All Questions
Tagged with ads-cft differential-geometry
22
questions
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48
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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 ...
2
votes
0
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84
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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 ...
0
votes
1
answer
259
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What does it mean for a quantum field theory to "live" on a manifold?
I was attending lectures om holography where the lecturer kept on mentioning that a QFT lives on a Cauchy slice. What does that mean?
Is it such that each point of the slice is associated to a unique ...
- 101
1
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132
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Stress- energy tensor in AdS
I´m trying to reproduce some of the equations from the paper
-- A Stress Tensor For Anti-de Sitter Gravity, by Balasubramanian and Kraus,
https://arxiv.org/abs/hep-th/9902121 -- and I keep getting one ...
- 11
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votes
1
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244
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Hyperbolic disks in AdS/CFT
The embedding of AdS space into Minkowski spacetime describes a hyperboloid as e.g. shown in the corresponding Wikipedia article on AdS space. Now my questions are:
How does this relate to the ...
2
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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 $AdS_3$:
$$ds^2=\frac{d\rho^2}{4\rho^2}...
- 21
1
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54
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Naked singularities in negative $M$ BTZ black hole geometry
Consider a BTZ black hole geometry,
\begin{equation}
ds^2=-N(r)^2dt^2+N(r)^{-2}dr^2+r^2(N^\phi dt+d\phi)^2,
\end{equation}
where $M>0$, $N(r)^2=-M+\frac{r^2}{l^2}+\frac{J}{4r^2}$ and $N^\phi(r)=-\...
- 699
1
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0
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175
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How to see that Poincaré coordinates cover only part of AdS
Consider (d+1)-dimensional AdS space of radius $\ell$ as defined by its embedding in $R^{2,d}$ :
$$
-X_0^2 + \sum_{i} X_i^2-X_{d+1}^2 = -\ell^2
$$
Now we can parametrize this surface by the Poincaré ...
- 2,296
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1
answer
462
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Metric form of $AdS_5 \times S^5$
I want to know the metric form of $AdS_5 \times S^5$.
I know there are two forms (maybe more?) Poincare patch and global patch.
And what is the difference between these two patches?
Can you state the ...
- 3,622
1
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46
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Is intrinsic curvature of an embedded surface a covariant quantity from the embedding space point of view?
Suppose I have a $(d+1)$-dimensional manifold with metric $g_{\mu\nu}$. In it I have an embedded codimension-$1$ surface, $\Gamma$, with induced metric $\gamma_{ab}$. Is Ricci scalar defined in terms ...
- 544
2
votes
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163
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How to define an Operator Product Expansion (OPE) on arbitrary Riemann surface for a CFT?
Whenever we define the OPE of a 2D CFT, we do so (at least in the literature that I have come across) on the complex plane. Similarly, the commutation relations between conformal generators $L_n$ and ...
- 129
1
vote
1
answer
679
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Isometry definition
I work in holography and I'm trying to get my feet when in non-relativistic holography. Can someone explain exactly what an "isometry" is in this context?
"the correspondence can be extended to a non-...
- 1,031
2
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0
answers
263
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Sign convention with the $AdS$ metric
One would say that $AdS_n$ satisfies the equations for the scalar curvature (R) and Ricci tensor ($R_{\mu \nu}$), $R = - \frac{n(n-1)}{L^2}$ and $R_{ab} = - \frac{n-1}{L^2}g_{ab}$.
But do the signs ...
- 4,561
3
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109
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Is it possible to build up holography in a closed manifold, i.e., in a manifold with a mathematical boundary?
I was wondering about the AdS/CFT correspondence basics. It is constructed on the idea of conformal compactification, in which a open manifold $M$ is homeomorphic related to a closed one $N$ through a ...
- 76
15
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1
answer
1k
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Asymptotic symmetry algebra
So after a lot of research, and tons and tons of papers that I've went through, I finally have some idea how to solve the equations that will give me candidates for the asymptotic symmetry group for ...
- 1,843