freidel edge states of gauge theories - https://arxiv.org/abs/1601.04744
[6] Tong, Turner quantum hall matrix model - https://arxiv.org/abs/1508.00580

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