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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$_3$
Jan
25
comment Measuring background radiation
The water in the nuclear power plants has boron in it that absorb neutrons if I recall correctly ;)
Jan
13
comment Squashed 3-sphere?
Yeah, that was what I was thinking. It's not really intuitive. I would expect something that was more standard 3 sphere metric looking... But thanks nonetheless :)
Jan
13
comment Squashed 3-sphere?
Oh, so that's where all the similarity with warped AdS${}_3$ comes from. Just a warped sphere in a sense...
Jan
13
asked Squashed 3-sphere?
Jan
10
accepted Different definition of SL(2,R) algebra?
Jan
10
comment Different definition of SL(2,R) algebra?
I was just reading something about structure constants and thought that that might be the answer! So it is only difference in the given representation after all.
Jan
10
comment How do I correctly choose signs for a falling particle?
Have you tried setting up a coordinate system? That should help...
Jan
10
comment Different definition of SL(2,R) algebra?
Sorry, forgot about that, corrected it now.
Jan
10
asked Different definition of SL(2,R) algebra?
Jan
7
comment Energy dispersion in graphene
See this: en.wikipedia.org/wiki/Density_of_states It has basically all you need ;)