NEQNET: Non-equilibrium Phenomena

35. Lectures on AdS/CFT by Maldacena

Posted by Dmitry

at May 2, 2008

Here are some links on excellent lectures on AdS/CFT by Juan Maldacena which I found on Google Video (quality is fascinating):

Lecture 1: Large N expansion (he starts with O(N) sigma model, large N matrix models and ends discussing Polyakov’s action; the lecture contains everything you need to know about condensation of Lagrangian multipliers - exactly the staff I am currently working on, dear Juan, thanks for the inspiration :-))

Lecture 2: Liouville mode and AdS background; why string theory on AdS (cross sphere) background is equivalent to N=4 SYM

and the Lecture 3 where he wants to go beyond conformal N=4 and discuss SYM theories with confinement

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AdS/CFT, Quantum field theory, String theory

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34. Several questions about de Sitter

Posted by Dmitry

at May 2, 2008

As it (probably) follows from my FireStats statistics, quite an impressive number of experts on the field are reading this blog. If this is indeed so, I have several questions about QFT in de Sitter space that you may be able to answer.

Here they are:

1) Consider d-dimensional de Sitter in global coordinates, where linear element looks like $ds^2=-dt^2+{\rm cosh}^2t{}d\Omega^2_{d-1}$ and QFT of a single massive free scalar field. Why $|in\rangle$ and $|out\rangle$ coinside, if d is odd? In other words, why dS_d is stable if is odd and unstable if is even?

2) Consider a general Green’s function of a massive scalar field in de Sitter space. As you know, it has a form

$\langle\phi(x)\phi(x') \rangle=c_1F\left(h_+,h_-,d/2,\frac{1+P}{2}\right)+c_2F\left(h_+,h_-,d/2,\frac{1-P}{2}\right)$ ,

where $P=\cos\Theta(x,x')$ and $\Theta$ is a geodesic distance between points and on de Sitter.

This Green’s function has a singularity at antipodal points ( P=-1 ) apart from the usual singularity at coincident points ( P=1 ). What is the physical meaning of singularity at antipodal points?

While giving answer to this question, please, don’t say anything like “antipodal singularity is beyond horizon” and/or do not mention “elliptic De Sitter”, because it is stupid.

3) This Green’s function has two branch cuts in the complex plane of : one at $-\infty<P<-1$ , another - at $1<P<+\infty$ . What is the physical meaning of these two branch cuts?