Flavored modular differential equations
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866914818167930880 |
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| author | Pan, Yiwen Wang, Yufan |
| author_facet | Pan, Yiwen Wang, Yufan |
| contents | Flavored modular differential equations sometimes arise from null states or their descendants in a chiral algebra with continuous flavor symmetry. In this paper we focus on Kac-Moody algebras $\widehat{\mathfrak{g}}_k$ that contain a level-four null state $|\mathcal{N}_T\rangle$ which implements the nilpotency of the Sugawara stress tensor. We study the properties of the corresponding flavored modular differential equations, and show that the equations exhibit almost covariance under modular $S$-transformation, connecting null states and their descendants at different levels. The modular property of the equations fixes the structure of $\mathfrak{g}$ and the level $k$, as well as the flavored characters of all the highest weight representations. Shift property of the equations can generate non-vacuum characters starting from the vacuum character. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_10569 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Flavored modular differential equations Pan, Yiwen Wang, Yufan High Energy Physics - Theory Flavored modular differential equations sometimes arise from null states or their descendants in a chiral algebra with continuous flavor symmetry. In this paper we focus on Kac-Moody algebras $\widehat{\mathfrak{g}}_k$ that contain a level-four null state $|\mathcal{N}_T\rangle$ which implements the nilpotency of the Sugawara stress tensor. We study the properties of the corresponding flavored modular differential equations, and show that the equations exhibit almost covariance under modular $S$-transformation, connecting null states and their descendants at different levels. The modular property of the equations fixes the structure of $\mathfrak{g}$ and the level $k$, as well as the flavored characters of all the highest weight representations. Shift property of the equations can generate non-vacuum characters starting from the vacuum character. |
| title | Flavored modular differential equations |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2306.10569 |