Holographic Entanglement Entropy of Mass-deformed ABJM Theory

TL;DR

This paper analytically studies how supersymmetry-preserving mass deformation affects entanglement entropy in ABJM theory using holography, revealing consistency with lower-dimensional c-function behavior and discussing geometric validity.

Contribution

It provides the first analytical calculation of the small mass effect on renormalized entanglement entropy in LLM geometries within the holographic ABJM framework.

Findings

REE properties align with c-function behavior in lower dimensions

Analytic small mass correction to entanglement entropy derived

Discussion on geometric validity and correlation length in LLM geometries

Abstract

We investigate the effect of supersymmetry preserving mass deformation near the UV fixed point represented by the ${\cal N}=6$ ABJM theory. In the context of the gauge/gravity duality, we analytically calculate the leading small mass effect on the renormalized entanglement entropy (REE) for the most general Lin-Lunin-Maldacena (LLM) geometries in the cases of the strip and disk shaped entangling surfaces. Our result shows that the properties of the REE in (2+1)-dimensions are consistent with those of the $c$-function in (1+1)-dimensions. We also discuss the validity of our computations in terms of the curvature behavior of the LLM geometry in the large $N$ limit and the relation between the correlation length and the mass parameter for a special LLM solution.