conjecture is the weak regime (in the SUGRA limit) which specializes further to the case in which $\lambda$ is large. In this limit, strongly coupled $\cal N = $4 $SU(N)$ Yang-Mills theory is mapped to supergravity on $AdS_5 \times
S^5$; the inverse string tension $\alpha'$ goes to zero.

A precise way in which the two theories can be mapped into each other was proposed independently by Gubser, Klebanov and Polyakov \[41\] and by Witten \[56\]. Since the boundary of the $AdS_5$ space, namely $S^3 \times R$, is equivalent to $R^{3,1}$ , which is a copy of the Minkowski space, plus a point at infinity, the authors suggested a recipe to link the gravity theory in the bulk (AdS space) to the field theory on the boundary (Minkowski space). In this sense, the AdS/CFT correspondence can be considered as a holographic projection of the supergravity theory in the bulk to the field theory on the boundary.

Despite the fact that there is no proof of the AdS/CFT correspondence taking account of its string-theoretical origin yet, the huge amount of symmetry present almost guarantees that the AdS/CFT correspondence should hold. When proceeding to less symmetrical situations below, generalized gauge/gravity dualities remain a 