The Higgs mechanism — Hasse diagrams for symplectic singularities View Full Text


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Article Info

DATE

2020-01-24

AUTHORS

Antoine Bourget, Santiago Cabrera, Julius F. Grimminger, Amihay Hanany, Marcus Sperling, Anton Zajac, Zhenghao Zhong

ABSTRACT

We explore the geometrical structure of Higgs branches of quantum field theories with 8 supercharges in 3, 4, 5 and 6 dimensions. They are symplectic singularities, and as such admit a decomposition (or foliation ) into so-called symplectic leaves, which are related to each other by transverse slices. We identify this foliation with the pattern of partial Higgs mechanism of the theory and, using brane systems and recently introduced notions of magnetic quivers and quiver subtraction, we formalise the rules to obtain the Hasse diagram which encodes the structure of the foliation. While the unbroken gauge symmetry and the number of flat directions are obtainable by classical field theory analysis for Lagrangian theories, our approach allows us to characterise the geometry of the Higgs branch by a Hasse diagram with symplectic leaves and transverse slices, thus refining the analysis and extending it to non-Lagrangian theories. Most of the Hasse diagrams we obtain extend beyond the cases of nilpotent orbit closures known in the mathematics literature. The geometric analysis developed in this paper is applied to Higgs branches of several Lagrangian gauge theories, Argyres-Douglas theories, five dimensional SQCD theories at the conformal fixed point, and six dimensional SCFTs. More... »

PAGES

157

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    55 flat directions
    56 foliation
    57 gauge symmetry
    58 gauge theory
    59 geometric analysis
    60 geometrical structure
    61 geometry
    62 leaves
    63 literature
    64 magnetic quivers
    65 mathematics literature
    66 mechanism
    67 nilpotent orbits
    68 non-Lagrangian theories
    69 notion
    70 number
    71 orbit
    72 paper
    73 patterns
    74 point
    75 quantum field theory
    76 quivers
    77 rules
    78 singularity
    79 slices
    80 structure
    81 subtraction
    82 supercharges
    83 symmetry
    84 symplectic leaves
    85 symplectic singularities
    86 system
    87 theory
    88 theory analysis
    89 transverse slices
    90 unbroken gauge symmetry
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