Quiver polymerisation

Abstract

Abstract Two new diagrammatic techniques on 3d N $$ \mathcal{N} $$ = 4 quiver gauge theories, termed chain and cyclic quiver polymerisation are introduced. These gauge a diagonal SU/U(k) subgroup of the Coulomb branch global symmetry of a quiver (or pair of quivers) with multiple legs. The action on the Coulomb branch is that of a SU/U(k) hyper-Kähler quotient. The polymerisation techniques build and generalise known composition methods from class S $$ \mathcal{S} $$ . Polymerisation is used to generate a wide range of magnetic quivers from various physical contexts. These include polymerisation constructions for Kronheimer-Nakajima quivers, which generalise the ADHM construction for the moduli space of k SU(N) instantons on ℂ 2 to A-type singularities. Also a polymerisation construction of the magnetic quiver for the 6d N $$ \mathcal{N} $$ = (1, 0) theory coming from two 1 2 $$ \frac{1}{2} $$ M5 branes probing an E 6 Klein singularity. We find a method of extending magnetic quivers for Class S $$ \mathcal{S} $$ theories to cure the incomplete Higgsing that arises when gluing punctures into the loops associated with higher genus theories. Other novel constructions include a unitary magnetic quiver for the closure of a height four nilpotent orbit of SO(7). We explore the relationships between the Coulomb and Higgs branches of quivers under polymerisation.

Keywords

• Supersymmetric Gauge Theory
• Extended Supersymmetry
• Global Symmetries
• Brane Dynamics in Gauge Theories