Orthosymplectic Chern-Simons Matter Theories: Global Forms, Dualities, and Vacua

TL;DR

The work develops a magnetic quiver framework to study maximal hyper-Kähler branches of 3d orthosymplectic Chern-Simons matter theories (CSM) arising from Type IIB brane setups with O3 planes, connecting Coulomb-branch geometry to the moduli spaces via orthosymplectic magnetic quivers. It extends Giveon–Kutasov dualities to the orthosymplectic setting, detailing precise fugacity maps for linear and circular quivers and providing comprehensive checks for unitary and orthosymplectic cases through supersymmetric indices and Coulomb-branch Hilbert series. The paper demonstrates the construction of magnetic quivers for a wide class of theories, including several linear and circular diagrams and even non-Lagrangian brane configurations, and uses index/Hilbert-series data to fix global forms and test dualities. While many results are validated for $ ext{N}\geq 4$, the work also offers predictions for $ ext{N}=3$ theories where direct index checks are not yet available, highlighting subtleties in global forms and fugacity mappings. The study opens avenues for Higgsing analyses, higher-symmetry structures, and broader classes of CSM theories, suggesting a robust framework for understanding 3d dualities and moduli in orthosymplectic contexts.

Abstract

A magnetic quiver framework is proposed for studying maximal branches of 3d orthosymplectic Chern--Simons matter theories with $\mathcal{N} \geq 3$ supersymmetry, arising from Type IIB brane setups with O3 planes. These branches are extracted via brane moves, yielding orthosymplectic $\mathcal{N}=4$ magnetic quivers whose Coulomb branches match the moduli spaces of interest. Global gauge group data, inaccessible from brane configurations alone, are determined through supersymmetric indices, Hilbert series, and fugacity maps. The analysis is exploratory in nature and highlights several subtle features. In particular, magnetic quivers are proposed as predictions for the maximal branches in a range of examples.

Figures (15)

• Figure 1: GK duality for a $\text{NS5}-(1,\kappa)-\text{D3}$ brane system. Taking the conservation of brane-charge and supersymmetry into account, one finds $N^{\prime}=L+R-N+\abs{\kappa}$. Below the gauge nodes, the corresponding topological fugacities have been written, while the fugacity reported under the flavour nodes are those of their background topological symmetries. This fugacity assignment is essential when one applies locally the GK duality (see Comi:2022aqoMarino:2025uub for more details).
• Figure 2: GK duality applied on a two nodes unitary CSM theory. Moving the $(1,\kappa)$ 5-brane to the right leads to the dual theory $(1)$, while moving it to the left yields the dual theory $(2)$. Close to each arrow, representing a GK transition, the associate fugacity map is indicated, as derived from the duality in Figure \ref{['fig:GK_Duality_Unitary']}.
• Figure 3: The basic OSp CSM dualities for the $\text{NS5}-(1,2\kappa)-\text{D3}$$\mathcal{N}=4$ brane system with the four possible combinations of O3 planes.
• Figure 4: The basic OSp CSM dualities for the $\text{NS5}-(1,2\kappa+1)-\text{D3}$$\mathcal{N}=4$ brane system with the four possible combinations of O3 planes.
• Figure 5: The four possible two node CSM theories (labelled $(0)$) realised from $N$ D3s in between two NS5s and one $(1,q)$ 5-brane in the presence of O3 planes. For all cases, moving the $(1,q)$ 5-brane through the right NS5, one realises the dual CSM theory labelled $(1)$. This is essential a basic $\mathrm{Sp}$-type duality \ref{['eq:SQCD_Duality_Sp']}. One the other hand, moving the $(1,q)$ 5-brane through the left NS5, the dual CSM theory $(2)$ is reached. Field-theoretically, this is an $\mathrm{SO}$-type duality \ref{['eq:SQCD_Duality_SO']}.