Fractional Branes and N=1 Gauge Theories

TL;DR

Fractional D3-branes on the orbifold C^3/(Z2 x Z2) realize N=1 quiver gauge theories with gauge group U(N1) x U(N2) x U(N3) x U(N4) and bifundamental matter. The authors derive the open- and closed-string spectra, construct boundary-state couplings to untwisted and twisted bulk fields, and obtain the large-distance supergravity solution for generic bound states of fractional branes. Through a brane-probe analysis they extract Wilsonian beta-functions for theories with chiral multiplets, obtaining a linear combination of the beta-functions that matches gauge theory predictions; for a two-brane bound state the result reduces to 1/g^2 = 1/g1^2 + 1/g2^2 and beta functions. They discuss an enhançon mechanism that excises the repulson singularity and comment on extrapolations to pure N=1 YM, noting agreement with the perturbative beta-function under justified assumptions.

Abstract

We discuss fractional D3-branes on the orbifold C^3/Z_2*Z_2. We study the open and the closed string spectrum on this orbifold. The corresponding N=1 theory on the brane has, generically, a U(N_1)*U(N_2)*U(N_3)*U(N_4) 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 beta-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.