Abelian mirror symmetry of N $$ \mathcal{N} $$ = (2, 2) boundary conditions
Abstract We evaluate half-indices of N $$ \mathcal{N} $$ = (2, 2) half-BPS boundary conditions in 3d N $$ \mathcal{N} $$ = 4 supersymmetric Abelian gauge theories. We confirm that the Neumann boundary condition is dual to the generic Dirichlet boundary condition for its mirror theory as the half-ind...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-03-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP03(2021)163 |
| _version_ | 1818576515840868352 |
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| author | Tadashi Okazaki |
| author_facet | Tadashi Okazaki |
| author_sort | Tadashi Okazaki |
| collection | DOAJ |
| description | Abstract We evaluate half-indices of N $$ \mathcal{N} $$ = (2, 2) half-BPS boundary conditions in 3d N $$ \mathcal{N} $$ = 4 supersymmetric Abelian gauge theories. We confirm that the Neumann boundary condition is dual to the generic Dirichlet boundary condition for its mirror theory as the half-indices perfectly match with each other. We find that a naive mirror symmetry between the exceptional Dirichlet boundary conditions defining the Verma modules of the quantum Coulomb and Higgs branch algebras does not always hold. The triangular matrix obtained from the elliptic stable envelope describes the precise mirror transformation of a collection of half-indices for the exceptional Dirichlet boundary conditions. |
| first_indexed | 2024-12-16T06:15:15Z |
| format | Article |
| id | doaj.art-d0c0716a57a74f2199fffd18990514d9 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-16T06:15:15Z |
| publishDate | 2021-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-d0c0716a57a74f2199fffd18990514d92022-12-21T22:41:18ZengSpringerOpenJournal of High Energy Physics1029-84792021-03-012021314410.1007/JHEP03(2021)163Abelian mirror symmetry of N $$ \mathcal{N} $$ = (2, 2) boundary conditionsTadashi Okazaki0Department of Mathematical Sciences, Durham UniversityAbstract We evaluate half-indices of N $$ \mathcal{N} $$ = (2, 2) half-BPS boundary conditions in 3d N $$ \mathcal{N} $$ = 4 supersymmetric Abelian gauge theories. We confirm that the Neumann boundary condition is dual to the generic Dirichlet boundary condition for its mirror theory as the half-indices perfectly match with each other. We find that a naive mirror symmetry between the exceptional Dirichlet boundary conditions defining the Verma modules of the quantum Coulomb and Higgs branch algebras does not always hold. The triangular matrix obtained from the elliptic stable envelope describes the precise mirror transformation of a collection of half-indices for the exceptional Dirichlet boundary conditions.https://doi.org/10.1007/JHEP03(2021)163Differential and Algebraic GeometryDuality in Gauge Field TheoriesSupersymmetric Gauge TheorySupersymmetry and Duality |
| spellingShingle | Tadashi Okazaki Abelian mirror symmetry of N $$ \mathcal{N} $$ = (2, 2) boundary conditions Journal of High Energy Physics Differential and Algebraic Geometry Duality in Gauge Field Theories Supersymmetric Gauge Theory Supersymmetry and Duality |
| title | Abelian mirror symmetry of N $$ \mathcal{N} $$ = (2, 2) boundary conditions |
| title_full | Abelian mirror symmetry of N $$ \mathcal{N} $$ = (2, 2) boundary conditions |
| title_fullStr | Abelian mirror symmetry of N $$ \mathcal{N} $$ = (2, 2) boundary conditions |
| title_full_unstemmed | Abelian mirror symmetry of N $$ \mathcal{N} $$ = (2, 2) boundary conditions |
| title_short | Abelian mirror symmetry of N $$ \mathcal{N} $$ = (2, 2) boundary conditions |
| title_sort | abelian mirror symmetry of n mathcal n 2 2 boundary conditions |
| topic | Differential and Algebraic Geometry Duality in Gauge Field Theories Supersymmetric Gauge Theory Supersymmetry and Duality |
| url | https://doi.org/10.1007/JHEP03(2021)163 |
| work_keys_str_mv | AT tadashiokazaki abelianmirrorsymmetryofnmathcaln22boundaryconditions |