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 |
| Summary: | 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 = z m w n . 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. |
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| ISSN: | 1029-8479 |