Entanglement Entropy of ABJM Theory and Entropy of Topological Black Hole

Jun Nian; Xinyu Zhang

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Entanglement Entropy of ABJM Theory and Entropy of Topological Black Hole

Jun Nian, Xinyu Zhang

High Energy Physics - Theory · Submitted 4 May 2017

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim It provides an explicit example of the identification of the entanglement entropy of the boundary conformal field theory with the bulk black hole entropy beyond the leading order given by the classical Bekenstein-Hawking formula, which consequently tests the AdS/CFT correspondence at the subleading order.

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What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.79 · human participants 0.01 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.15 · compares with prior results 0.98 · mentions code or data availability 0.02.

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In this paper we discuss the supersymmetric localization of the 4D $\mathcal{N}=2$ off-shell gauged supergravity in the background of the $\textrm{AdS}_4$ neutral topological black hole, which is the gravity dual of the ABJM theory defined on the boundary $\textrm{S}^1 \times \mathbb{H}^2$. We compute the large-$N$ expansion of the supergravity partition function. The result gives the black hole entropy with the logarithmic correction, which matches the previous result of the entanglement entropy of the ABJM theory up to some stringy effects. Our result is consistent with the previous on-shell one-loop computation of the logarithmic correction to black hole entropy. It provides an explicit example of the identification of the entanglement entropy of the boundary conformal field theory with the bulk black hole entropy beyond the leading order given by the classical Bekenstein-Hawking formula, which consequently tests the AdS/CFT correspondence at the subleading order.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	In this paper we discuss the supersymmetric localization of the 4D $\mathcal{N}=2$ off-shell gauged supergravity in the background of the $\textrm{AdS}_4$ neutral topological black hole, which is the gravity dual of the ABJM theory defined on the boundary $\textrm{S}^1 \times \mathbb{H}^2$.	contribution 0.72	0.45	0.05	asserted 0.99
s1	We compute the large-$N$ expansion of the supergravity partition function.	method 0.62	0.96	0.04	asserted 1.00
s2	The result gives the black hole entropy with the logarithmic correction, which matches the previous result of the entanglement entropy of the ABJM theory up to some stringy effects.	result 0.99	0.88	0.50	asserted 0.97
s3	Our result is consistent with the previous on-shell one-loop computation of the logarithmic correction to black hole entropy.	result 0.71	0.43	0.09	hedged possibility 0.85
s4	It provides an explicit example of the identification of the entanglement entropy of the boundary conformal field theory with the bulk black hole entropy beyond the leading order given by the classical Bekenstein-Hawking formula, which consequently tests the AdS/CFT correspondence at the subleading order.	interpretation 1.00	0.73	0.79	asserted 0.98

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.92.

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In this paper we discuss the supersymmetric localization of the 4D $\mathcal{N}=2$ off-shell gauged supergravity in the background of the $\textrm{AdS}_4$ neutral topological black hole, which is the gravity dual of the ABJM theory defined on the boundary $\textrm{S}^1 \times \mathbb{H}^2$. We compute the large-$N$ expansion of the supergravity partition function. The result gives the black hole entropy with the logarithmic correction, which matches the previous result of the entanglement entropy of the ABJM theory up to some stringy effects. Our result is consistent with the previous on-shell one-loop computation of the logarithmic correction to black hole entropy. It provides an explicit example of the identification of the entanglement entropy of the boundary conformal field theory with the bulk black hole entropy beyond the leading order given by the classical Bekenstein-Hawking formula, which consequently tests the AdS/CFT correspondence at the subleading order.

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Cited by 8 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Black holes in 4d $\mathcal{N}=4$ Super-Yang-Mills
hep-th 2018-12 accept novelty 7.0 of 10

The large N superconformal index of 4d N=4 SU(N) SYM contains an exponentially large contribution whose Legendre transform reproduces the Bekenstein-Hawking entropy of rotating BPS black holes in AdS5.
Moduli-dependent one-loop entropy of hyperbolic BPS black hole in AdS$_4$
hep-th 2026-02 conditional novelty 6.0 of 10

The one-loop logarithmic entropy correction for a hyperbolic BPS black hole in AdS4 depends on the unfixed horizon scalar modulus and acts as a quantum potential that lifts the classical flat direction.
6D attractors and black hole microstates
hep-th 2018-09 conditional novelty 6.0 of 10

A family of six-dimensional AdS2 x M4 black hole horizons has an entropy that matches the large-N topologically twisted index of the dual five-dimensional USp(2N) gauge theory, extending microstate counting to six dimensions.
Topologically twisted indices in five dimensions and holography
hep-th 2018-08 conditional novelty 6.0 of 10

A contour-integral gluing formula for the 5D topologically twisted index on M4 x S1, with large-N limits reproducing AdS7 holography and predicting AdS6 black hole entropy.
Toward Microstate Counting Beyond Large N in Localization and the Dual One-loop Quantum Supergravity
hep-th 2017-07 conditional novelty 6.0 of 10

The topologically twisted index of ABJM theory carries a -1/2 log N correction, while the near-horizon one-loop supergravity computation gives -2 log N, a discrepancy the authors report but do not resolve.

Show 3 more citing papers

Universal Entropy and Hawking Radiation of Near-Extremal AdS$_4$ Black Holes
hep-th 2020-09 conditional novelty 5.0 of 10

Near-extremal AdS4 electrically charged rotating black hole entropy is shown to equal S* plus (C/TH)_* times TH, with the same expression obtained from gravity, near-horizon Kerr/CFT, and boundary ABJM computations.
Microscopic Entropy of Rotating Electrically Charged AdS$_4$ Black Holes from Field Theory Localization
hep-th 2019-09 conditional novelty 5.0 of 10

Localization of the ABJM theory on a complexified S^2-fibered-over-S^1 background yields, at large N and in the Cardy limit, the entropy function of rotating electrically charged BPS AdS4 black holes.
Black hole entropy in massive Type IIA
hep-th 2017-07 accept novelty 5.0 of 10

The Bekenstein-Hawking entropy of dyonic BPS black holes in AdS4 x S6 in massive Type IIA matches, at leading order in N, the large-N limit of the topologically twisted index of the dual SU(N) Chern-Simons theory.

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15 arXiv papers cite this in 15 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 7 sentences without a confident label

Uses its method or tool 1 paper

Alternatively, one could attempt a full supergravity localization following the work [ref] and the more recent effort in [ref] .

Toward Microstate Counting Beyond Large N in Localization and the Dual One-loop Quantum Supergravity · Discussion · 0.88

Compares with it 1 paper

If we identify the field theory parameters with the ones on the gravity side in the following way [ref] 1/G = 2 √(2)/3 g^2 k^1/2 N^3/2 , Q_BH = g/2 Q , J_BH = J , we can rewrite the black hole entropy [ref] and the angular momentum as [equation] which are consistent with both the thermodynamic quantities on the gravity side [ref] [ref] and the black hole entropy in the gravitational Cardy limit from the Cardy formula [ref].

Gravitational Cardy Limit and AdS Black Hole Entropy · Comparison with Results from Boundary CFT · 0.90

Cites it as background 6 papers

The first successful entropy match in AdS$_4$ has been done in [ref] (see [ref] for subsequent work and generalizations).

Black hole entropy in massive Type IIA · Introduction · 0.81
In the context of the AdS/CFT correspondence, there have been some developments in matching the gravity computation to the coefficient of $logN$ term on the field theory side [ref] .

Universal Logarithmic Behavior in Microstate Counting and the Dual One-loop Entropy of AdS$_4$ Black Holes · One-loop entropy in eleven dimensional supergravity · 0.83
[See also [ref] for related works in a similar context or other dimensions.] A gravity dual for $$-extremization was recently proposed in a series of interesting papers [ref] .

Geometry of $\mathcal{I}$-extremization and black holes microstates · Introduction · 0.93

What it cites · 92 sentences without a confident label

Builds on 3 papers

For instance, one can compute supersymmetric Rényi entropy of the boundary ABJM theory via supergravity localization on backgrounds of charged topological black holes, which generalizes the classical results of Refs. [ref] on the gravity side and can also be compared with the exact results on the field theory side discussed in Ref. [ref] .

Three-Dimensional Superconformal Field Theory on Conic Space as Hologram of Charged Topological Black Hole · Conclusion and Discussion · 0.83
For instance, one can compute supersymmetric Rényi entropy of the boundary ABJM theory via supergravity localization on backgrounds of charged topological black holes, which generalizes the classical results of Refs. [ref] on the gravity side and can also be compared with the exact results on the field theory side discussed in Ref. [ref] .

The Gravity Dual of Supersymmetric Renyi Entropy · Conclusion and Discussion · 0.83
For instance, one can compute supersymmetric Rényi entropy of the boundary ABJM theory via supergravity localization on backgrounds of charged topological black holes, which generalizes the classical results of Refs. [ref] on the gravity side and can also be compared with the exact results on the field theory side discussed in Ref. [ref] .

ABJM on ellipsoid and topological strings · Conclusion and Discussion · 0.83

Uses the method or tool of 10 papers

Instead we follow the approach applied in Ref. [ref] by requiring $δζ= 0$ for all 8 Killing spinors, which consequently leads to the solutions F_i ^α= - 2 i g/√(8 πG) (σ_3)^α _j (H·P) , 2 g (J·P) = - 1/L with $F_i ^α$ and $P_I$ given by F_i ^α= a A_i ^α(z) , t_I A_i ^α= P_I (i σ_3)^α _βA_i ^β .

Localization in Supergravity and Quantum $AdS_4/CFT_3$ Holography · Localization Action · 0.99
To resolve the conical singularity, it was proposed in Refs. [ref] to perform a conformal transformation, which maps the branched three-sphere into $S^1 ×ℍ^2$, i.e., [equation] where $τ∈[0, 2 π)$, $τ̃ = q τ∈[0, 2 q π)$, and sinh u = - cot θ .

Three-Dimensional Superconformal Field Theory on Conic Space as Hologram of Charged Topological Black Hole · Introduction · 0.83
To resolve the conical singularity, it was proposed in Refs. [ref] to perform a conformal transformation, which maps the branched three-sphere into $S^1 ×ℍ^2$, i.e., [equation] where $τ∈[0, 2 π)$, $τ̃ = q τ∈[0, 2 q π)$, and sinh u = - cot θ .

The Gravity Dual of Supersymmetric Renyi Entropy · Introduction · 0.83

Uses data or values from 2 papers

The result for the partition function of the ABJM theory from the Fermi gas approach was obtained by Mariño and Putrov, which can be written in terms of the Airy function [ref] : Z^ABJM ∝Ai [(π^2 k/2 )^1/3 (N - k/24 - 1/3 k ) ] .

ABJM theory as a Fermi gas · Results for ABJM Theory · 0.84
Together with the identification of the logarithmic terms, we deduce that in our case a_0 = -1/6 , which is twice the contribution of one vector multiplet $a_0^vec = -1/12$ [ref] .

Functional determinants, index theorems, and exact quantum black hole entropy · Black Hole Entropy and Entanglement Entropy · 0.80

Compares with 7 papers

This expression of the finite action is exactly equal to the on-shell action of the $AdS_4$ neutral topological black hole [ref] .

Three-Dimensional Superconformal Field Theory on Conic Space as Hologram of Charged Topological Black Hole · Holographic Renormalization · 0.98
This expression of the finite action is exactly equal to the on-shell action of the $AdS_4$ neutral topological black hole [ref] .

The Gravity Dual of Supersymmetric Renyi Entropy · Holographic Renormalization · 0.98
From the partition function, we can compute the entanglement entropy of the ABJM theory across a circle $S^1$ on the boundary, which matches the previous results [ref] .

Supersymmetric Renyi Entropy · Introduction · 0.92

Cites as support 2 papers

The free energy and the Killing spinor equations can also be evaluated in the bulk gravity theory, which supports the holographic interpretation [ref] .

Three-Dimensional Superconformal Field Theory on Conic Space as Hologram of Charged Topological Black Hole · Introduction · 0.98
The free energy and the Killing spinor equations can also be evaluated in the bulk gravity theory, which supports the holographic interpretation [ref] .

The Gravity Dual of Supersymmetric Renyi Entropy · Introduction · 0.98

Cites as background 22 papers

The gravity dual of the supersymmetric Rényi entropies of 3D superconformal field theories (including the ABJM theory) has been constructed in Refs. [ref] .

The Gravity Dual of Supersymmetric Renyi Entropy · Gravity Dual of Supersymmetric Rényi Entropy · 0.95
The gravity dual of the supersymmetric Rényi entropies of 3D superconformal field theories (including the ABJM theory) has been constructed in Refs. [ref] .

Three-Dimensional Superconformal Field Theory on Conic Space as Hologram of Charged Topological Black Hole · Gravity Dual of Supersymmetric Rényi Entropy · 0.95
The gravity dual of the ABJM theory is the 11-dimensional M-theory on $AdS_4×S^7 / ℤ_k$ [ref] .

N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals · Introduction · 0.98

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