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Physics graduate, web developer. Graphic design enthusiast :D


Oct
15
awarded  Autobiographer
Oct
15
accepted How would one experimentally prove AdS/CFT correspondence?
Jul
30
awarded  Popular Question
Jul
2
awarded  Inquisitive
Jul
2
awarded  Curious
May
5
awarded  Yearling
Apr
27
comment Have we ever seen an atom? If not, how do we know they exists?
Google STM (scanning tunneling microscope) or AFM (atomic force microscopy). And how do we know they exist... well the answer is physics...
Feb
16
comment How would one experimentally prove AdS/CFT correspondence?
Yeah, but that's only for string theory. AdS/CFT doesn't necessary need string theory in some cases (Kerr/CFT and AdS${}_3$/CFT${}_2$ where you work within the framework of asymptotic symmetries).
Feb
16
asked How would one experimentally prove AdS/CFT correspondence?
Feb
15
comment Wald General Relativity, Chap 7.1
Well, I think you need to just write it out. (7.1.19) is the metric in ($t,\phi,\rho,z$) basis, and V,X and W are defined on a page before. So you need to calculate (you can always use Mathematica and GRTensor for checking your result) the first equation, and then the second equation, and they should be the same.
Feb
7
comment Warped AdS${}_3$ and symmetry breaking
Oh, cool :D I was worried for a bit that I did something wrong :D
Feb
7
comment Warped AdS${}_3$ and symmetry breaking
Really? Because when I compare it to the near horizon extreme Kerr, with the $\Lambda(\theta)=1$ factor, I get the AdS${}_3$, where by just comparing I have $r\to\sinh\omega$ and $\varphi\to\sigma$ :S Plus I solved the Killing equation and got that for warped metric only $2\partial_\sigma$ is a Killing vector, and of all three of $SL(2,\mathbb{R})_R$ are too :S
Feb
7
comment Warped AdS${}_3$ and symmetry breaking
Thanks for the explanation :)
Feb
6
comment Warped AdS${}_3$ and symmetry breaking
So it's just putting them in Killing equation and seeing that they're no longer Killing vectors. I was thinking that there is some more profound way than that. How did they know that the warping will break the symmetry of $SL(2,\mathbb{R})$ to $U(1)$? Is it because the $\sigma$ part represents the rotation, and the wrapping factor is in front of that part of the metric which contains it?
Feb
6
asked Warped AdS${}_3$ and symmetry breaking
Feb
6
comment Changing vector basis in AdS$_3$
I should be able to change the basis with: $V^{\mu\prime}=V^\mu g_{\mu\nu} \frac{\partial x^\nu}{\partial x^{\nu\prime}} g^{\mu\prime \nu\prime}$, where primed are new coordinates ($\tau,\sigma,\phi$), and not primed are old ($x,y,u,v$), but I'm not getting a good result :\
Feb
5
comment Changing vector basis in AdS$_3$
I'll try this and see the result.
Feb
5
comment Changing vector basis in AdS$_3$
I can make $\partial_\tau=\frac{\partial x}{\partial \tau}\partial_x+\frac{\partial y}{\partial \tau}\partial_y+\frac{\partial u}{\partial \tau}\partial_u+\frac{\partial v}{\partial \tau}\partial_v$, but that doesn't help much :\
Feb
4
comment Changing vector basis in AdS$_3$
I did this on paper, for which I get: $\partial_x=\frac{\partial \tau}{\partial x}\partial_\tau+\frac{\partial \sigma}{\partial x}\partial_\sigma+\frac{\partial \omega}{\partial x}\partial_\omega$, but I kinda got stuck there :S Should I express $\tau,\sigma,\omega$ in terms of $x,y,u,v$ then? Is that even possible? :\
Feb
4
asked Changing vector basis in AdS$_3$