Theoretical Physics Colloquium: Entanglement and Emergent Space from Large Matrices

The locality in space of interactions between elementary particles is a key property of our universe. This locality is hardwired into quantum field theoretic descriptions of nature. However, locality and indeed space itself are likely not fundamental concepts. In holographic duality, local interactions on a dynamical spacetime emerge from "large N" matrices where no locality is manifest in the microscopic Hamiltonian. The emergence of locality from matrix theories is well-established but not well-understood. In recent years it has been appreciated that locally is closely tied up with so-called “area law” entanglement of the microscopic degrees of freedom. I will discuss a particularly robust notion of entanglement in matrix theories that is rooted in an underlying Gauss law constraint and show how simple models of matrix, or ‘fuzzy' geometry contain area law entanglement.