Towards Mass Deformed N=4 SO(n) and Sp(k) gauge configurations

TL;DR

This paper explores the realization of N=4 SO(n) and Sp(k) gauge theories with mass deformations using type IIA brane configurations with orientifold planes, providing geometric insights and extending to non-zero mass sums.

Contribution

It introduces a framework for realizing mass-deformed N=4 SO(n) and Sp(k) theories with orientifold planes and interprets dualities geometrically, including models with non-zero hypermultiplet mass sums.

Findings

Embedded models in M-theory for vanishing hypermultiplet mass sums.

Geometric interpretation of Montonen-Olive duality.

Construction of new Sp(k) models with flavors and massive hypermultiplets.

Abstract

We study the introduction of orientifold six-planes in the type IIA brane configurations known as elliptic models. The N=4 SO(n) and $Sp(k)$ theories softly broken to N=2 through a mass for the adjoint hypermultiplet can be realized in this framework in the presence of two orientifold planes with opposite RR charge. A large class of $\b=0$ models is solved for vanishing sum of hypermultiplet masses by embedding the type IIA configuration into M-theory. We also find a geometric interpretation of Montonen-Olive duality based on the properties of the curves. We make a proposal for the introduction of non-vanishing sum of hypermultiplet masses in a sub-class of models. In the presence of two negatively charged orientifold planes and four D6-branes other interesting $\beta=0$ theories are constructed, e.g. $Sp(k)$ with four flavours and a massive antisymmetric hypermultiplet. We comment on the difficulties in obtaining the curves within our framework due to the arbitrary positions of the D6-branes.