10 - Duality with D-branes in supergravity

Summary

So far we have studied examples of the AdS/CFT correspondence which are motivated by the near-horizon limit of a stack of D-branes placed either in flat space or in a more involved geometry such as the conifold. In this chapter we will consider examples where additional D-branes are placed in the supergravity solution after the near-horizon limit has been taken. This approach has several motivations. One possible application is to wrap branes on non-trivial cycles in the geometry resulting from the near-horizon limit. Such branes correspond to soliton-like states in the dual conformal field theory. These states are non-perturbative from the point of view of the 1/N expansion. Consequently, they allow information about the stringy nature of the correspondence to be uncovered even in its weakest form, where λ and N are large. The soliton-like field theory states include the pointlike baryon vertex, one-dimensional flux tubes and higher dimensional domain walls.

Here, however, we will focus on the second important application of embedding additional D-branes into the near-horizon geometry, the flavour branes. Adding additional D-branes to the supergravity solution in the near-horizon limit gives rise to a modification of the original AdS/CFT correspondence which involves field theory degrees of freedom that transform in the fundamental representation of the gauge group. This is in contrast to the fields of N = 4 Super Yang–Mills theory which transform in the adjoint representation of the gauge group. This is particularly useful for describing strongly coupled quantum field theories which are similar to QCD, since the quark fields in QCD transform in the fundamental representation. From an anti-fundamental and a fundamental field, a gauge invariant bilinear or meson operator may be formed. The key idea is then to conjecture that the meson operators are dual to the fluctuations of flavour branes embedded in the dual supergravity background.