Sine-Gordon Theory : Entanglement entropy and holography

TL;DR

This paper compares perturbative entanglement entropy calculations in the 1+1 dimensional sine-Gordon model with holographic results from AdS/CFT correspondence, showing agreement near marginality.

Contribution

It demonstrates the matching of entanglement entropy changes computed via field theory and holography for sine-Gordon perturbations.

Findings

Perturbative entanglement entropy matches holographic calculations near marginality.

The results validate the holographic approach for sine-Gordon deformations.

Agreement holds up to leading order in the coupling.

Abstract

We compute change in entanglement entropy for a single interval in $1+1$ dimensional sine-Gordon model perturbatively in the coupling. The sine-Gordon perturbation can be thought of as deformation of the free CFT by a primary operator with dimension $\Delta$. In an independent computation we calculate holographic entanglement entropy for that interval from three dimensional bulk AdS which has a massive scalar with its mass satisfying $m^2= \Delta(\Delta-2)$. We show that the two results match for near-marginal perturbations upto leading order in the coupling.