dingo_d
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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 ;)