Fractional branes and /N=1 gauge theories

We discuss fractional D3-branes on the orbifold C³/ Z₂× Z₂. We study the open and the closed string spectrum on this orbifold. The corresponding N=1 theory on the brane has, generically, a U( N₁)× U( N₂)× U( N₃)× U( N₄) gauge group with matter in the bifundamental. In particular, when only one type of brane is present, one obtains pure N=1 Yang-Mills. We study the coupling of the branes to the bulk fields and present the corresponding supergravity solution, valid at large distances. By using a probe analysis, we are able to obtain the Wilsonian β-function for those gauge theories that possess some chiral multiplet. Although, due to the lack of moduli, the probe technique is not directly applicable to the case of pure N=1 Yang-Mills, we point out that the same formula gives the correct result also for this case.