We saw in the previous chapter that the ‘holographic’, duality between AdS5 physics and the physics of the conformally invariant four dimensional Yang–Mills theory can be extended to the properties of solutions which are only asymptotically AdS5, in keeping with the basic dictionary of the correspondence. We studied the properties of Schwarzschild and Reissner–Nordstrom black holes in AdS, arising naturally as limits of non-extremal and spinning D3-branes, and found that their properties make considerable physical sense in the holographically dual field theory.

It is very clear that this duality between gravitational physics and that of gauge theory is potentially a powerful tool for studying gauge theory. The prototype example is, of course, a highly specialised sort of gauge theory, since it has sixteen supercharges, and is conformally invariant. Of great interest is the study of gauge theories which might be closer to the theories we use to model interactions in particle physics, such as QCD. Perhaps there are gravitational duals of such theories. More generally, of course, we would like to also find and study full string theory duals, if we want to study more than just very large N. At the time of writing, this is subject of considerable research effort.

In this chapter we shall have a brief look at extending the intuition we have developed about the AdS/CFT correspondence a bit further, and address the issue of studying less symmetric gauge theories by deforming the AdS/CFT example.