30,899 research outputs found

### Gravity from Entanglement and RG Flow in a Top-down Approach

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.Comment: 42 pages, no figure, minor corrections, references adde

### Abelian Gauge Invariance of the WZ-type Coupling in ABJM Theory

We construct the interaction terms between the worldvolume fields of multiple
M2-branes and 3-form gauge field of 11-dimensional supergravity, in the context
of ABJM theory. The obtained Wess-Zumino-type coupling is simultaneously
invariant under the U$_{\textrm{L}}(N)\times$U$_{\textrm{R}}(N)$ non-Abelian
gauge transformation of the ABJM theory and the Abelian gauge transformation of
the 3-form field in 11-dimensional supergravity.Comment: 16 pages, minor corrections, published versio

### Exact Holography of the Mass-deformed M2-brane Theory

We test the holographic relation between the vacuum expectation values of
gauge invariant operators in ${\cal N} = 6$ ${\rm U}_k(N)\times {\rm
U}_{-k}(N)$ mass-deformed ABJM theory and the LLM geometries with
$\mathbb{Z}_k$ orbifold in 11-dimensional supergravity. To do that, we apply
the Kaluza-Klein reduction to construct a 4-dimensional gravity theory and
implement the holographic renormalization procedure. We obtain an exact
holographic relation for the vacuum expectation values of the chiral primary
operator with conformal dimension $\Delta = 1$, which is given by $\langle
{\cal O}^{(\Delta=1)}\rangle= N^{\frac32} \, f_{(\Delta=1)}$, for large $N$ and
$k=1$. Here factor $f_{(\Delta)}$ is independent of $N$. Our results involve
infinite number of exact dual relations for all possible supersymmetric Higgs
vacua and so provide a nontrivial test of gauge/gravity duality away from the
conformal fixed point. We also extend our results to the case of $k\ne 1$ for
LLM geometries represented by rectangular-shaped Young-diagrams.Comment: 6 pages, major corrections in section 3 and 4, references added,
title change

### Mass-deformed ABJM Theory and LLM Geometries: Exact Holography

We present a detailed account and extension of our claim in arXiv:1610.01490.
We test the gauge/gravity duality between the ${\cal N} = 6$ mass-deformed ABJM
theory with U$_k(N)\times$U$_{-k}(N)$ gauge symmetry and the 11-dimensional
supergravity on LLM geometries with SO(4)/${\mathbb Z}_k$
$\times$SO(4)/${\mathbb Z}_k$ isometry, in the large $N$ limit. 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 holography to the LLM geometries. We focus
on the chiral primary operator with conformal dimension $\Delta = 1$. We show
that $\langle {\cal O}^{(\Delta=1)}\rangle= N^{\frac32} \, f_{(\Delta=1)}$ for
all supersymmetric vacuum solutions and LLM geometries with $k=1$, where the
factor $f_{(\Delta)}$ is independent of $N$. We also confirm that the vacuum
expectation value of the the energy momentum tensor is vanishing as expected by
the supersymmetry. We extend our results to the case of $k\ne 1$ for LLM
geometries represented by rectangular-shaped Young-diagrams. In analogy with
the Coulomb branch of the ${\cal N} = 4$ super Yang-Mills theory, we argue that
the discrete Higgs vacua of the mABJM theory as well as the corresponding LLM
geometries are parametrized by the vevs of the chiral primary operators.Comment: 44 pages, 1 figure, major corrections in section 3 and 5, references
added, title change

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