Flavored modular differential equations

作者：Yiwen Pan, Yufan Wang · 发表于：Physical review. D/Physical review. D. · 年份：2023 · DOI：10.1103/physrevd.108.085027 · 被引用次数：8 · 研究领域：Algebraic structures and combinatorial models、Nonlinear Waves and Solitons、Black Holes and Theoretical Physics

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 ${\stackrel{^}{{g}}}_{k}$ that contain a level-four null state $|{\mathcal{N}}_{T}⟩$ 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 ${g}$ and the level $k$, as well as the flavored characters of all the highest weight representations. Shift property of the equations can generate nonvacuum characters starting from the vacuum character.