N=1 Dualities of SO and USp Gauge Theories and T-Duality of String Theory

TL;DR

This paper explores dualities in N=1 SO and USp gauge theories through string theory models, revealing how T-duality in type IIB string theory underpins these gauge theory dualities.

Contribution

It constructs local string models for SO and USp gauge theories using type IIB orientifolds, linking gauge dualities to T-duality transformations.

Findings

Dualities originate from T-duality exchanging D7 and D3 branes.

Higgs branches match instanton moduli spaces on D7 branes.

D3 charge of D7 branes and orientifold planes is crucial for duality realization.

Abstract

Extending recent work on SU gauge theory, we engineer local string models for N=1 four-dimensional SO and USp gauge theories coupled to matter in the fundamental. The local models are type IIB orientifolds with D7 branes on a curved orientifold 7-plane, and matter realized by adding D3 branes on the orientifold plane. The Higgs branches of the SO and USp theories can be matched with the moduli spaces of SO and USp instantons on the compact four-dimensional part of the D7 branes worldvolume. The R-charge of the gauge theories is identified with a U(1) symmetry on the worldvolume of an Euclidean D3 brane instanton. We argue that the quantum field theory dualities of these gauge theories arise from T-dualities of type IIB strings exchanging D7 and D3 charges. A crucial role is played by the induced D3 charge of D7 branes and an orientifold 7-plane, both partially compactified on a $Z_2$ orbifold of K3.