The Higgs mechanism — Hasse diagrams for symplectic singularities
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 transve...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-01-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP01(2020)157 |
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| author | Antoine Bourget Santiago Cabrera Julius F. Grimminger Amihay Hanany Marcus Sperling Anton Zajac Zhenghao Zhong |
| author_facet | Antoine Bourget Santiago Cabrera Julius F. Grimminger Amihay Hanany Marcus Sperling Anton Zajac Zhenghao Zhong |
| author_sort | Antoine Bourget |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-ace0598ec4c94172bf279c20f7f678b8 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-ace0598ec4c94172bf279c20f7f678b82025-02-09T12:05:59ZengSpringerOpenJournal of High Energy Physics1029-84792020-01-012020116710.1007/JHEP01(2020)157The Higgs mechanism — Hasse diagrams for symplectic singularitiesAntoine Bourget0Santiago Cabrera1Julius F. Grimminger2Amihay Hanany3Marcus Sperling4Anton Zajac5Zhenghao Zhong6Theoretical Physics Group, The Blackett Laboratory, Imperial College LondonTheoretical Physics Group, The Blackett Laboratory, Imperial College LondonTheoretical Physics Group, The Blackett Laboratory, Imperial College LondonTheoretical Physics Group, The Blackett Laboratory, Imperial College LondonYau Mathematical Sciences Center, Tsinghua UniversityTheoretical Physics Group, The Blackett Laboratory, Imperial College LondonTheoretical Physics Group, The Blackett Laboratory, Imperial College LondonAbstract 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.https://doi.org/10.1007/JHEP01(2020)157Extended SupersymmetryField Theories in Higher DimensionsSupersymmetric Gauge Theory |
| spellingShingle | Antoine Bourget Santiago Cabrera Julius F. Grimminger Amihay Hanany Marcus Sperling Anton Zajac Zhenghao Zhong The Higgs mechanism — Hasse diagrams for symplectic singularities Journal of High Energy Physics Extended Supersymmetry Field Theories in Higher Dimensions Supersymmetric Gauge Theory |
| title | The Higgs mechanism — Hasse diagrams for symplectic singularities |
| title_full | The Higgs mechanism — Hasse diagrams for symplectic singularities |
| title_fullStr | The Higgs mechanism — Hasse diagrams for symplectic singularities |
| title_full_unstemmed | The Higgs mechanism — Hasse diagrams for symplectic singularities |
| title_short | The Higgs mechanism — Hasse diagrams for symplectic singularities |
| title_sort | higgs mechanism hasse diagrams for symplectic singularities |
| topic | Extended Supersymmetry Field Theories in Higher Dimensions Supersymmetric Gauge Theory |
| url | https://doi.org/10.1007/JHEP01(2020)157 |
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