Entanglement Edge Modes of General Noncommutative Matrix Backgrounds

Abstract: We explore the structure of entanglement edge modes on noncommutative backgrounds that arise from matrix quantum mechanics. For the fuzzy sphere, despite nonlocality and UV/IR mixing, we find area law behavior in the dominant $U(N)$ representations governing the state of the edge modes. For general noncommutative backgrounds with no global symmetry, nonlocal effects resum into a smoothly varying coupling constant that deforms the metric to a different frame. The effect is analogous to the relationship between string frame and Einstein frame in string theory.