Exact Holography of Massive M2-brane Theories and Entanglement Entropy

Abstract

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 S O(4)/Z k × S O(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 ∆ = 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.

Holographic entanglement entropy with momentum relaxation

“…Further studies with the method show us new universal properties of generic CFT e.g., [12][13][14][15][16]. Even for a particular non-conformal field theory, it turns out that Ryu and Takayanagi's proposal is still useful by considering a top-down study on the field theory and the corresponding supergravity solution [17][18][19][20][21][22][23].…”

Mass-deformed ABJM theory and LLM geometries: exact holography

“…However, we need to accumulate more analytic evidences for CPOs with ∆ (≥ 2) and k (≥ 1) to completely determine the supersymmetric vacua at arbitrary N B . We leave these issues for future study [32].…”

“…When we are interested only in the CPO with conformal dimension ∆ = 1, the linearized equations are sufficient. However, for CPOs with ∆ ≥ 2, one has to consider non-linear equations [32], where some non-trivial field redefinitions are required to relate 4-dimensional and 11-dimensional fields. See [13,[33][34][35] for non-linear results on the AdS 5 × S 5 background.…”