Toward an Effective CFT$_2$ from $\mathcal{N}=4$ Super Yang-Mills and Aspects of Hawking Radiation

Jun Nian; Leopoldo A. Pando Zayas

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Toward an Effective CFT$_2$ from $\mathcal{N}=4$ Super Yang-Mills and Aspects of Hawking Radiation

Jun Nian, Leopoldo A. Pando Zayas

High Energy Physics - Theory · Submitted 5 Mar 2020

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The authors' main claim Using $\mathcal{N}=4$ supersymmetric Yang-Mills theory we recover important aspects of the near-extremal thermodynamics of AdS$_5$ black holes including both the outer and the inner horizons with their corresponding entropy and energy.

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arXiv ID2003.02770 (version 3)

Pith IDWL3O473Y, Pith's permanent record of this paper and its review

CitationJun Nian, Leopoldo A. Pando Zayas. "Toward an Effective CFT$_2$ from $\mathcal{N}=4$ Super Yang-Mills and Aspects of Hawking Radiation." arXiv:2003.02770 (2020). https://pith.science/paper/WL3O473Y

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Using $\mathcal{N}=4$ supersymmetric Yang-Mills theory we recover important aspects of the near-extremal thermodynamics of AdS$_5$ black holes including both the outer and the inner horizons with their corresponding entropy and energy. This $\mathcal{N}=4$ supersymmetric Yang-Mills theory approach to black hole thermodynamics leads to an effective CFT$_2$ interpretation similar to the work by Callan and Maldacena. We corroborate this effective CFT$_2$ by implementing a particular near-horizon limit that geometrizes the Virasoro algebras as asymptotic symmetries. Using the effective CFT$_2$ picture, we discuss aspects of the Hawking radiation rate for a region of the near-extremal AdS$_5$ black hole quantum evolution.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Using $\mathcal{N}=4$ supersymmetric Yang-Mills theory we recover important aspects of the near-extremal thermodynamics of AdS$_5$ black holes including both the outer and the inner horizons with their corresponding entropy and energy.	result 0.89	0.90	0.50	asserted 1.00
s1	This $\mathcal{N}=4$ supersymmetric Yang-Mills theory approach to black hole thermodynamics leads to an effective CFT$_2$ interpretation similar to the work by Callan and Maldacena.	interpretation 0.97	0.72	0.29	asserted 0.99
s2	We corroborate this effective CFT$_2$ by implementing a particular near-horizon limit that geometrizes the Virasoro algebras as asymptotic symmetries.	method 0.78	0.91	0.16	asserted 1.00
s3	Using the effective CFT$_2$ picture, we discuss aspects of the Hawking radiation rate for a region of the near-extremal AdS$_5$ black hole quantum evolution.	contribution 0.94	0.84	0.18	asserted 0.81

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Using $\mathcal{N}=4$ supersymmetric Yang-Mills theory we recover important aspects of the near-extremal thermodynamics of AdS$_5$ black holes including both the outer and the inner horizons with their corresponding entropy and energy. This $\mathcal{N}=4$ supersymmetric Yang-Mills theory approach to black hole thermodynamics leads to an effective CFT$_2$ interpretation similar to the work by Callan and Maldacena. We corroborate this effective CFT$_2$ by implementing a particular near-horizon limit that geometrizes the Virasoro algebras as asymptotic symmetries. Using the effective CFT$_2$ picture, we discuss aspects of the Hawking radiation rate for a region of the near-extremal AdS$_5$ black hole quantum evolution.

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Cited by 3 Pith papers

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

Sub-leading Structures in Superconformal Indices: Subdominant Saddles and Logarithmic Contributions
hep-th 2020-07 conditional novelty 6.0 of 10

The superconformal index of N=4 SYM and a class of N=1 quiver theories contains a universal log N correction that agrees between the saddle-point and Bethe-Ansatz approaches.
The large-$N$ limit of the 4d $\mathcal{N}=1$ superconformal index
hep-th 2020-05 conditional novelty 6.0 of 10

For a broad class of 4d N=1 quiver theories, the large-N superconformal index is dominated by saddle points whose effective action is a universal cubic function of the anomaly coefficients.
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.

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15 arXiv papers cite this in 36 sentences

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Papers citing it · 29 sentences without a confident label

Uses its method or tool 1 paper

Based on the analyses in [ref] , the quantum temperature $T_q$ can be estimated using the heat capacity of the AdS$_4$ black hole (or black brane).

Quantum Corrections to Holographic Strange Metal at Low Temperature · A sweet spot scenario for quantum corrections · 0.82

Compares with it 1 paper

In contrast to [ref] , which are intrinsically 2d models, both [ref] and our work include both higher-dimensional CFTs on the boundary and a near-horizon 2d CFT, which may be more robust.

Universal Entropy and Hawking Radiation of Near-Extremal AdS$_4$ Black Holes · Introduction · 0.99

Cites it as background 5 papers

Connections with AdS$_3$/CFT$_2$, specifically the two-dimensional Cardy formula and near horizon limits of the AdS$_5$ black holes, were explored in [ref] .

$SL(3,\mathbb{Z})$ Modularity and New Cardy Limits of the $\mathcal{N}=4$ Superconformal Index · Introduction and summary · 0.96
[An incomplete subset of relevant references in both gravity and field theory sides is [ref] [ref] [ref] [ref] [ref] [ref] [ref] [ref] , [ref] .

From multi-gravitons to Black holes: The role of complex saddles · Introduction and summary · 0.92
The analysis of AdS$_5$ spacetime with a black hole and/or compactified extra-dimensional space has been done mainly for holographic applications [ref] .

Global study of the scalar quasi-normal modes of Kerr-AdS${}_5$ black holes: Stability, thermality, and horizon area quantization · Introduction · 0.99

What it cites · 60 sentences without a confident label

Builds on 3 papers

To find the entropy excess of the near-extremal black holes compared to the BPS ones, we should relate the function $h$ in [ref] to the temperatures $T_±$, similar to the extremal near-BPS case discussed in [ref] .

AdS$_5$ Black Hole Entropy near the BPS Limit · Inner and Outer Horizons · 0.88
Our picture provides a concrete path to the understanding of the rate of Hawking radiation for near-extremal asymptotically AdS$_5$ black holes from the dual $𝒩=4$ SYM, which generalizes the previous work by Callan and Maldacena [ref] for asymptotically flat black holes and the work by Gubser, Klebanov and Peet on near-extremal black D3-branes [ref] .

D-brane Approach to Black Hole Quantum Mechanics · Introduction · 1.00
Our picture provides a concrete path to the understanding of the rate of Hawking radiation for near-extremal asymptotically AdS$_5$ black holes from the dual $𝒩=4$ SYM, which generalizes the previous work by Callan and Maldacena [ref] for asymptotically flat black holes and the work by Gubser, Klebanov and Peet on near-extremal black D3-branes [ref] .

Entropy and Temperature of Black 3-Branes · Introduction · 1.00

Uses the method or tool of 11 papers

In this subsection we discuss the extremization process for the near-BPS AdS$_5$ black holes, following closely [ref] .

AdS$_5$ Black Hole Entropy near the BPS Limit · Inner and Outer Horizons · 0.93
We follow closely [ref] .

Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS$_{\bf 5}$ black holes · Microstate Counting of BPS AdS$_5$ Black Holes · 0.94
The left central charge $c_L$ can be computed by applying the standard Kerr/CFT correspondence [ref] to the near-horizon metric [ref] in the global coordinates: 1/8 πG ∫_∂Σ k_ζ_(m) [ℒ_ζ_(n) g, g] = - i/12 c_L (m^3 + αm) δ_m+n, 0 , with the mode expansion of a diffeomorphism generating vector $ζ$ as ζ_(n) = - e^- i n ϕ ∂/∂ϕ - i n r e^- i n ϕ ∂/∂r̂ , while $k_ζ$ stands for a 2-form defined for a general perturbation $h_μν$ around the background metric $g_μν$: [equation] and $ℒ_ζ$ denotes the Lie derivative with respect to $ζ$: ℒ_ζg_μν ≡ζ^ρ∂_ρg_μν + g_ρν ∂_μζ^ρ+ g_μρ ∂_νζ^ρ .

The Kerr/CFT Correspondence · Near-Horizon Metric and Cardy Formula · 0.98

Uses data or values from 1 paper

At the outer horizon, the following relations have been obtained from the near-extremal Kerr-Newman AdS$_5$ black holes in [ref] : S_+ = S_* + (C/T )_* T_+ , E = E_* + 1/2 (C/T )_* T_+^2 , (C/T )_* = π^2 g^-1 [8 (Q / g)^3 + 1/4 N^4 (J_1 + J_2) ]/3 (Q / g)^2-1/2 N^2 (J_1 + J_2 ) + (3 Q / g + 1/2 N^2)^2 , with $Q$ and $J_i$ taking the values for the BPS black holes.

AdS$_5$ Black Hole Entropy near the BPS Limit · Near-Extremal AdS$_5$ Black Hole Thermodynamics · 0.91

Compares with 9 papers

This also agrees with the result on the gravity side [ref] .

1/16-BPS Black Holes and Giant Gravitons in the AdS_5 X S^5 Space · Microstate Counting of BPS AdS$_5$ Black Holes · 0.96
A similar expression of the first law has been seen in the previous study on the asymptotically flat black holes [ref] .

Universal properties and the first law of black hole inner mechanics · Near-Extremal AdS$_5$ Black Hole Thermodynamics · 0.91
These relations are consistent with the ones for the asymptotically flat black holes [ref] .

A String Model of Black Hole Microstates · An Effective CFT$_2$ Near Extremality · 1.00

Cites as background 26 papers

The leading expression for the superconformal index has been obtained for generic $N=1$ supersymmetric field theories exploiting a Cardy-like limit in [ref] .

Entropy function from toric geometry · Microstate Counting of BPS AdS$_5$ Black Holes · 0.83
The leading expression for the superconformal index has been obtained for generic $N=1$ supersymmetric field theories exploiting a Cardy-like limit in [ref] .

A 4d N=1 Cardy Formula · Microstate Counting of BPS AdS$_5$ Black Holes · 0.83
The leading expression for the superconformal index has been obtained for generic $N=1$ supersymmetric field theories exploiting a Cardy-like limit in [ref] .

The asymptotic growth of states of the 4d N=1 superconformal index · Microstate Counting of BPS AdS$_5$ Black Holes · 0.83

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