Gravity from Entanglement and RG Flow in a Top-down Approach

TL;DR

This paper investigates how gravity emerges from quantum entanglement in a deformed ABJM theory by extending KK reduction and comparing entanglement entropy calculations, confirming the duality between entanglement and gravity.

Contribution

It extends KK reduction beyond linear order and establishes non-trivial KK maps, enabling detailed comparison of entanglement entropy methods in a top-down holographic setup.

Findings

Entanglement entropy calculations agree under linearized Einstein equations.

Asymptotic LLM geometry encodes emergent gravity from entanglement.

Confirms the duality between quantum entanglement and gravity in a deformed ABJM context.

Abstract

The duality between a $d$-dimensional conformal field theory with relevant deformation and a gravity theory on an asymptotically AdS$_{d+1}$ geometry, has become a suitable tool in the investigation of the emergence of gravity from quantum entanglement in field theory. Recently, we have tested the duality between the mass-deformed ABJM theory and asymptotically AdS$_4$ gravity theory, which is obtained from the KK reduction of the 11-dimensional supergravity on the LLM geometry. In this paper, we extend the KK reduction procedure beyond the linear order and establish non-trivial KK maps between 4-dimensional fields and 11-dimensional fluctuations. We rely on this gauge/gravity duality to calculate the entanglement entropy by using the Ryu-Takayanagi holographic formula and the path integral method developed by Faulkner. We show that the entanglement entropies obtained using these two methods agree when the asymptotically AdS$_4$ metric satisfies the linearized Einstein equation with nonvanishing energy-momentum tensor for two scalar fields. These scalar fields encode the information of the relevant deformation of the ABJM theory. This confirms that the asymptotic limit of LLM geometry is the emergent gravity of the quantum entanglement in the mass-deformed ABJM theory with a small mass parameter. We also comment on the issue of the relative entropy and the Fisher information in our setup.