Generalised-Edged Quivers and Global Forms

TL;DR

This paper introduces a new class of quivers with edges labeled by two parameters, generalising non-simply laced quivers, and explores their moduli spaces, anomalies, and connections to instanton moduli spaces in supersymmetric theories.

Contribution

It generalises non-simply laced unitary quivers to include $(p,q)$-labeled edges and studies their moduli spaces, anomalies, and global forms using Hilbert series and superconformal index.

Findings

Parametrisation of magnetic flux lattices for $(p,q)$-edged quivers.

Identification of global forms via discrete gauging.

Alternative realization of $ ext{SO}(2n+1)$ instanton moduli spaces.

Abstract

Non-simply laced quivers, despite the lack of complete Lagrangian descriptions, play an important role in characterising moduli spaces of supersymmetric field theories. Notably, the moduli space of instantons in non-simply laced gauge groups can be understood by means of such quivers. We generalise the notion of non-simply laced unitary quivers to those whose edges carry two labels $(p,q)$, dubbed $(p,q)$-edged quivers. The special case of $(p,1)$ corresponds to a conventional non-simply laced edge studied in the literature. In the case of unframed $(p,q)$-edged quivers, we show how to parametrise the lattice of magnetic fluxes upon ungauging the decoupled $\mathrm{U}(1)$, and how one can pick sublattices thereof corresponding to different global forms of the quiver related by discrete gauging. This form of discrete gauging can be applied to any unframed unitary quivers, not just ones with generalised edges. We utilise both the Hilbert series and the superconformal index to study moduli spaces and 't Hooft anomalies. In particular, we study mixed 't Hooft anomalies between a one-form symmetry and a zero-form continuous topological symmetry in various $(p,q)$-edged quivers. We also provide an alternative realisation of the moduli space of $\mathfrak{so}(2n+1)$ instantons via gauging discrete symmetries in supersymmetric QCD with a symplectic gauge group and a large number of flavours.