All Questions
17
questions
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15
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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 ...
- 785
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94
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In AdS/CFT, do we have Weyl-invariance or only conformal invariance?
The asymptotic symmetry group of $AdS_{d+1}$ is $SO(d,2)$, which just so happens to be the conformal group of $d$-dimensional Minkowski spacetime. Therefore the boundary dual, if it exists, has ...
- 1,455
4
votes
1
answer
350
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What is the symmetry group of asymptotically AdS spacetime?
The isometry group of global $AdS_{d+1}$ is well-known to be $SO(d,2)$. I have a suspicion that when the spacetime is asymptotically AdS, with dynamical gravity in the bulk, the symmetry group gets ...
- 1,455
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1
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184
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How is the Virasoro symmetry realised on $AdS_3$?
In the context of the Holographic correspondence, $AdS_{n}/CFT_{n-1}$, it is often cited as a "confirmation" that the two symmetry groups of the theories correspond. Indeed, in dimensions $n&...
- 2,296
2
votes
0
answers
288
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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 ...
- 463
6
votes
1
answer
200
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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}...
- 1,723
1
vote
1
answer
240
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Isometries or Isometry direction of $AdS_5 \times S^5$
This is a consequent question with my previous question https://physics.stackexchange.com/q /610501/
I want to know the isometries (or isometry direction) of $AdS_5 \times S^5$. Usually, when we ...
- 3,622
2
votes
0
answers
62
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Lie derivative and Goldstone modes
Systems with a gravity dual might experience the spontaneous breaking of a symmetry. In such a case, the dynamics of the dual QFT is determined by the Goldstone bosons.
But, what do the Goldstones ...
- 314
2
votes
0
answers
101
views
How different Rindler wedges are placed on the AdS$_2$ spacetime via $SL(2)$ isometries?
I am currently reading the paper https://arxiv.org/abs/1606.01857. In it they state that there are different choices for placing different Rindler wedges on the AdS$_2$ Poincaré patch via $SL(2)$ ...
3
votes
0
answers
191
views
Dirac bracket and Poisson bracket, asymptotic symmetry
I am reading the paper arXiv:9906126. https://arxiv.org/abs/gr-qc/9906126 on the symmetry algebra at horizon (see also well known work done by Brown and Henneaux about the asymptotic algebra of AdS$...
- 669
3
votes
0
answers
141
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Matching AdS and CFT symmetries
The isometries of AdS in $D+1$ dimensions and the conformal symmetries in $D$ are isomorphic as Lie algebras. However, the generators on each side have a physical interpretation. In the bulk we have ...
- 1,354
1
vote
1
answer
679
views
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
7
votes
1
answer
173
views
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 ...
- 2,071
4
votes
0
answers
146
views
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(...
- 536
2
votes
0
answers
123
views
What is the global Virasoro symmetry generators in BTZ spacetime?
This is the case of AdS3, how about BTZ? The picture is from arxiv:1506.01353.
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