On Sp(0) factors and orientifolds

TL;DR

This paper explores how orientifold effects influence the gauge group structure in geometric engineering of SO/Sp theories, revealing the origin of rank zero factors through flux contributions post-transition.

Contribution

It demonstrates that rank zero gauge factors are due to orientifold effects surviving the geometric transition, linking Konishi constraints to flux contributions in these models.

Findings

Rank zero gauge factors are caused by orientifold effects.

Mapping Konishi constraints to U(N) theories explains rank shifts.

Flux contributions of orientifolds affect gauge group ranks.

Abstract

We discuss the geometric engineering of SO/Sp gauge theories with symmetric or antisymmetric tensor matter and show that the `mysterious' rank zero gauge group factors observed by a few authors can be traced back to the effects of an orientifold which survives the geometric transition. By mapping the Konishi constraints of such models to those of the U(N) theory with adjoint matter, we show that the required shifts in the ranks of the unbroken gauge group components is due to the flux contribution of the orientifold after the transition.