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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BTZ black hole as a quotient of AdS space
I am trying to understand this paper 1 and trying to reproduce some calculations and had some questions about that. In section 3.2, page 12, eq. 3.9, the authors are writing normal geodesics of an ...
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Why Is There No Oscillator Representation for Operators in Planar ${\cal N}=4$ SYM Theory?
I'm studying the planar ${\cal N}=4$ Super Yang-Mills (SYM) theory and I'm curious about the representations of its operators, specifically the Hamiltonian and the dilatation operator. In many quantum ...
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What is the dual asymptotic spacetime of a CFT on a particular flat manifold?
According to AdS/CFT correspondence, the dual theory of a boundary CFT on flat spacetime is defined on an asymptotically AdS spacetime. The nature of the bulk spacetime depends on the topology of the ...
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How to derive Feffermann-Graham expansion for AdS Vaidya geometries?
Introduction
The Feffermann-Graham expansion for an asymptotically AdS spacetime [0] looks like Poincare AdS but with the flat space replaced by a more general metric i.e.
$$ds^2=\frac{1}{z^2}(g_{\mu \...
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Conformal compactification of AdS spacetime
In this paper https://homes.psd.uchicago.edu/~ejmartin/course/JournalClub/Basic_AdS-CFT_JournalClub.pdf, page 2, the authors state "The boundary of the conformal compactified $AdS_{d+1}$ is ...
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What are the implications of supersymmetry generators satisfying a majorana condition?
hoping to resolve some confusion I have about this paper (https://arxiv.org/abs/hep-th/9904017) regarding the holographic dual of a flow from ${\cal N}=4$ SYM to an ${\cal N}=1$ SUSY theory.
Broadly ...
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Partial integration of the Gibbons-Hawking-York boundary term
In https://arxiv.org/abs/1402.6334 on page 16 in their Eq. (5.21), they go from the equation
$$S_G+S_\chi\approx\int d^2x\sqrt{-g}XR+\int dt\sqrt{-\gamma}XK$$
to the equation
$$=\int d^2x \sqrt{-g}\...
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Bulk-to-bulk propagator in 3-point function in AdS-CFT correspondence. Trouble solving a PDE
I have encountered an issue in a PDE (A Green's function actually). I am solving it in $(d+1)$-dimensions and I use Poincare coordinates in AdS spacetime, meaning I have a dimension $z$ and I also ...
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Trouble in complex integral while calculating 2-point function in AdS-CFT correspondence [closed]
Upon calculating the 2-point function of a scalar, I ran in a problem in the final calculations. For reference, I am basiccaly following the methodology of https://www.sissa.it/tpp/phdsection/...
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How do hyperbolic tessellations like {7,3} in Anti de-Sitter space relate to our intuition of 3D space (or 4D structure if you include time)?
I just ran into the AdS/CFT correspondence, as I am looking at various use-cases of hyperbolic tessellations, specifically related to the pentagrid and heptagrid as defined by Maurice Margenstern in ...
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Replica wormholes in $AdS_5 \times S^5$ holography
I have a question about replica wormholes and the CFT ensembles in AdS/CFT. To make sure that my question isn't coming from a simple misunderstanding, I'll first sketch out my current understanding on ...
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Definition of “quasi-locality” in Wilsonian RG scheme
I’m studying about the holographic RG with this paper.
In that paper they say Wilsonian action expects quasi locality, but I’m not sure what “quasi-locality" exactly means.
If quasi-locality ...
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Is there any proposed holographic/thermodynamic interpretation of gravitational time dilation?
In AdS/CFT and holography more generally, many proposals of various degrees of plausibility have been made linking apparently physical notions on the bulk side to more information-theoretic, ...
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AdS$_3$ Geodesics' Length in ambient space as done in "Aspects of Holographic Entanglement Entropy"
I have been following the mentioned paper ("Aspects of Holographic Entanglement Entropy" hep-th/0605073 by Shinsei Ryu and Tadashi Takayanagi), trying to get into AdS/CFT. In section 6.2 ...
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What are single-, double- and multi-trace operators in AdS/CFT?
Can someone explain what are single-, double- and multi-trace operators are in AdS/CFT? I am a senior undergrad and only recently started studying AdS/CFT from TASI lectures and could not make much ...
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Why does no one add Einstein-Hilbert term to CFT in AdS/CFT?
As I work through AdS/CFT exercises, it struck me that there seemed no one doing the following.
Suppose we have a holographic CFT. By some reeconstruction method, we can write CFT operators in terms ...
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How does the bulk-to-boundary propagator transform under diffeomorphisms?
In AdS/CFT, the bulk-to-bulk propagator can be obtained as the limit of the bulk-to-bulk
propagator with one point approaching the boundary. For example in the scalar case
\begin{equation}
K_{\Delta}(...
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Are there AdS/CFT duals all the way down?
Last night I was thinking about the AdS/CFT correspondence, and I thought of the following scenario:
Consider a 4D AdS universe with only a single black hole. Assuming the bulk and boundary are ...
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Energy conservation in string theory?
From what i understand string theory usually lives in a Minkowski Spacetime or AdS spacetime.
In Minkowski Spacetime conservation of energy is usually very straightforward, is this also the case in ...
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Why and how we study different limits in quantum gravity?
While I'm reading an article, I get confused by why and how we study different limits in quantum limit.
In this paper, the author introduced four limits in D0-brane quantum mechanics: the DKPS (...
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Relationship between CFT coupling constants and gravity parameters in the AdS/CFT correspondence
The AdS/CFT correspondence relates a string theory in AdS to quantum field theory. Various versions of this correspondence exist, and I want to know the map between parameters in the field theory and ...
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Why $N\to \infty$ limit implies $g_s \to 0$ in holographic QCD?
One basic difficulty in QCD is that it does not contain a small dimensionless quantity that would allow for perturbative calculation of low-energy observables.
A remarkable feature of holographic ...
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Gravity dual of the string world-sheet CFT?
The AdS/CFT correspondence conjectures a duality between a $(D+1)$ dimensional gravity theory in asymptotic AdS spacetime with a $D$ dimensional conformal field theory. Is there any sense in asking ...
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AdS compactification of Minkowski space
I am trying to understand the paper "Anti De Sitter Space And Holography" by E. Witten (cf. https://arxiv.org/abs/hep-th/9802150).
One of the first point it makes is that "Minkowski ...
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(Why) does the late radiation after page time entangle with the early radiation?
In Jerusalem lectures by Harlow Pg. 53 it is said that
At the beginning of the
evaporation process the radiation that comes out is entangled with the remaining black
hole. But eventually it must ...
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Do all small-large AdS black hole phase transitions have swallow tail like behaviour for the Free Energy v/s Temperature plot?
In the literature the swallow tail like behaviour is prominently seen for small-large AdS black hole phase transition for the Free Energy vs Temperature Plot. Recently I was trying to reproduce the ...
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Why do we expect isometries of bulk side to be equivalent to symmetries of the CFT?
One can clearly see that the AdS bulk isometries form the $SO(d,2)$ symmetry of the $d$ dimensional CFT explicitly. Why does this occur: why don't the isometries of the spacetimes match up or the ...
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Why is empty AdS identified with CFT vacuum and what do excited states correspond to?
I have a few questions regarding the AdS/CFT dictionary regarding the state-state map.
I have seen people identifying the empty AdS spacetime with a CFT vacuum.
What do they mean by "empty" ...
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Unitarity in the 't Hooft limit
Consider a quantum gauge theory with a holographic dual at infinite $N$ and 't Hooft coupling, in which the gauge theory is described by classical (super)gravity.
If I initialize the system in a pure ...
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How to derive the probability distribution of reduced density matrix eigenvalues for randomly chosen pure states in Page's theorem?
Motivation
I am trying to reproduce the proof in Page's theorem as conjectured in the seminal paper Average Entropy of a Subsystem by Don N. Page. It is crucial in various resolutions of black hole ...
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Measuring "complexity"
A recently popular idea in the quantum theory of black holes is that there is an isomorphism between the interior state's volume and the computational complexity of the CFT dual (in an AdS/CFT setting)...
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Quantum corrections in Holography
AdS/CFT stablish that there is some kind of correspondence between the ${\cal N}=4$ SYM theory and strings in $AdS_5\times S^5$ space-time. I know, for instance that 1/2 BPS operators like Tr$(\phi_1^...
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Boundary conditions and field quantization in AdS
While studying the AdS/CFT correspondence, one encounters very early the example of a scalar field in AdS. The general solution to the Klein-Gordon equation in the limit $z\rightarrow 0$ may be ...
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Confusion regarding the Susskind-Uglum conjecture
I have a very basic confusion regarding entropies in holography. In AdS/CFT, the Susskind-Uglum conjecture states that the generalized entropy of a bulk region, given by
$$S_{\text{gen}}(A) = \frac{\...
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Reparameterization invariance in gravity
It's often said that gravity/general relativity has 'reparameterization invariance.' In particular, this comes up when people talk about the duality between the Sachdev-Ye-Kitaev (SYK) model and ...
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What's physical meaning of 2-point correlation function in holographic condensed matter?
Background: In AdS/CFT, we can do calculations in AdS spacetime, and get the result in CFT. When we consider RN-AdS black hole/brane, 2-point correlation functions in CFT can be obtained, which are ...
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What are Bubbling Geometries?
I know that Wilson loops in certain higher rank representations are dual to Bubbling Geometries. Also, certain local operators are dual to this kind of solutions. But (independently from holography), ...
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Does AdS/CFT correspondence apply to entire AdS space or those covered by Poincare patch?
I am getting confused as I study the AdS/CFT correspondence, so I ask this question. CFT is given on the conformal boundary of AdS, which can be derived from Poincare coordinate patch to AdS. Would ...
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Phase shift in holographic one-point function
I have a simple question about the response of an operator one-point function to an external source $\propto e^{-i\omega t}$ in AdS/CFT.
I consider a real scalar probe of mass $m$ in $AdS_{d+1}$ which ...
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Reverse AdS/CFT correspondence?
$\text{AdS}_{n}/\text{CFT}_{n-1}$ correspondence provides a dictionary for one-to-one mapping observables in bulk gravity to boundary conformal field theories. However, does the reverse correspondence ...
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Equation of motion of scalar field [closed]
I have the metric of the five dimensional Schwarzschild AdS space with metric $$ds^2=-\frac{L^2}{z^2}(1-\frac{z^4}{z_H^4})dt^2+\frac{L^2}{z^2}\frac{1}{(1-\frac{z^4}{z_H^4})}dz^2+\frac{L^2}{z^2}(dx_1^2+...
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Schwarzschild AdS Black Hole
Why do we study the five dimensional Schwarzschild AdS Black Hole in AdS/CFT? Does it have to do with the symmetries that these theories have?
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OPE Coefficients in Holography
I am having trouble reproducing a calculation from the paper "Holography from Conformal Field Theory".
In a 2d CFT, consider an operator $\mathcal{O}$ in mean field theory (MFT) with ...
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ODE singular point
I want to study the equation of motion of a scalar field in the Schwarzschild $AdS_5$ black hole
$$\frac{\hat{\omega}^2\phi(\hat{z})}{(-1+\hat{z}^4)^2}+\frac{(3+\hat{z}^4)\phi(\hat{z})}{\hat{z}(-1+\...
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Definitions of Thermodynamics and Holography
There are many differences between the laws of thermodynamics and the laws of black hole thermodynamics (BHT):
Zeroth Law: In thermodynamics, the Zeroth Law establishes the notion of thermal ...
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Is the Ryu-Takayanagi (RT) formula calculating coarse-grained or fine-grained entropy?
I think it is computing the fine-grained entropy. However, I am confused by the case that when there is a black hole in the bulk. The Ryu-Takayanagi surface may include the horizon of the black hole ...
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Jafferis-Lewkowycz-Maldacena-Suh (JLMS) formula and tensor networks
While working with AdS/CFT, I am trying to look at the nature of the Jafferis-Lewkowycz-Maldacena-Suh (JLMS) formula in AdS/CFT, which is the statement that $S(\rho _{A}|\sigma _{A})=S_{\text{bulk}}(\...
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Lorentz transformation relations (in AdS space) between coordinates of observers derived from the generators of symmetries in the AdS space
I have a question related to the Anti de Sitter Space in General Relativity. Please help me understand it:
In Anti de Sitter (AdS) spacetime, the symmetry generator operators are associated with ...
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Question about large $N$ limit of CFT in the boundary
I read that in the limit of large $N$, the CFT on the boundary becomes classical. My question is if in such limit the physics in the bulk also becomes classical, or if we can still have a quantum ...
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Relating phase transition with symmetry-breaking according to Landau Theory
I am trying to reproduce the results from this paper where they find out the expression for the Landau functional to be
$$\psi(x,t,p)=\frac{1}{4}(\frac{1}{x}+6x+px^3-4tx^2)$$
Now we plot Landau ...
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