Sphere quantization of Higgs and Coulomb branches and Analytic Symplectic Duality
Abstract We employ the protected sphere correlation functions of three-dimensional Super Conformal Field Theories with eight supercharges in order to define a quantization of their Higgs and Coulomb branches of vacua as real phase spaces. We also employ hemisphere correlation functions to define a q...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-01-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP01(2025)188 |
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| author | Davide Gaiotto |
| author_facet | Davide Gaiotto |
| author_sort | Davide Gaiotto |
| collection | DOAJ |
| description | Abstract We employ the protected sphere correlation functions of three-dimensional Super Conformal Field Theories with eight supercharges in order to define a quantization of their Higgs and Coulomb branches of vacua as real phase spaces. We also employ hemisphere correlation functions to define a quantization of certain real loci in the Higgs and Coulomb branches. Localization formulae and dualities applied to these quantizations result in a body of predictions about unitary representations of certain algebras, which may perhaps be understood as an “analytic” form of the symplectic duality program. In particular, the protected correlation functions in the class of theories denoted as T[G] are naturally related to the theory of unitary representations of complex or real semi-simple Lie groups. |
| format | Article |
| id | doaj-art-2e83220a9c09409f9b39ad70f6873dc1 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-2e83220a9c09409f9b39ad70f6873dc12025-02-09T12:07:44ZengSpringerOpenJournal of High Energy Physics1029-84792025-01-012025117310.1007/JHEP01(2025)188Sphere quantization of Higgs and Coulomb branches and Analytic Symplectic DualityDavide Gaiotto0Perimeter Institute for Theoretical PhysicsAbstract We employ the protected sphere correlation functions of three-dimensional Super Conformal Field Theories with eight supercharges in order to define a quantization of their Higgs and Coulomb branches of vacua as real phase spaces. We also employ hemisphere correlation functions to define a quantization of certain real loci in the Higgs and Coulomb branches. Localization formulae and dualities applied to these quantizations result in a body of predictions about unitary representations of certain algebras, which may perhaps be understood as an “analytic” form of the symplectic duality program. In particular, the protected correlation functions in the class of theories denoted as T[G] are naturally related to the theory of unitary representations of complex or real semi-simple Lie groups.https://doi.org/10.1007/JHEP01(2025)188Duality in Gauge Field TheoriesIntegrable HierarchiesNon-Commutative GeometrySupersymmetric Gauge Theory |
| spellingShingle | Davide Gaiotto Sphere quantization of Higgs and Coulomb branches and Analytic Symplectic Duality Journal of High Energy Physics Duality in Gauge Field Theories Integrable Hierarchies Non-Commutative Geometry Supersymmetric Gauge Theory |
| title | Sphere quantization of Higgs and Coulomb branches and Analytic Symplectic Duality |
| title_full | Sphere quantization of Higgs and Coulomb branches and Analytic Symplectic Duality |
| title_fullStr | Sphere quantization of Higgs and Coulomb branches and Analytic Symplectic Duality |
| title_full_unstemmed | Sphere quantization of Higgs and Coulomb branches and Analytic Symplectic Duality |
| title_short | Sphere quantization of Higgs and Coulomb branches and Analytic Symplectic Duality |
| title_sort | sphere quantization of higgs and coulomb branches and analytic symplectic duality |
| topic | Duality in Gauge Field Theories Integrable Hierarchies Non-Commutative Geometry Supersymmetric Gauge Theory |
| url | https://doi.org/10.1007/JHEP01(2025)188 |
| work_keys_str_mv | AT davidegaiotto spherequantizationofhiggsandcoulombbranchesandanalyticsymplecticduality |