When the usual derivation for AdS/CFT is given for the most famous example of Type IIB string theory on $AdS_5 \times S^5$, the AdS space is clearly seen as the near horizon geometry of a stack of D3 branes. The resulting AdS space is written in Poincare coordinates, with the Poincare horizon corresponding to the location of the D3's. For convenience, the line element of $AdS_5$ in Poincare coordinates is$ ds^2 = \frac{r^2}{L^2} dx_{\mu}dx^{\mu} + \frac{L^2}{r^2} dr^2$, and the dual field theory lives on the 4d Minkowski space.

However, AdS/CFT is quite often discussed with the AdS written in global coordinates (and sometimes in even more exotic coordinates as well). In global coordinates, the line element is $ds^2 = -\left(\frac{r^2}{L^2}+1\right) dt^2 + \left(\frac{r^2}{L^2}+1\right)^{-1} dr^2 + r^2 d\Omega_3^2$, and the dual field theory lives on $\mathbb{R}_t \times S^3$.

My question is: is there a derivation of AdS/CFT which results in global coordinates analogous to Maldacena's original derivation based on the Poincare patch?

This post imported from StackExchange Physics at 2015-01-31 12:15 (UTC), posted by SE-user Surgical Commander