In principle yes, but there are several conceptual and technical issues that make it unclear how this could be achieved. Even though the AdS/CFT correspondence is conjectured to be exact(with much evidence hinting at this), it is hard to prove this essentially because in order to do calculations, one still has to use approximations and perturbation theory on one side or the other. This is essentially due to its dual nature: it relates a strongly coupled theory on the one side to a weakly coupled one on the other.

This can be understood much better in terms of the fundamental coupling constants of the theory: the string coupling is given by $g_s$ and the Yang-Mills coupling by $g_{YM}$, they are related by $g_{YM}^2=4\pi g_s$.

On the gravity/string side, calculations are feasible (unless you want to solve string theory on curved backgrounds, which is essentially an open problem) in the supergravity approximation of the theory. This is valid if we take $g_s\rightarrow0$ and also assume that the degree of the gauge group (the number of colours) $N$ is taken to infinity. Their product, the 't Hooft coupling $\lambda=g_{YM}^2N=4\pi g_sN$ however must be held fixed but much larger than one. For the Yang-Mills theory, perturbation theory is valid just on the other end of the parameter range, namely when $\lambda$ is very small.

This is useful for many calculations, since it allows one to chart the nonperturbative region of one theory by looking at the perturbative region of the other, but it makes it hard to prove anything in a rigorous way, especially within the axiomatic approach required for the solution of the Millenium problem. The requirement of large $N$ further restricts the applicability of the duality with respect to proving something for the generic gauge group $SU(N)$.

Apart from this, as mentioned in the other answer, the original and most well-known formulation of is, as the name suggests, between string theory and a conformal field theory, which by definition has no mass gap. In order to adress issues like confinement and the associated mass gap, one would have to work in other versions of the duality, e.g. the Witten model, which is $AdS_7\times S^4$, with a compactified dimension on the $AdS$ part, which breaks supersymmetry and introduces a mass scale.

This post imported from StackExchange Physics at 2014-10-14 10:40 (UTC), posted by SE-user Frederic Brünner