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Questions tagged [ads-cft]

AdS/CFT is a special case of the holographic principle. It states that a quantum gravitating theory in Anti-de-Sitter (AdS) space is exactly equivalent to the gauge theory/Conformal Field Theory (CFT) on its boundary.

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Mixed states in field theories and their AdS duals

I am trying to self study aspects of AdS-CFT, particularly the implication of the Ryu-Takayanagi entanglement entropy formula. I have been thinking about the following question and it would be a great ...
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Holographic entanglement entropy for measures other than the Von Neumann entropy

In Ads-CFT, the Ryu-Takayanagi Entanglement entropy formula gives a nice geometric interpretation (in the bulk) for the entanglement of a region in a CFT. Also, it is much easier to calculate the ...
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633 views

AdS Space Black Holes Penrose Diagram

How do we construct the Penrose diagram for an AdS Space Schwarzschild solution? We start with the AdS Schwarzschild Metric and then do some transformation to compactify the coordinate ranges? What ...
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What is fundamental in the AdS/CFT holographic universe formulation of String theory?

I have a lot of confusion about the AdS/CFT with holography. Does it show that strings and branes are excitations of fields on the conformal boundary of the universe (CFT)? Can someone explain the AdS/...
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1answer
107 views

Why is it possible to have a consistent CFT defined just on a Poincare patch?

I have a good picture of AdS/CFT correspondence when the AdS space is given in terms of Global coordinates. In global coordinates, the AdS space is just a cylinder (up to a conformal factor) and ...
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1answer
207 views

Holography on non-AdS spacetime

I have a question regarding AdS/CFT and what it teaches about our world. AdS/CFT if often treated as our best tool to explore quantum gravity, and people have worked very hard in trying to understand ...
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Are all the asymptotic symmetries always infinite dimensional?

We know that the asymptotic symmetry of AdS$_3$ is the Virasoro symmetry, which is infinite dimensional. For flat spacetimes, the BMS group is also infinite dimensional. So are all the asymptotic ...
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1answer
176 views

Issues with de Sitter Space and Conformal Field Theory

As a de Sitter universe is more convenient for cosmology, what are the current issues with a dS/CFT type correspondence? Earlier work by Strominger, seemed promising but I haven't heard of additional ...
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117 views

Do Liouville theory have a gravity dual?

Does Liouville theory have a gravity dual? I think the answer is not. But what's wrong with Liouville theory? What features of Liouville theory are universal for other CFTs?
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AdS/CFT at small and large central charge

We know that the AdS/CFT duality is a valid correspondence for large central charge (in the semi-classical limit). If this duality is valid for small central charge (in the quantum regime) is unclear. ...
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37 views

Appropriate gauge-invariant counterterms for Maxwell field in $AdS_5$

I am starting with the bulk Maxwell field in $AdS_5$, and want to calculate the on-shell action. My metric is $$ds^2 = \dfrac{dz^2 - dt^2 + \vec{dx^2}}{z^2}$$ from which I calculate the on-shell ...
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69 views

$\mathbb{R}\times\mathbb{S}^{n-1}$ for n>1, in Gravity , QFT, CFT,

Edited: I'm searching for some application of this manifold in CFT $\mathbb{R}\times\mathbb{S}^{n-1}$ for n>1. However, I need some examples of this kind of manifold in QFT, CFT, Gravity, etc. of any ...
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102 views

How is AdS / CFT a “successful realisation” of the holographic principle?

According to the Wikipedia articles of both AdS/CFT correspondence and the Holographic principle state that the former was a 'successful realisation of the latter. Does that mean that the Holographic ...
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Near Horizon Vector Field

I am studying this paper https://arxiv.org/pdf/0811.4393.pdf. I find a probem to find the near horizon form of the vector (2.17) and electromagnetic (2.18) field. I have tried to use the near horizon ...
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1answer
160 views

Supersymmetry in AdS/CFT

In the original form of Maldacena's AdS/CFT, the bulk is classical supergravity and the boundary is superconformal field theory in the Maldacena's limit. However, in many applications of AdS/CFT, for ...
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250 views

Is there non-locality in the AdS/CFT?

Many String theorists are trying to restore bulk locality in the AdS/CFT. So does that mean the CFT, the boundary, is non-local? Does matter travel faster than light on the CFT?
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168 views

Virasoro descendants in Big Yellow Book

Equation 6.137 (page 175) of the Conformal field theory book by Philippe Di Francesco, Pierre Mathieu, David Sénéchal, is $$(L_{-n-2}A)(w)=\frac{1}{n!}(\partial^nTA)(w)$$. Is this equivalent to $$(...
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1answer
458 views

Quenched systems - disorder average (SYK model)

In a system with quenched disorder one is usually looking for self-averaging quantities, i.e., quantities such that the average over the couplings produces a ``typical" configuration in the ...
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1answer
203 views

Wilson loop in AdS/CFT : string interpretation

It is well known that Wilson loop is a quite hard observable to compute. In the case in which the QFT is dual to a gravitation theory in AdS space, we can use holography to compute the Wilson loop, ...
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2answers
143 views

CFT energy scale in AdS/CFT correspondence

In the context of the AdS/CFT correspondence, the coordinate $z$ of AdS in Poincarè coordinates is often identified with an (inverse) energy scale for a CFT. I don't quite understand this ...
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97 views

The AdS in AdS/CFT correspondence is really a class of spacetimes which asymptotes to a subclass of spacetimes with the same causal structure as AdS

On page 131 of these notes, a precise formulation of the AdS/CFT correspondence is given by the GKPW dictionary $$Z_{\text{grav}}[\phi_{0}^{i};\partial M] = \langle \exp \left( - \frac{1}{\hbar} \...
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1answer
85 views

The gravitational path integral in the AdS/CFT correspondence depends on the boundary submanifold of the bulk manifold

On page 131 of these notes, a precise formulation of the AdS/CFT correspondence is given by the GKPW dictionary $$Z_{\text{grav}}[\phi_{0}^{i};\partial M] = \langle \exp \left( - \frac{1}{\hbar} \...
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1answer
60 views

Infrared and ultraviolet limits of the bulk scalar mass and CFT operator dimension in the AdS/CFT correspondence

On page 131 of these notes, a precise formulation of the AdS/CFT correspondence is given by the GKPW dictionary $$Z_{\text{grav}}[\phi_{0}^{i};\partial M] = \langle \exp \left( - \frac{1}{\hbar} \...
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0answers
289 views

Partition function of a conformal field theory in the AdS/CFT correspondence

Background: The following question is from page 131 of Tom Hartman's notes on Quantum Gravity and Black Holes. The GKPW dictionary states that $$Z_{\text{grav}}[\phi_{0}^{i};\partial M] = \langle \...
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93 views

How to interpret this image of $AdS_5\times S^5$?

In the context of AdS/CFT an image like the following (coming from this article by David Mateos) is often shown: but I'm not really sure if I interpret it correctly. As the article says, we have a ...
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1answer
81 views

Boundary conditions due to local and global diffeomorphisms

Consider the following extract from page 2 of this paper. $AdS_3$ is the $SL(2, \mathbb{R})$ group manifold and accordingly has an $SL(2, \mathbb{R})_{L} \times SL(2, \mathbb{R})_{R}$ isometry ...
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37 views

Finite mass excitations of $AdS_{3}$

Consider the following extract from page 2 of this paper. AdS3 is the $SL(2, \mathbb{R})$ group manifold and accordingly has an $SL(2, \mathbb{R})_{L} \otimes SL(2, \mathbb{R})_{R}$ isometry ...
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296 views

Understanding the Monster CFT

I try to understand what the Monster CFT and its possible connection to 3 dimensional gravity at ($c=24$) is about (see https://arxiv.org/abs/0706.3359) To my best understanding (and please correct ...
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2answers
161 views

References for AdS/CFT correspondence between dimensions 3 and 2

I would like to inquire about references for the AdS/CFT correspondence in dimensions 3 and 2, namely between $AdS^3$ (and gravity there) and its 2-dimensional boundary at infinity (and CFT there). ...
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1answer
84 views

Holographic geodesic derivation in AdS3 and BTZ

I am trying to derive equation 2.4 in the article https://arxiv.org/pdf/hep-th/0603001.pdf The AdS3 metric in global coordinates $(t,\rho,\theta)$ is given by \begin{align} ds^2=R^2(-\cosh^2\rho dt^2+...
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When to trust Holography?

AdS/CFT correspondence allows us to compute $n$-point functions of a CFT by means of solving on-shell gravitational action in anti-de Sitter space. If I understand correctly, considering classical ...
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1answer
525 views

Deriving the Poincare patch from global coordinates in AdS$_{3}$

I have been reading Thomas Hartman's lecture notes on Quantum Gravity and Black Holes. In page 97, he derives (9.4), which is the metric of AdS$_{3}$ in global coordinates: $$ds^{2} = \ell^{2}(-\...
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Identifying superalgebras with fixed points under Cartan involution

I am making my way through the "Foundations of the $AdS_5 x S^5$ Superstring: Part I" paper by Arutyunov/Frolov 2009 (https://arxiv.org/abs/0901.4937v2) and am hoping someone can help me bridge a ...
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107 views

CFT dual to rotating black hole

It is known that the dual CFT to Schwarzschild black hole (BH) in AdS is at finite temperature and the temperature is same as the Hawking temperature of the BH. For Reissner-Nordstrom BH in AdS the ...
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Question about general direction of development of application of Tensor Networks to AdS/CFT

I am quite interested in the area of application of Tensor Networks(TNs) to AdS/CFT correspondence. I would like to clarify certain points in order to get better general picture. What is the main ...
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Global $SU(N)$ on the gravity side in AdS/CFT

For AdS/CFT to make sense, symmetries must match between the AdS side and the CFT side. Gauge symmetries are redundancies, not symmetries, therefore the CFT can have a (large) gauge symmetry, say $SU(...
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1answer
119 views

Definitive form of M/String theory and AdS/CFT role

What is the principal/more actual strategy in order to find the definitive form of M/String theory? I mean, you have a (for example) $10^{500}$ string theory possibilities landscape (given by the ...
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182 views

$\mathrm{AdS_3}$ bulk with BTZ black holes and particles in AdS/CFT

Consider three-dimensional anti-de Sitter space $\mathrm{AdS_3}$ treated as the $SL(2,\mathbb{R})$ group manifold, thus parametrised by elements $g \in SL(2,\mathbb{R})$. This space has as isometry ...
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1answer
225 views

Is metric a classical or a quantum field in General Relativity?

I am currently reading the article of A Castro about $AdS_3/CFT_2$. I have a confusion in reconciling several definitions. It appears that I've understood them imprecisely or may be wrong. These ...
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1answer
168 views

CFT with noncompact target space => no well-defined vacuum state?

In Maldacena & Nunez's paper, on page 6, when they discuss the compactification of Type-IIB on $\textbf{R}^6 \times K3$ (with D3 branes wrapped on $\textbf{R}^{1,1} \times \Sigma$ where $\Sigma$ ...
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1answer
257 views

Why don't we consider the representation theory of isometry groups of space-times in curved QFT?

In relativistic quantum field theory, physical quantities such as tensor and spinor can be considered as representations of the Poincaré group $\mathrm{ISO}(d,1)$, the isometry group of the given $(d+...
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1answer
159 views

holography dual in flat spacetime

In AdS/CFT the bulk geometry is AdS spacetime, the flat limit of AdS is taking to the radius of AdS to infinity. By taking this limit can one get the holography dual in flat spacetime from AdS/CFT, or ...
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233 views

$\mathrm{AdS}_3$ Bulk-to-bulk propagator in global coordinates

What is the expression of Bulk-to-bulk propagator in global coordinates? I mean, I know that there is the standard expression in terms of hypergemotric funciton depending on the invariant chordal ...
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130 views

Central Charge of large $N$ Gauge theory in 't Hooft limit

It is well known that large N gauge theory in t'Hooft limit has central charge ~ $N^2$ I want to convince myself in this by considering simple example of: 1 flavor(meaning that we have only one ...
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3answers
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Why is Sachdev-Ye-Kitaev (SYK) Model model important?

In the past one or two years, there are a lot of papers about the Sachdev-Ye-Kitaev Model (SYK) model, which I think is an example of $\mathrm{AdS}_2/\mathrm{CFT}_1$ correspondence. Why is this model ...
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1answer
121 views

Differences and relations between CFTs defined on the complex plane and CFTs defined on the torus?

What are the differences and relations between CFTs defined on the complex plane and CFTs defined on the torus? Are they supposed to be the same CFTs? I think they should have the same spectra of ...
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1answer
148 views

Distinction between holographic entanglement entropy and thermal entropy

Given a system $A$ and its complement $\bar{A}$, we know that the entanglement entropy is given by $$ S_A = - \text{Tr} ( \rho_A \log \rho_A ), $$ where $\rho_A$ is the reduced density matrix ...
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2answers
765 views

Why is there a Cardy formula in 2D CFT?

In 2d CFTs, we have the Cardy formula which tells us the number of states, which can be derived from the partition function by using modular invariance. What special property of 2D CFTs make it ...
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2answers
359 views

Relation between CS/WZW and AdS/CFT

One precise example of realization of the holographic principle is the CS/WZW correspondence, which relates 3d Chern-Simons theory with the 2d Wess-Zumino-Witten model. As explained for example in ...
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1answer
357 views

Applicability of Ryu-Takayanagi formula for boundary regions which do not belong to constant time slice

While reading article "Entanglement Entropy of Extremal BTZ" I saw a phrase: In the more general case where the entangling interval does not lie in a single time slice of the boundary, the Ryu–...