Flavored modular differential equations

Yiwen Pan; Yufan Wang

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arXiv · 2306.10569

Flavored modular differential equations

Yiwen Pan·Yufan Wang

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Abstract

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.

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Yiwen Pan, Yufan Wang. 2023-06-18. Flavored modular differential equations. https://arxiv.org/abs/2306.10569

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