2023/06/18 by Pan, Yiwen, Wang, Yufan · 1 citation
#FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.2306.10569
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\mathfrakgk that contain a level-four null state |NT⟩ 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 \mathfrakg 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.