I often heard AdS/CFT correspondence provides a powerful framework to study strong coupled system, which perturbation is not applicable. However, lattice method still works in non-perturbative domain. My question is, what is the advantage of AdS/CFT? Is there any example impoosible to access by lattice method (I don't mind lattice get numerical than analytic results)?
In general, lattice calculations are quite cumbersome and require advanced numerical techniques and computational power. In the AdS/CFT correspondence, the involved concepts surpass those of lattice QCD greatly in complexity, as they involve string theory and general relativity in geometric backgrounds that are far from trivial. On the computational side, however, many (but definitely not all) calculations can be done analytically or by solving relatively simple (ordinary) numerical problems. Determining particle spectra for example can be as easy as solving a simple eigenvalue problem in the context of an ordinary differential equation.
There are also specific aspects of strong coupling physics (or to be more precise, QCD) where AdS/CFT is quite useful while lattice techniques are still struggling. One are would be the calculation of decay rates, where the correspondence is far ahead of what lattice is capable of. For example, in a specific model of holographic QCD, the Witten-Sakai-Sugimoto (WSS) model, decay rates of various mesons can be determined with relative ease and considerable success in reproducing experimental data.