Paper
Matrix Quantum Mechanics and Entanglement Entropy: A Review
Authors
Jackson R. Fliss, Alexander Frenkel
Abstract
We review aspects of entanglement entropy in the quantum mechanics of matrices, i.e. matrix quantum mechanics (MQM), at large . In doing so we review standard models of MQM and their relation to string theory, D-brane physics, and emergent non-commutative geometries. We overview, in generality, definitions of subsystems and entanglement entropies in theories with gauge redundancy and discuss the additional structure required for definining subsystems in MQMs possessing a gauge redundancy. In connecting these subsystems to non-commutative geometry, we review several works on `target space entanglement,' and entanglement in non-commutative field theories, highlighting the conditions in which target space entanglement entropy displays an `area law' at large . We summarize several example calculations of entanglement entropy in non-commutative geometries and MQMs. We review recent work in connecting the area law entanglement of MQM to the Ryu-Takayanagi formula, highlighting the conditions in which invariance implies a minimal area formula for the entanglement entropy at large . Finally, we make comments on open questions and research directions.