Punctures for theories of class S Γ $$ {\mathcal{S}}_{\varGamma } $$
Abstract With the aim of understanding compactifications of 6D superconformal field theories to four dimensions, we study punctures for theories of class S Γ $$ {\mathcal{S}}_{\varGamma } $$ . The class S Γ $$ {\mathcal{S}}_{\varGamma } $$ theories arise from M5-branes probing ℂ 2/Γ, an ADE singular...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-03-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP03(2017)171 |
| _version_ | 1819091549678469120 |
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| author | Jonathan J. Heckman Patrick Jefferson Tom Rudelius Cumrun Vafa |
| author_facet | Jonathan J. Heckman Patrick Jefferson Tom Rudelius Cumrun Vafa |
| author_sort | Jonathan J. Heckman |
| collection | DOAJ |
| description | Abstract With the aim of understanding compactifications of 6D superconformal field theories to four dimensions, we study punctures for theories of class S Γ $$ {\mathcal{S}}_{\varGamma } $$ . The class S Γ $$ {\mathcal{S}}_{\varGamma } $$ theories arise from M5-branes probing ℂ 2/Γ, an ADE singularity. The resulting 4D theories descend from compactification on Riemann surfaces decorated with punctures. We show that for class S Γ $$ {\mathcal{S}}_{\varGamma } $$ theories, a puncture is specified by singular boundary conditions for fields in the 5D quiver gauge theory obtained from compactification of the 6D theory on a cylinder geometry. We determine general boundary conditions and study in detail solutions with first order poles. This yields a generalization of the Nahm pole data present for 1/2 BPS punctures for theories of class S $$ \mathcal{S} $$ . Focusing on specific algebraic structures, we show how the standard discussion of nilpotent orbits and its connection to representations of s u 2 $$ \mathfrak{s}\mathfrak{u}(2) $$ generalizes in this broader context. |
| first_indexed | 2024-12-21T22:41:30Z |
| format | Article |
| id | doaj.art-b994921cee754701bbc86d6a083571fc |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-21T22:41:30Z |
| publishDate | 2017-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-b994921cee754701bbc86d6a083571fc2022-12-21T18:47:50ZengSpringerOpenJournal of High Energy Physics1029-84792017-03-012017313410.1007/JHEP03(2017)171Punctures for theories of class S Γ $$ {\mathcal{S}}_{\varGamma } $$Jonathan J. Heckman0Patrick Jefferson1Tom Rudelius2Cumrun Vafa3Department of Physics, University of North CarolinaJefferson Physical Laboratory, Harvard UniversityJefferson Physical Laboratory, Harvard UniversityJefferson Physical Laboratory, Harvard UniversityAbstract With the aim of understanding compactifications of 6D superconformal field theories to four dimensions, we study punctures for theories of class S Γ $$ {\mathcal{S}}_{\varGamma } $$ . The class S Γ $$ {\mathcal{S}}_{\varGamma } $$ theories arise from M5-branes probing ℂ 2/Γ, an ADE singularity. The resulting 4D theories descend from compactification on Riemann surfaces decorated with punctures. We show that for class S Γ $$ {\mathcal{S}}_{\varGamma } $$ theories, a puncture is specified by singular boundary conditions for fields in the 5D quiver gauge theory obtained from compactification of the 6D theory on a cylinder geometry. We determine general boundary conditions and study in detail solutions with first order poles. This yields a generalization of the Nahm pole data present for 1/2 BPS punctures for theories of class S $$ \mathcal{S} $$ . Focusing on specific algebraic structures, we show how the standard discussion of nilpotent orbits and its connection to representations of s u 2 $$ \mathfrak{s}\mathfrak{u}(2) $$ generalizes in this broader context.http://link.springer.com/article/10.1007/JHEP03(2017)171Conformal Field TheoryField Theories in Higher DimensionsSupersymmetric Gauge Theory |
| spellingShingle | Jonathan J. Heckman Patrick Jefferson Tom Rudelius Cumrun Vafa Punctures for theories of class S Γ $$ {\mathcal{S}}_{\varGamma } $$ Journal of High Energy Physics Conformal Field Theory Field Theories in Higher Dimensions Supersymmetric Gauge Theory |
| title | Punctures for theories of class S Γ $$ {\mathcal{S}}_{\varGamma } $$ |
| title_full | Punctures for theories of class S Γ $$ {\mathcal{S}}_{\varGamma } $$ |
| title_fullStr | Punctures for theories of class S Γ $$ {\mathcal{S}}_{\varGamma } $$ |
| title_full_unstemmed | Punctures for theories of class S Γ $$ {\mathcal{S}}_{\varGamma } $$ |
| title_short | Punctures for theories of class S Γ $$ {\mathcal{S}}_{\varGamma } $$ |
| title_sort | punctures for theories of class s γ mathcal s vargamma |
| topic | Conformal Field Theory Field Theories in Higher Dimensions Supersymmetric Gauge Theory |
| url | http://link.springer.com/article/10.1007/JHEP03(2017)171 |
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