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3d Mirrors and Phase Diagrams of Abelian Gauge Theories

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arxiv 2503.08791 v1 pith:IW5ZR3KJ submitted 2025-03-11 hep-th

Julius F. Grimminger , Amihay Hanany , Deshuo Liu This is my paper · ORCID
classification hep-th
keywords theoriesabelianbranchcoulombgaugehiggsmirrormirrors
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This paper presents new developments in the study of 3d mirror symmetry and the phase structure of Abelian gauge theories. Previous works identified 3d mirrors for a specific class of theories, termed ``simple" Abelian theories. This work extends this framework by proposing 3d mirrors for ``non-simple" Abelian theories with both discrete and continuous gauge group factors. The proposal is supported by evidence from an exact operator map between the Higgs/Coulomb branch of one theory and the Coulomb/Higgs branch of its 3d mirror. Further support is provided by explicit Hilbert series computations. An algorithm for computing the Hasse (phase) diagram of the Higgs branch of both simple and non-simple Abelian theories is introduced, uncovering a recently discovered family of isolated singularities among the elementary slices. A bottom-up algorithm for computing the Coulomb branch Hasse diagram of these theories is also introduced, and the two algorithms are tested against each other via 3d mirror symmetry.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. New symplectic singularities from $SU(2)$ gauge theories

    hep-th 2026-08 conditional novelty 8.0 of 10

    An SU(2) gauge theory with one Sym^k half-hypermultiplet and N fundamental half-hypermultiplets yields isolated symplectic singularities for k=1,3,5,7, with k=5,7 giving the new families hSO(N) and iSO(N).

  2. Bootstrapping mirror pairs: The beginning of the end

    hep-th 2025-10 conditional novelty 6.0 of 10

    A growth-and-fusion algorithm completes a quartet of quiver operations that bootstrap 3d mirror pairs, demonstrated on a new family of circular 'sunshine' quivers.

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