Sine-Gordon Theory : Entanglement entropy and holography

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.

34 pages, 7 figures; v2 : analysis generalized to finite sub-systems, computation using twist fields added as an appendix, references added, matches version to be published in Phys. Rev. D