Matrix Entanglement

Abstract

In gauge/gravity duality, matrix degrees of freedom on the gauge theory side play important roles for the emergent geometry. In this paper, we discuss how the entanglement on the gravity side can be described as the entanglement between matrix degrees of freedom. Our approach, which we call 'matrix entanglement', is different from 'target-space entanglement' proposed and discussed recently by several groups. We consider several classes of quantum states to which our approach can play important roles. When applied to fuzzy sphere, matrix entanglement can be used to define the usual spatial entanglement in two-brane or five-brane world-volume theory nonperturbatively in a regularized setup. Another application is to a small black hole in AdS 5 ×S 5 that can evaporate without being attached to a heat bath, for which our approach suggests a gauge theory origin of the Page curve. The confined degrees of freedom in the partially-deconfined states play the important roles.

Finiteness of entanglement entropy in collective field theory

“…The notion of target space entanglement for multiple matrices has been formulated and explored in [39]- [42]. In terms of matrices explicitly, entanglement is discussed in [52,53]. On the other hand, a collective formalism for the BMN matrix model has been established in [54,55].…”