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

TL;DR

This paper explores dual descriptions of N=1 brane worlds and geometric singularities with flux in M-theory, demonstrating their equivalence through different Kaluza Klein reductions and geometric transitions.

Contribution

It introduces an equivalence between brane world descriptions and geometric singularities with flux via two distinct Kaluza Klein reductions.

Findings

Two dual descriptions of N=1 gauge theories are established.

Geometric transitions relate singular backgrounds to brane configurations.

Linear sigma-models provide alternative descriptions of these backgrounds.

Abstract

We consider Kaluza Klein reductions of M-theory on the Z_N orbifold of the spin bundle over S^3 along two different U(1) isometries. The first one gives rise to the familiar ``large N duality'' of the N=1 SU(N) gauge theory in which the UV is realized as the world-volume theory of N D6-branes wrapped on S^3, whereas the IR involves N units of RR flux through an S^2. The second reduction gives an equivalent version of this duality in which the UV is realized geometrically in terms of an S^2 of A_{N-1} singularities, with one unit of RR flux through the S^2. The IR is reached via a geometric transition and involves a single D6 brane on a lens space S^3/Z_N or, alternatively, a singular background (S^2\times R^4)/Z_N, with one unit of RR flux through S^2 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 sigma-model descriptions of these backgrounds.