(Anti)symmetric matter and superpotentials from IIB orientifolds

TL;DR

This paper explores how certain N=1 gauge theories with specific matter representations can be engineered via IIB orientifolds, revealing the role of orientifold planes in superpotential contributions and dualities.

Contribution

It demonstrates the construction of these theories as Z2 orientifolds of Calabi-Yau fibrations and analyzes the impact of orientifold planes on the superpotential during geometric transitions.

Findings

Orientifold 5-planes survive geometric transitions, affecting superpotentials.

Matrix model techniques match geometric data for superpotential contributions.

Higgs branch recovers SO/Sp theories with consistent superpotentials.

Abstract

We study the IIB engineering of N=1 gauge theories with unitary gauge group and matter in the adjoint and (anti)symmetric representations. We show that such theories can be obtained as Z2 orientifolds of Calabi-Yau A2 fibrations, and discuss the explicit T-duality transformation to an orientifolded Hanany-Witten construction. The low energy dynamics is described by a geometric transition of the orientifolded background. Unlike previously studied cases, we show that the orientifold 5-`plane' survives the transition, thus bringing a nontrivial contribution to the effective superpotential. We extract this contribution by using matrix model results and compare with geometric data. A Higgs branch of our models recovers the engineering of SO/Sp theories with adjoint matter through an O5-`plane' T-dual to an O6-plane. We show that the superpotential agrees with that produced by engineering through an O5-`plane' dual to an O4-plane, even though the orientifold of this second construction is replaced by fluxes after the transition.