On the equivalence ofN=1 brane worlds and geometric singularities with flux

Abstract

We consider Kaluza Klein reductions of M-theory on the N orbifold of the spin bundle over S3 along two different U(1) isometries. The first one gives rise to the familiar ``large-N duality'' of the = 1 SU(N) gauge theory in which the UV is realized as the world-volume theory of N D6-branes wrapped on S3, whereas the IR involves N units of RR flux through an S2. The second reduction gives an equivalent version of this duality in which the UV is realized geometrically in terms of a 1 of AN−1 singularities, with one unit of RR flux through the 1. The IR is reached via a geometric transition and involves a single D6 brane on a lens space S3/N or, alternatively, a singular background (S2 × 4)/N, with one unit of RR flux through S2 and, localized at the singularities, an action of their stabilizer group in the U(1) RR gauge bundle, so that no massless twisted states occur. We also consider linear σ-model descriptions of these backgrounds.