The AdS/CFT correspondence gives a precise relation between certain 3+1 dimensional (super-)conformal gauge theories and type IIB strings on spaces of the form AdS_5 x X_5. AdS_5 is the 4+1 dimensional Anti-de Sitter space, and X_5 is a compact Einstein (constant curvature) space. The simplest example of X_5 is the 5-dimensional sphere which corresponds to maximally supersymmetric SU(N) gauge theory. An important problem in this field is to extend the correspondence to non-conformal field theories. The approach reviewed in this talk relies on the so-called fractional Dirichlet branes to break the conformal invariance and to construct 3+1 dimensional gauge theories with logarithmic flow of coupling constants. Fractional D3-branes may be thought of as D5-branes wrapped over a 2-sphere in the compact Einstein space. An example of 5-dimensional Einstein space containing a 2-sphere is T^{1,1}. Type IIB theory on AdS_5 x T^{1,1} is dual to N=1 supersymmetric SU(N) x SU(N) gauge theory. This duality follows from studying D3-branes on a conical space known as the conifold. The base of the conifold is T^{1,1} which is topologically a product of a 2-sphere and a 3-sphere, so that D5-branes may be wrapped over the 2-sphere. Adding M wrapped D5-branes to a stack of N D3-branes produces a non-conformal SU(N) x SU(N+M) gauge theory. In this theory the relative gauge coupling runs logarithmically both in the field theory and in the supergravity description. Furthermore, along the flow the gauge group factors repeatedly drop in size by M units, until finally the gauge group may become simply SU(M). This N=1 supersymmetric SU(M) theory exhibits chiral symmetry breaking and confinement. Klebanov and Strassler showed that this unusual flow is in fact an infinite series of Seiberg duality transformations - a ``duality cascade'' - in which the number of colors repeatedly drops by M units. The chiral symmetry breaking of the gauge theory has an interesting geometrical manifestation: the smoothing of the cone. The resulting space, a warped deformed conifold, is completely nonsingular and without a horizon, leading to confinement. A variety of interesting dynamical phenomena in gauge theory nicely appear in the dual supergravity description.

References : hep-th/0007191