First, the $R \rightarrow \infty$ limit is subtle in $AdS_5$ spacetime, because the symmetry group of stringy $\sigma$-model on $AdS_5$ is $PSU(2,2 \vert 4)$, while the symmetry of flat space $\sigma$-model is super-Poincare group. One has to appropriately scale the generators of $SU(2,2 \vert 4)$ before taking the limit in order to get the flat space.

Second, the dictionary of $AdS/CFT$ correspondence states that the 't Hooft parameter of the gauge theory $\lambda=g_{YM}^2 N$ is dual to $R^4/\alpha^{\prime 2}$ on the $AdS$ side. Thus, the limit of infinite radius is the extremely strong coupling limit of the gauge theory. The interesting limit corresponding (presumably) to weakly coupled SYM theory is $R \rightarrow 0$ limit which was extensively studied using Pure Spinor formalism.

These (and many other) topics are discussed in Superstrings in $AdS$ by Mazzucato.

This post imported from StackExchange Physics at 2017-02-17 15:59 (UTC), posted by SE-user Andrey Feldman