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3

There is really no complication in arriving at equation (5) given equation (5). We have: $$\frac{d}{d\rho}\left[\frac{\rho^3}{\sqrt{1+\left(\frac{dy_6}{d\rho}\right)^2}}\frac{dy_6}{d\rho}\right]=0.$$ We solve this differential equation. $$\frac{\rho^3}{\sqrt{1+\left(\frac{dy_6}{d\rho}\right)^2}}\frac{dy_6}{d\rho}=\tilde{c}$$ $\tilde{c}$ being a ...

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This type of calculation can be done in Mathematica using the xTensor package (its free). There is a bit of a learning curve, but the documentation is great and they have a very active google-group. Typically you will need to write the Lagrangian explicitly as a polynomial in the Riemann Tensor. Once you do this, the VarD command (xTensor) can handle the ...

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To be clear what we're talking about (as I'm not totally sure this is what the question intended), I'll talk about the paradigmatic example of AdS/CFT, the equivalence between $\mathcal N=4$ Yang-Mills on the one hand, and IIB string on (asymptotically) $AdS_5\times S^5$ on the other (at general parameters: no t'Hooft limits etc). We are very much closer ...

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In principle yes, but there are several conceptual and technical issues that make it unclear how this could be achieved. Even though the AdS/CFT correspondence is conjectured to be exact(with much evidence hinting at this), it is hard to prove this essentially because in order to do calculations, one still has to use approximations and perturbation theory on ...

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To see why the relation has to hold, you have to acknowledge that it needs to transform the line elements you have written down into each other. One can see that this is true by taking the logarithm on both sides, which yields $$\rho=\log{x^i}-\log{z}.$$ Taking the derivative of this expression and squaring it gives $\mathrm{d}\rho^2=\mathrm{d}z^2/z^2$, ...

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Holographic renormalization for non-conformal branes, i.e. non-AdS/non-CFT systems, was systematically developed in this paper by Kanitscheider, Skenderis and Taylor. They even work it out for the example of the Witten model, which is the background of the Sakai-Sugimoto model. The key principle that permits one to extend the formalism of holographic ...

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The little group is the subgroup of the Lorentz group that leaves an arbitrary four-momentum vector invariant, i.e. for an element of the group $g$ and momentum $V$ we have $gV=V$. This group is in general different for massive and massless particles. If you now find that the little group of your holomorphic primaries corresponds to that of massive states, ...

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