Gravity from entanglement and RG flow in a top-down approach

Abstract

The duality between a d-dimensional conformal field theory with relevant deformation and a gravity theory on an asymptotically AdS d+1 geometry, has become a suitable tool in the investigation of the emergence of gravity from quantum entanglement in field theory. Recently, we have tested the duality between the mass-deformed ABJM theory and asymptotically AdS 4 gravity theory, which is obtained from the KK reduction of the 11-dimensional supergravity on the LLM geometry. In this paper, we extend the KK reduction procedure beyond the linear order and establish non-trivial KK maps between 4-dimensional fields and 11-dimensional fluctuations. We rely on this gauge/gravity duality to calculate the entanglement entropy by using the Ryu-Takayanagi holographic formula and the path integral method developed by Faulkner.We show that the entanglement entropies obtained using these two methods agree when the asymptotically AdS 4 metric satisfies the linearized Einstein equation with nonvanishing energy-momentum tensor for two scalar fields. These scalar fields encode the information of the relevant deformation of the ABJM theory. This confirms that the asymptotic limit of LLM geometry is the emergent gravity of the quantum entanglement in the mass-deformed ABJM theory with a small mass parameter. We also comment on the issue of the relative entropy and the Fisher information in our setup.

Holography of massive M2-brane theory with discrete torsion

“…, (5.68) 4 Following [11], we have also tested the case of CPO of conformal dimension ∆ = 2 and we found the holographic vev is still N exact and is given by…”

“…A detailed KK reduction procedure at non-linear order is carried out in [9][10][11]. Here, for clarity, we briefly summarize the procedure and write the equations of motion for a few 4-dimensional modes which are necessary for our purpose.…”

Aspects of massive ABJM models with inhomogeneous mass parameters

“…in the right-hand-side of (3.58) was calculated [40,41] for all possible supersymmetric vacua for given k and N in the mABJM theory and it was generalized to the mABJ theory with discrete torsions [42]. To write down the quantity K| x→x i , we briefly review the supersymmetric vacua of the mABJM theory.…”

“…For a given supersymmetric vacuum with a set of occupation numbers {N n , N n }, we have [40][41][42],…”

Exotic RG flow of entanglement entropy

“…In this circumstance, the holographic calculation [8,9] based on AdS/CFT correspondence [1,2,10,11] provides a more tractable tool because it enables us to interpret the entanglement entropy of strongly interacting systems as a geodesic of the dual classical Einstein gravity. In this work, we investigate the holographic renormalization group (RG) flow of the entanglement entropy and the property of the c-function along the RG trajectory when the boundary conformal field theory is deformed by a relevant operator [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29].…”