Abstract
We test the gauge/gravity duality between the N = 6 mass-deformed ABJM theory with Uk(N) × U-k(N) gauge symmetry and the 11-dimensional supergravity on LLM geometries with SO(4)=ℤk × SO(4)=ℤk 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.
Highlights
We consider a non conformal quantum field theory and test the gauge/gravity duality away from the conformal fixed point in the large N limit
We carried out the KK reduction and the holographic renormalization procedure for the mABJM theory and the LLM geometry in 11-dimensional supergravity
By calculating the vevs of chiral primary operator (CPO) with ∆ = 1 in field theory side and the corresponding asymptotic coefficients in gravity side, we found a supporting evidence for an exact gauge/gravity duality with k = 1 in the large N limit
Summary
We consider a non conformal quantum field theory and test the gauge/gravity duality away from the conformal fixed point in the large N limit. The novelty of gauge/gravity duality is that, quantities which are difficult to calculate on one side of the duality can be obtained on the other side One such case is the calculation of entanglement entropy in dimension higher than two, which is very difficult to obtain from the quantum field theory. Ryu and Takanayagi (RT) suggested a holographic method of entanglement entropy calculation, for d-dimensional conformal field theory from the AdSd+1 solution of the dual gravity [9]. We extend RT conjecture to non-conformal case and calculate the entanglement entropy for mABJM from an asymptotically AdS4 solution of 4-dimensional supergravity, which is obtained by the KK reduction of the LLM solutions
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