In search for anti-de Sitter space (II)

I want to continue the discussion started here about a metric that may yield anti-de Sitter space as some limit.

In search for anti-de Sitter space (I)

Let us start by considering the direct product of a 3d Minkowski space with a 4d Minkowski space. The coordinates for this space then go as

If we impose the condition we obtain the following relation:

A certain background for strings (II)

Today I will approach the problem I started here from a different angle. In the work of Alday and Maldacena, the authors used the following parameterization when calculating the action near a cusp:

   ,      and  

In this form the scale and boost transformations are more explicit. But these coordinate come for the case of exact anti-de Sitter space and I want to consider the metric with

with being a function of the extra (fifth) coordinate only. This space will not have the same isometries as AdS, so we should not use the same parameterizations mentioned above. By in the UV limit we should obtain AdS space, so the parameterization should not be that different.

Maybe I should start with the 3d case. The metric goes as

We expect the parameterization of the worldsheet to change. But what if we keep it the same and look for a constant solution? The action will still diverge. [To be started...]

Scattering amplitudes à la Alday-Maldacena (II)

Continuing what we started before, I would like to discuss the four-point scattering amplitude using AdS/CFT methods.

Scattering amplitudes à la Alday-Maldacena (I)

I would like to summarize the work of Luis Fernando Alday and Juan Maldacena on gluon scattering amplitudes at strong coupling via AdS/CFT methods. I will follow mostly (i.e. verbatim) these two preprints from the arXiv:

0804.0951 and 0705.0303

A certain background for strings (I)

We would like to consider bosonic strings in the following gravitational background:

What we have in mind is something along the lines of