Holographic Entanglement Entropy for noncommutative Anti-de Sitter space

TL;DR

This paper introduces a noncommutative AdS metric to study quantum effects on holographic entanglement entropy, revealing how noncommutativity influences the dual CFT's properties and the effective Hilbert space dimension.

Contribution

It proposes a new noncommutative AdS metric and applies the RT algorithm to compute entanglement entropy, linking noncommutativity to changes in the dual CFT's Hilbert space.

Findings

Noncommutativity induces a gravitoelectric field in AdS.

Entanglement entropy depends on UV-IR cutoff and central charge.

Noncommutativity increases the effective Hilbert space dimension.

Abstract

A metric is proposed to explore the noncommutative form of the Anti-de Sitter space due to quantum effects. It has been proved that the non commutativity in AdS space induces a single component gravitoelectric field. The holographic Ryu-Takayanagi (RT) algorithm is then applied to compute the entanglement entropy in dual $CFT_2$. This calculation can be exploited to compute UV-IR cutoff dependent central charge of the certain noncommutative $CFT_2$. This non commutative computation of the entanglement entropy can be interpreted in the form of the surface/state correspondence. We have shown that non commutativity increases the dimension of the effective Hilbert space of the dual CFT.