Exact Holography of Massive M2-brane Theories and Entanglement Entropy

¹ Department of Physics, BK21 Physics Research Division, Institute of Basic Science, Sungkyunkwan University, Suwon 440-746, South Korea
² University College, Sungkyunkwan University, Suwon 440-746, South Korea

^* e-mail: dongmin@skku.edu
^** e-mail: yoonbai@skku.edu
^*** e-mail: okab@skku.edu
^**** e-mail: ddtolla@skku.edu

Published online: 9 January 2018

Abstract

We test the gauge/gravity duality between the N = 6 mass-deformed ABJM theory with U_k(N) × U_-k(N) gauge symmetry and the 11-dimensional supergravity on LLM geometries with SO(4)=ℤ_k × SO(4)=ℤ_k isometry. Our analysis is based on the evaluation of vacuum expectation values of chiral primary operators from the supersymmetric vacua of mass-deformed ABJM theory and from the implementation of Kaluza-Klein (KK) holography to the LLM geometries. We focus on the chiral primary operator (CPO) with conformal dimension Δ = 1. The non-vanishing vacuum expectation value (vev) implies the breaking of conformal symmetry. In that case, we show that the variation of the holographic entanglement entropy (HEE) from it’s value in the CFT, is related to the non-vanishing one-point function due to the relevant deformation as well as the source field. Applying Ryu Takayanagi’s HEE conjecture to the 4-dimensional gravity solutions, which are obtained from the KK reduction of the 11-dimensional LLM solutions, we calculate the variation of the HEE. We show how the vev and the value of the source field determine the HEE.