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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String theory hilbert space - Gas of free gravitons

I am trying to understand the arguments given in MAGOO in chapter 3.4.1(Hilbert Space of String Theory). The authors give descriptions of the Hilbert space of String Theory when we consider our theory ...
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AdS-CFT correspondance from 1D to 4D

From what I understand the AdS-CFT correspondence states that the bulk dynamics of a $n$-dimensional gravitational theory are encoded in the degrees of freedom of its dual CFT in the $(n-1)$ ...
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Boundary conditions for bulk partition function in AdS/CFT

In AdS/CFT, we are told that the bulk and boundary functions are equal: $$ \tag{1}Z_{bulk}[J]= Z_{CFT}[J], $$ where on the left hand side of the equality, $J$ is interpreted as a boundary condition at ...
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Holograhpic Dual of Replica Manifold

Following https://arxiv.org/abs/1501.05315, the conformal map $w=z^\alpha$ can be interpreted as a conical defect geometry on the bulk side. In particular, we can obtain the replica manifold by the ...
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Dimensionless bulk coordinate in AdS?

I just had a look at the AdS-C metric that can be expressed as follows $$\begin{equation} ds^2 = l_4^2 d\sigma^2 + \frac{l_4^2}{l_3^2} \cosh^2(\sigma) \left( -f(r)dt^2 = f(r)^{-1} dr^2 + r^2d\theta^2 \...
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Computing the DBI action on $S^5$

I've been looking at this paper (arXiv: 1103.4079). On page 7, from the metric of the giant gravtiton on $AdS_5 \times S^5$, $$ds^2 = -\cosh^2\rho \, dt^2 + d\rho^2 + \sinh^2 \rho \, d\tilde \Omega_3^...
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How to apply the boundary condition in the derivation of the 2-point function in MAGOO?

In the famous AdS/CFT review, in section 3.3.1 the authors give the two-point function of the operator $\mathcal{O}$ for which $\phi_0$ is a source, we write $$ \langle\mathcal{O}(p)\mathcal{O}(q)\...
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MAGOO 2-Point Correlation function derivation

I am studying the famous MAGOO review and I am trying to understand section 3.3 where we calculate the correlation functions from the AdS side. In subsection 3.3.1 the authors go through the 2-point ...
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Does AdS/CFT help solve the singularity of a black hole?

How does thinking of a black hole as encoding its information in its surface help solve what happens inside it, more specifically geodesic incompleteness. Doesn't it tell us that if we can see how ...
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Kubo formula for viscosity tensor

Viscosity tensor in terms of the retarded Green function is as follows : \begin{equation} \eta_{ijkl}=-\lim_{\omega\to 0}\frac{1}{\omega}Im G^{R}_{ij,kl}(\omega,0)~~~~(1), \end{equation} where $G^{R}_{...
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AdS/CFT correspondence [closed]

Can the AdS/CFT correspondence, which states that the anti-de Sitter space in $n$ dimensions is equivalent to a Conformal Field Theory in $n-1$ dimensions, for quantum gravity be seen as an analogue ...
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Semi-classical spinning strings and AdS-CFT

I'm trying to understand how the AdS/CFT correspondence is precisely formulated when on the bulk side people are working with the string theory as a sigma model on the worldsheet expanded about some ...
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Fourier transformation in AdS space

For flat spacetime $x \in \mathbb{R}^n$, we know The fourier transformation of $f(x)$ is well defined via the kernel $e^{ik x}$. i.e., \begin{align} \hat{f}(k) = \int f(x) e^{ik x} dx \end{align} what ...
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Scalar field Bulk propagator

For a massless scalar field in $AdS_{d+1}$ the bulk propagator is \begin{align*} \Box_{\vec x, z} K_B(\vec x, z;\vec x') = \delta^{d} (\vec x - \vec x') \end{align*} if the solution to $K_B$ is \begin{...
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Isn't AdS/CFT an end to String theory as a fundamental theory?

I start with the Large $N$ QCD paper by 't Hooft. When 't Hooft published his paper on Large $N$ QCD it was clear why the string theory of hadrons due to Gabriele Veneziano could make sense. But at ...
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Mellin transformation in a coordinate vector form

In QFT, we usually deal with Fourier transformation. In AdS space, there is a similar formulation called "Mellin transformation" I want to know some physical expression of Mellin ...
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How can holographic duals (eg. AdS/CFT) be used to study magnetic monopoles? [closed]

What useful things are possible to find out about magnetic monopoles through the use of dual theories? I'm thinking of characteristics such as stability (or chaoticness), expectation values, central ...
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Spin-2 operators from metric fluctuations in the AdS/CFT

This is a computational question. I am pretty sure that there is a simple explanation, and something obvious that I am missing but I cannot figure it out. I want to add that this is not meant to be a &...
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Transition amplitudes in AdS/CFT

Consider $AdS_{d+1}/ CFT_d$ duality. Suppose the bulk metric in Poincare coordinates is $$ds^2=\frac{l^2}{z^2}\left(dz^2+h_{ij}(x)dx^idx^j\right)$$ near the boundary, i.e. as $z\to 0$. Let $\sigma_1,\...
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Embedding metric (projection) on AdS and Casimir operator

Recently, I am trying to follow up the appendix of arXiv:2106.10822, Embedding space formalism on $AdS_{d+1}$. Basically, I am trying to prove equation A.8 in the above figure. Let $X$ be a ...
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Casimir conformal generator of $SO(d+1,1)$

The purpose of this post is to ask the help of derivation of equation 2.8 of https://arxiv.org/abs/2106.10822 Let $P_i$ be a point on the conformal boundary of $AdS_{d+1}$ and $Z_i$ be a polarization ...
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Current State of Research on high $T_c$ Superconductors

After looking at these two RevModPhys articles, I have found myself perplexed by the current state of high $T_c$ superconductivity research. Seeing as I cannot find any SE articles more recent than 5 ...
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Confusion about Generating Functionals in AdS/CFT

I have a question regarding an equation in the book "Gauge/Gravity Duality" by Martin Ammon and Johanna Erdmenger which however can also be found in other AdS/CFT books or lecture notes. The ...
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Boundary terms of action in AdS

Let's consider the action of a free scalar field in a space-time with metric $g_{\mu \nu}$ $$ S = -\frac{\eta}{2} \int d^{d+1}x \, \sqrt{g} \{g^{AB} \partial_{A} \phi \partial_{B} \phi + \frac{1}{2} m^...
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Coefficient of the three-point function of two identical scalars and stress tensor in CFT in $D>2$

The three-point function of two scalars with a spin-$l$ tensor is given by $$ \langle \phi_{1}(x_1) \phi_{2}(x_2) J^{\mu_1 ...\mu_l}(x_3) \rangle = f_{\phi \phi J} \frac{(Z^{\mu_1}...Z^{\mu_l}-\text{...
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How to derive the AdS spacetime metric

So I have been working on AdS/CFT for a while now and realized that I have never actually seen the derivation for the metric. In every literature, introductory or advanced, they just give you the AdS ...
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4 votes
1 answer
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Computers, quantum information and computational complexity in Kerr-AdS black hole backgrounds

A Kerr-AdS black hole is eternal, never evaporates and has a Malament-Hogarth metric. Bob, a universally programmable reversible classical computer with a fixed maximum memory who only outputs one ...
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Question regarding the asymptotic values of out-of-time order correlators (OTOCs)

Quoting A bound on chaos by Maldacena, Shenker and Stanford: Strong chaos, the butterfly effect, is a ubiquitous phenomenon in physical systems, explaining thermal behavior, among other things. In ...
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Can AdS/CFT still give bulk locality on small scales if the CFT has a nontrivial phase diagram?

The AdS/CFT correspondence is a well-supported conjecture about the equivalence between an ordinary conformal field theory (CFT) and a theory of quantum gravity in asymptotically anti-de Sitter (AdS) ...
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$AdS_2/CFT_1$ toy model of a magnetic monopole

Is it possible to create a holographic $AdS_2/CFT_1$ (2D/1D) toy model, which contains a magnetic monopole solution in the bulk? I would like to study certain behaviours on the boundary of a toy model ...
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2 votes
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Resources to start research on the SYK model, with AdS/CFT in mind

What are the main resources to learn the SYK model, focusing more on the AdS/CFT side rather than pure condensed matter theory, assuming a comfortable background in QFT, GR, and a bit of bosonic ...
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Understanding scalar bulk field in $\rm AdS$

I don't really understand the standard result in Holography and AdS/CFT that a source field can be expressed at \begin{equation} \phi_0 = \lim_{z \rightarrow 0} z^{\Delta -d} \phi(z,x) \end{equation} ...
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The linearized solution for the Vasiliev scalar field in stereographic coordinates [arXiv:1712.02401]

I am reading [arXiv:1712.02401] and struggling to reproduce equation (5.3), using iso(3) invariance. My goal is to write a similar so(1,3) invariant solution in using (3.12a). The equation I am trying ...
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Action in AdS/CFT correspondence

I am a beginner trying to study AdS/CFT correspondence. Could someone please explain, can we connect action in the gravity side to the field theory side by this correspondence? Can we write the ...
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2 votes
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Global and gauge symmetries in AdS/CFT correspondence

Based on the AdS/CFT dictionary, global symmetries of the boundary theory are related to the gauge symmetries in the bulk theory, but I could not find a relation between gauge symmetries of the ...
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Deriving the large $E$ expansion for geodesic boundary time from paper arXiv:2004.01192

In equation (14) of the paper "Holographic flows from CFT to the Kasner universe" https://arxiv.org/abs/2004.01192, they express the boundary time as $$\label{1} t(0) = -P \int^{r_{\star}}_{...
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Boundary in AdS / CFT correspondence

In AdS / CFT correspondence, the boundary with 2D conformal field theory refers to the observer who is at the center of the 3D AdS space. What will happen when the coordinates of the observer change? ...
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6 votes
1 answer
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Conformal blocks in AdS/CFT

In a CFT one can expand correlation functions in conformal blocks, for example the four-point function can be written (schematically) as: $$\langle \mathcal{O}_1 (x_1) \mathcal{O}_2 (x_2) \mathcal{O}...
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Busemann function & entanglement entropy

In seminal paper by Ryu & Takayanagi it was proposed and shown that entanglement entropy for CFT$_2$ can be computed with help of AdS$_3$ consideration or, more conretely, $$S_{EE}\propto L(\...
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2 votes
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Non-factorization of partition functions in AdS/CFT

I have seen this comment a lot in recent papers. This has to do with the AdS/CFT correspondence and Euclidean asymptotically AdS wormholes. So when we calculate the partition function of two $D-1$ ...
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What is the difference between AdS and BTZ conditions in (2+1)-D gravity?

On the BCFT, at lower Temperatures, the AdS condition is favored while at higher ones, BTZ conditions are. But, I do not understand how the conditions for either one change the gravitational theory. ...
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How AdS/CFT solves the non-renormalizability of gravity?

According to AdS/CFT, all gravity calculation in AdS can be mapped to CFT calculations on the boundary. Then what are the loop divergences in AdS gravity be mapped to the CFT side? Or put it ...
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Why can't we define mathematical observables in asymptotic $dS$ or flat space for gravitational theories?

In higher spin currents, the boundary CFT is dual to an asymptotic $AdS$. I have heard that $dS$ is not quantizable. But I don't understand why we want it to be in the first place. Isn't Chern-Simons ...
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Is a Wilson line evaluated in zero cosmological constant equal to correlation functions in 2D CFT's?

The path Integral defined by the Wilson lines over some connection $A\subset Hol$ for correlation functions dominated by the vacuum block is $e^{2iL_0}$ evacuated at <0|$e^{2iL_0}$|0>. Does this ...
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What does it mean for correlation functions to be dominated by the vacuum block for a 2D CFT?

In a 2D CFT, correlation functions dominated by the vacuum block have no conical defects. You can calculate the OPE and determine the correlation function using the D-S equations and cancel out UV ...
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Temperature of AdS-Schwarzchild black holes ? how physics is the same for different temperatures?

The five dimensional Schwarzchild-AdS black brane's metric is given by $$ ds^2_5=-\left(\frac{r}{L}\right)^2h(r)dt^2+\frac{dr^2}{\left(\frac{r}{L}\right)^2h(r)}+\left(\frac{r}{L}\right)^2(dx^2+dy^2+dz^...
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7 votes
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String theory in ${\rm AdS}_3$ and the ${\rm SL}{(2,\mathbb{R})}$ WZW model on the worldsheet

The WZW model on the sphere $S^2$ with group $G$ and level $k$ is described by the action for a $G$-valued field $g : S^2\to G$ (see these notes by Lorenz Eberhardt): $$S[g]=\dfrac{1}{4\lambda^2}\int_{...
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Holographic dual of a star?

In AdS/CFT, we know that the AdS-Schwarzschild black hole is dual to a thermal state (or the thermofield double for the two-sided case). Suppose, instead of a black hole, we have a star in the bulk ...
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3 votes
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AdS/CFT spacetime visualization

I was inspired by comments under this answer to ask this question. In the context of AdS/CFT, one often finds an embedding diagram of the $10d$ spacetime that I don't find particularly enlightening, ...
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Derivation of e.q. ( 5.9 ) and ( 5.10 ) in a paper of Kraus et al

I want to derivate equation (5.9) and (5.10) in the paper 3D gravity in a box, https://arxiv.org/abs/2103.13398 by Kraus et al. First of all, we have a metric in $AdS_3$: $$ds^2=\frac{d\rho^2}{4\rho^2}...
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