Fefferman-Gramah expansion

[Giorgos Anastasiou]

Dear all,

I would like your help.I'm new in xTensor and I'm confused with some things. Does anyone have any

idea about how we could apply Fefferman-Graham expansion in xTensor?

Thank you in advance for your response!

[pedram karimi]

hi,

I have the same problem let me clarify the question in  detail(Fefferman-Graham expansion use in the context of AdS/CFT Renormalization holographic actually it's expansion of induced metric on conformal boundary)

1st: Is there any possibility to add the logarithmic term to perturbation series in xPert?

I mean some things like this equation

g[-a,-b] + r * h[LI[1],-a,-b] + r * Log[r] * L[Li[1],-a,-b]

2nd: I want perturbation parameter to be conformal factor of other metric but xTensor show error when I set conformal factor the same as perturbation parameter(how can someone do this?)

For more detail you can see this paper arxiv:hep-th/0002230

thanks,

 Pedram

[ghadir jafari]

Hi

just perturb around the background metric g0[-a,-b] using standard methods in xpert. and then use a simple rule like the following to write metric perturbation in terms of FG expansion:

Rule1=MakeRule[{ h[LI[1],-a,-b] ,r g1[-a,-b]+r^2 g2[-a,-b]+..}]

On Friday, January 22, 2016 at 6:16:13 PM UTC+3:30, Giorgos Anastasiou wrote:

[mcnees]

I'm attaching a notebook showing how I did it a few years ago. The tricky part was working out the perturbations of quantities involving derivatives with respect to the AdS radial coordinate -- my solution is explained in the notebook.

I'm sure there are many ways to improve on what I've done here. (At the very least, I'm sure there are more elegant approaches.)

My calculation assumes a Weyl-flat conformal class at spatial infinity, so the Fefferman-Graham expansion does not include any log terms. Extending this to non-Weyl flat boundary metrics is left as an exercise for the reader :) 

Best,

Bob

----------------------------

Robert McNees

Associate Professor

Department of Physics

Loyola University Chicago

http://jacobi.luc.edu

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[Marco Sanchioni]

Someone knows how to repeat the procedure to the lagrangian formalism with xTensor?