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Emergent Area Laws from Entangled Matrices

Speaker(s) / Presenter(s):
Alexander Frenkel (Cambridge/Stanford)

Arguments such as those due to Susskind and Uglum show that open strings ending on an entangling surface are crucial to understanding the nature of black hole microstates in string theory and the degrees of freedom being partitioned by Ryu-Takayanagi surfaces in holography. We seek an understanding of these edge modes from the perspective of the boundary theory. 
In this talk, we will focus on a particular Matrix Quantum Mechanics model known as mini-BMN that describes an emergent noncommutative Yang-Mills theory on a fuzzy sphere. In mini-BMN and similar models, an analogous problem involves correctly treating the off-diagonal matrix elements that connect eigenvalues on either side of the entanglement cut. We show that these operators, which may be thought of as open strings stretching between D0-branes on either side of the cut, carry representations under the theory's SU(N) symmetry which store information about the size of the entangling surface in the emergent geometry.

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