On extensions of gl m n ⏜ $$ \mathfrak{gl}\widehat{\left(\left.m\right|n\right)} $$ Kac-Moody algebras and Calabi-Yau singularities
Abstract We discuss a class of vertex operator algebras W m n × ∞ $$ {\mathcal{W}}_{\left.m\right|n\kern0.33em \times \kern0.33em \infty } $$ generated by a super- matrix of fields for each integral spin 1, 2, 3, . . . . The algebras admit a large family of truncations that are in correspondence wit...
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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)042 |
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| author | Miroslav Rapčák |
| author_facet | Miroslav Rapčák |
| author_sort | Miroslav Rapčák |
| collection | DOAJ |
| description | Abstract We discuss a class of vertex operator algebras W m n × ∞ $$ {\mathcal{W}}_{\left.m\right|n\kern0.33em \times \kern0.33em \infty } $$ generated by a super- matrix of fields for each integral spin 1, 2, 3, . . . . The algebras admit a large family of truncations that are in correspondence with holomorphic functions on the Calabi-Yau singularity given by solutions to xy = zmwn. We propose a free-field realization of such truncations generalizing the Miura transformation for W N $$ {\mathcal{W}}_N $$ algebras. Relations in the ring of holomorphic functions lead to bosonization-like relations between different free-field realizations. The discussion provides a concrete example of a non-trivial interplay between vertex operator algebras, algebraic geometry and gauge theory. |
| format | Article |
| id | doaj-art-fa8c744fb9db458b8146fc63959fdc94 |
| 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-fa8c744fb9db458b8146fc63959fdc942025-02-09T12:06:22ZengSpringerOpenJournal of High Energy Physics1029-84792020-01-012020113510.1007/JHEP01(2020)042On extensions of gl m n ⏜ $$ \mathfrak{gl}\widehat{\left(\left.m\right|n\right)} $$ Kac-Moody algebras and Calabi-Yau singularitiesMiroslav Rapčák0Perimeter Institute for Theoretical PhysicsAbstract We discuss a class of vertex operator algebras W m n × ∞ $$ {\mathcal{W}}_{\left.m\right|n\kern0.33em \times \kern0.33em \infty } $$ generated by a super- matrix of fields for each integral spin 1, 2, 3, . . . . The algebras admit a large family of truncations that are in correspondence with holomorphic functions on the Calabi-Yau singularity given by solutions to xy = zmwn. We propose a free-field realization of such truncations generalizing the Miura transformation for W N $$ {\mathcal{W}}_N $$ algebras. Relations in the ring of holomorphic functions lead to bosonization-like relations between different free-field realizations. The discussion provides a concrete example of a non-trivial interplay between vertex operator algebras, algebraic geometry and gauge theory.https://doi.org/10.1007/JHEP01(2020)042Conformal and W SymmetryConformal Field Models in String TheorySupersymmetric Gauge TheoryDifferential and Algebraic Geometry |
| spellingShingle | Miroslav Rapčák On extensions of gl m n ⏜ $$ \mathfrak{gl}\widehat{\left(\left.m\right|n\right)} $$ Kac-Moody algebras and Calabi-Yau singularities Journal of High Energy Physics Conformal and W Symmetry Conformal Field Models in String Theory Supersymmetric Gauge Theory Differential and Algebraic Geometry |
| title | On extensions of gl m n ⏜ $$ \mathfrak{gl}\widehat{\left(\left.m\right|n\right)} $$ Kac-Moody algebras and Calabi-Yau singularities |
| title_full | On extensions of gl m n ⏜ $$ \mathfrak{gl}\widehat{\left(\left.m\right|n\right)} $$ Kac-Moody algebras and Calabi-Yau singularities |
| title_fullStr | On extensions of gl m n ⏜ $$ \mathfrak{gl}\widehat{\left(\left.m\right|n\right)} $$ Kac-Moody algebras and Calabi-Yau singularities |
| title_full_unstemmed | On extensions of gl m n ⏜ $$ \mathfrak{gl}\widehat{\left(\left.m\right|n\right)} $$ Kac-Moody algebras and Calabi-Yau singularities |
| title_short | On extensions of gl m n ⏜ $$ \mathfrak{gl}\widehat{\left(\left.m\right|n\right)} $$ Kac-Moody algebras and Calabi-Yau singularities |
| title_sort | on extensions of gl m n ⏜ mathfrak gl widehat left left m right n right kac moody algebras and calabi yau singularities |
| topic | Conformal and W Symmetry Conformal Field Models in String Theory Supersymmetric Gauge Theory Differential and Algebraic Geometry |
| url | https://doi.org/10.1007/JHEP01(2020)042 |
| work_keys_str_mv | AT miroslavrapcak onextensionsofglmnmathfrakglwidehatleftleftmrightnrightkacmoodyalgebrasandcalabiyausingularities |