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Questions tagged [anti-de-sitter-spacetime]

Anti-de-Sitter (AdS) spacetime is a spacetime with a constant negative Ricci Scalar.

Anti-de-Sitter (AdS) spacetime is a spacetime with a constant negative Ricci Scalar. It has a pseudo-metric:

$${\text{d}}{s^2} = \sum\limits_{i = 1}^p {{\text{d}}x_i^2 - \sum\limits_{j = 1}^{q + 1} {{\text{d}}t_j^2} } $$

AdS Spacetime has played an important role in the correspondence.

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Why are anti-de Sitter spaces so interesting when we believe the universe is expansionary?

Perhaps this is a naive question, but in my recent (admittedly limited) readings about AdS spaces, I keep wondering why they seem to be such a hotbed for theoretical research (AdS/CFT correspondence, etc.). To my understanding, an AdS space has…
JotThisDown
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When one discusses the "boundary" of Anti-de Sitter space, what do they mean precisely?

The AdS/CFT correspondence refers to the "boundary" of AdS space but I'm a little confused about what this means. Typically, one writes the AdS metric in the form $$ds^2= \frac{L^2}{z^2}(-dt^2+d\vec x^2+dz^2)$$ and then refers to the point $z=0$…
user26866
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What's so special about AdS?

This question is coming from someone who has very little experience with M-Theory but is intrigued by the AdS/CFT correspondence and is beginning to study it. Why is the gauge/gravity duality discussed almost always in the context of anti-deSitter…
dbrane
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Mass of empty AdS$_5$

Five dimensional empty AdS$_5$ space has mass $$ E = \frac{3 \pi \ell^2}{32 G}. $$ Is the above equation correct? Let's do some dimensional analysis to confirm. In natural units, in 5 dimensions $[G] = -3$ where $[...]$ is the mass dimension. Also…
Prahar
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Is decoherence even possible in anti de Sitter space?

Is decoherence even possible in anti de Sitter space? The spatial conformal boundary acts as a repulsive wall, thus turning anti de Sitter space into an eternally closed quantum system. Superpositions remain superpositions and can never decohere. A…
theorist
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Symmetries of AdS$_3$, $SO(2,2)$ and $SL(2,\mathbb{R})\times SL(2,\mathbb{R})$

Basically, I want to know how one can see the $SL(2,\mathbb{R})\times SL(2,\mathbb{R})$ symmetry of AdS$_3$ explicitly. AdS$_3$ can be defined as hyperboloid in $\mathbb{R}^{2,2}$ as $$ X_{-1}^2+X_0^2-X_1^2-X_2^2=L^2 $$ where $L$ is the AdS radius.…
physicus
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Role of the canonical ensemble and electric charge in AdS/CFT

If we consider a charged black hole in AdS spacetime, we can either do thermodynamics in the grand canonical or the canonical ensemble. In the former, we fix the electrostatic potential $\Phi=A_t(r=\infty)$ at the boundary of the bulk such that…
ScroogeMcDuck
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AdS Space Boundary and Geodesics

I'm new to working with AdS space and am primarily concerned with black holes. I'm just playing round with the metric for AdS$_4$ $$ds^2=-f(r)dt^2+f^{-1}(r)dr^2+r^2d\zeta^2$$ for $f(r)=r^2+m $, $\space\space\space\zeta=d\theta^2+\sin^2\theta…
Phibert
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Why is BTZ black hole asymptotically $AdS_3$?

The metric for the BTZ black hole is $ds^2=-N^2dt^2+N^{-2}dr^2+r^2(N^\phi dt +d\phi)^2$ where $N^2=-M+\frac{r^2}{l^2}+\frac{J^2}{4r^2}$ and $N^\phi=-\frac{J}{2r^2}$. It is often said that BTZ black hole is asymptotically AdS$_3$, but if I take…
Michael Shaw
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Generalisations of AdS/CFT with string theory on both sides

From my previous post, I found out from the comments that there are various generalisations of AdS/CFT with different things replacing the CFT on the RHS; such as AdS/CMT, AdS/QCD, and also with the AdS replaced on the LHS, like Kerr/CFT a…
Abhimanyu Pallavi Sudhir
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Classical theories and AdS/CFT

While editing the tag wiki for ads-cft, I initially wrote something on the lines of: The AdS/CFT correspondence is a special case of the holographic principle. It states that a gravitating theory in Anti-de-Sitter (AdS) space is exactly equivalent…
Abhimanyu Pallavi Sudhir
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AdS/CFT and boundary translational invariance

I work in quantum information theory/condensed matter and have some very basic questions about AdS/CFT correspondence. For simplicity, I would like to restrict to 1+1 CFT <-> 2+1 AdS. I apologize in advance if the following questions are too basic…
quantumOrange
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Thermal AdS and the Hawking Page phase transition

I have some difficulty understanding the concept of pure thermal radiation, as described in Hawking and Page's paper on the Hawking-Page phase transition. The four-dimensional thermal AdS solution (with cosmological constant $\Lambda<0$) is given…
ScroogeMcDuck
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What is the exact relationship between on-shell amplitudes and off-shell correlators in AdS/CFT?

In this answer to a question, it is mentioned that in the AdS/CFT correspondence, on-shell amplitudes on the AdS side are related to off-shell correlators on the CFT side. Can somebody explain this to me in some more (technical) details, maybe by an…
Dilaton
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Pohlmeyer reduction of string theory for flat and AdS spaces

The definition of Pohlmeyer invariants in flat-space (as per eq-2.16 in Urs Schreiber's DDF and Pohlmeyer invariants of (super)string) is the following: $ Z^{\mu_1...\mu_N} (\mathcal{P}) = \frac{1}{N} \int\limits_0^{2\pi} d\sigma^1…
GuSuku
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