Mirror symmetry and line operators
Abstract We study half-BPS line operators in 3d N $$ \mathcal{N} $$ = 4 gauge theories, focusing in particular on the algebras of local operators at their junctions. It is known that there are two basic types of such line operators, distinguished by the SUSY subalgebras that they preserve; the two t...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-02-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP02(2020)075 |
| _version_ | 1818957936754425856 |
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| author | Tudor Dimofte Niklas Garner Michael Geracie Justin Hilburn |
| author_facet | Tudor Dimofte Niklas Garner Michael Geracie Justin Hilburn |
| author_sort | Tudor Dimofte |
| collection | DOAJ |
| description | Abstract We study half-BPS line operators in 3d N $$ \mathcal{N} $$ = 4 gauge theories, focusing in particular on the algebras of local operators at their junctions. It is known that there are two basic types of such line operators, distinguished by the SUSY subalgebras that they preserve; the two types can roughly be called “Wilson lines” and “vortex lines,” and are exchanged under 3d mirror symmetry. We describe a large class of vortex lines that can be characterized by basic algebraic data, and propose a mathematical scheme to compute the algebras of local operators at their junctions — including monopole operators — in terms of this data. The computation generalizes mathematical and physical definitions/analyses of the bulk Coulomb-branch chiral ring. We fully classify the junctions of half-BPS Wilson lines and of half-BPS vortex lines in abelian gauge theories with sufficient matter. We also test our computational scheme in a non-abelian quiver gauge theory, using a 3d-mirror-map of line operators from work of Assel and Gomis. |
| first_indexed | 2024-12-20T11:17:46Z |
| format | Article |
| id | doaj.art-361b003a7198484dba5ae30c37953f51 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-20T11:17:46Z |
| publishDate | 2020-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-361b003a7198484dba5ae30c37953f512022-12-21T19:42:34ZengSpringerOpenJournal of High Energy Physics1029-84792020-02-0120202115010.1007/JHEP02(2020)075Mirror symmetry and line operatorsTudor Dimofte0Niklas Garner1Michael Geracie2Justin Hilburn3Department of Mathematics and Center for Quantum Mathematics and Physics (QMAP), University of CaliforniaDepartment of Mathematics and Center for Quantum Mathematics and Physics (QMAP), University of CaliforniaDepartment of Mathematics and Center for Quantum Mathematics and Physics (QMAP), University of CaliforniaDepartment of Mathematics, University of PennsylvaniaAbstract We study half-BPS line operators in 3d N $$ \mathcal{N} $$ = 4 gauge theories, focusing in particular on the algebras of local operators at their junctions. It is known that there are two basic types of such line operators, distinguished by the SUSY subalgebras that they preserve; the two types can roughly be called “Wilson lines” and “vortex lines,” and are exchanged under 3d mirror symmetry. We describe a large class of vortex lines that can be characterized by basic algebraic data, and propose a mathematical scheme to compute the algebras of local operators at their junctions — including monopole operators — in terms of this data. The computation generalizes mathematical and physical definitions/analyses of the bulk Coulomb-branch chiral ring. We fully classify the junctions of half-BPS Wilson lines and of half-BPS vortex lines in abelian gauge theories with sufficient matter. We also test our computational scheme in a non-abelian quiver gauge theory, using a 3d-mirror-map of line operators from work of Assel and Gomis.https://doi.org/10.1007/JHEP02(2020)075Differential and Algebraic GeometrySupersymmetric Gauge TheorySuper-symmetry and DualityTopological Field Theories |
| spellingShingle | Tudor Dimofte Niklas Garner Michael Geracie Justin Hilburn Mirror symmetry and line operators Journal of High Energy Physics Differential and Algebraic Geometry Supersymmetric Gauge Theory Super-symmetry and Duality Topological Field Theories |
| title | Mirror symmetry and line operators |
| title_full | Mirror symmetry and line operators |
| title_fullStr | Mirror symmetry and line operators |
| title_full_unstemmed | Mirror symmetry and line operators |
| title_short | Mirror symmetry and line operators |
| title_sort | mirror symmetry and line operators |
| topic | Differential and Algebraic Geometry Supersymmetric Gauge Theory Super-symmetry and Duality Topological Field Theories |
| url | https://doi.org/10.1007/JHEP02(2020)075 |
| work_keys_str_mv | AT tudordimofte mirrorsymmetryandlineoperators AT niklasgarner mirrorsymmetryandlineoperators AT michaelgeracie mirrorsymmetryandlineoperators AT justinhilburn mirrorsymmetryandlineoperators |