## 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:

We can notice that if we fix the value of the coordinate we obtain one of the conditions for five-dimensional anti-de Sitter space. This will not produce anti-de Sitter space since the surface is not embeded in . Nevertheless, I am not looking for anti-de Sitter space: I am looking for some space that will reduce to anti-de Sitter space in some limit. Defining we can write

with the understanding that the etas will represent flat metrics. Going back to the original, seven-dimensional metric we need

Now define the following tensors:

, and .

Then I claim the metric can be written as

Now we impose the condition that . With this condition we can use the five coordinates used in the Alday & Maldacena article as a starting point:

, and .

The next task is to write the metric in terms of these coordinates and hope that we get something that will look like anti-de Sitter space with some extra terms.

In search for anti-de Sitter space (II) « Index Concordiasaid, on June 30, 2008 at 7:26 pm[…] under: AdS/CFT, Relativity — Index Guy @ 7:26 pm I want to continue the discussion started here about a metric that may yield anti-de Sitter space as some […]