Fractional branes and N=1 gauge theories Original Research Article

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.