Abstract
This paper introduces two operations in quiver gauge theories. The first operation, collapse, takes a quiver with a permutation symmetry Sn and gives a quiver with adjoint loops. The corresponding 3d \( \mathcal{N} \) = 4 Coulomb branches are related by an orbifold of Sn. The second operation, multi-lacing, takes a quiver with n nodes connected by edges of multiplicity k and replaces them by n nodes of multiplicity qk. The corresponding Coulomb branch moduli spaces are related by an orbifold of type \( {\mathbb{Z}}_q^{n-1} \). Collapse generalises known cases that appeared in the literature [1–3]. These two operations can be combined to generate new relations between moduli spaces that are constructed using the magnetic construction.
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Acknowledgments
The authors would like to thank Mathew Bullimore, Michael Finkelberg, Lorenzo Foscolo, Paul Levy, Constantin Teleman for insightful discussions and interesting comments. The authors would like to thank the organisers of the Symplectic Singularities and Supersymmetric QFT workshop in Amiens where many inspiring discussions took place. The work of AH, GK, CL, and DL is partially supported by STFC Consolidated Grants ST/T000791/1 and ST/X000575/1. The work of GK is supported by STFC DTP research studentship grant ST/X508433/1. MS is supported Austrian Science Fund (FWF), START project “Phases of quantum field theories: symmetries and vacua” STA 73-N. MS also acknowledges support from the Faculty of Physics, University of Vienna.
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Hanany, A., Kumaran, G., Li, C. et al. Actions on the quiver: discrete quotients on the Coulomb branch. J. High Energ. Phys. 2024, 318 (2024). https://doi.org/10.1007/JHEP05(2024)318
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DOI: https://doi.org/10.1007/JHEP05(2024)318