Abstract
We study particular families of bad 3d \( \mathcal{N} \) = 4 quiver gauge theories, whose Higgs branches consist of many cones. We show the role of a novel brane configuration in realizing the Higgs moduli for each distinct cone. Through brane constructions, magnetic quivers, Hasse diagrams, and Hilbert series computations we study the intricate structure of the classical Higgs branches. These Higgs branches are both non-normal (since they consist of multiple cones) and non-reduced (due to the presence of nilpotent operators in the chiral ring). Applying the principle of inversion to the classical Higgs branch Hasse diagrams, we conjecture the quantum Coulomb branch Hasse diagrams. These Coulomb branches have several most singular loci, corresponding to the several cones in the Higgs branch. We propose the Hasse diagrams of the full quantum moduli spaces of our theories. The quivers we study can be taken to be 5d effective gauge theories living on brane webs. Their infinite coupling theories have Higgs branches which also consist of multiple cones. Some of these cones have decorated magnetic quivers, whose 3d Coulomb branches remain elusive.
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Acknowledgments
We are indebted to Santiago Cabrera for many insightful discussions and collaboration at an early stage of this work. AH would like to thank Hirotaka Hayashi, Sung-Soo Kim, Kimyeong Lee and Futoshi Yagi for discussions. AB is supported by the ERC Consolidator Grant 772408-Stringlandscape, and by the LabEx ENS-ICFP: ANR-10-LABX-0010/ANR-10-IDEX-0001-02 PSL*. The work of AB, JFG, AH, RK and ZZ is partially supported by STFC grant ST/T000791/1. The work of MS was in part supported by the Yau Mathematical Sciences Center at Tsinghua University, the National Natural Science Foundation of China (grant no. 11950410497), and the China Postdoctoral Science Foundation (grant no. 2019M650616). ZZ is partially supported by the ERC Consolidator Grant # 864828 “Algebraic Foundations of Supersymmetric Quantum Field Theory” (SCFTAlg).
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Bourget, A., Grimminger, J.F., Hanany, A. et al. A tale of N cones. J. High Energ. Phys. 2023, 73 (2023). https://doi.org/10.1007/JHEP09(2023)073
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DOI: https://doi.org/10.1007/JHEP09(2023)073