Spectral flow, twisted modules and MLDE of quasi-lisse vertex algebras

Abstract

We calculate the fusion rules among ${\mathbb{Z}}_2$-twisted modules $L_{{\mathfrak{sl}}_2}(\ell ,0)$ at admissible levels. We derive a series MLDEs for normalized characters of ordinary twisted modules of quasi-lisse vertex algebras. Examples include affine VOAs of type $A_1^{(1)}$ at boundary admissible level, admissible level $k=-1/2$, $A_2^{(1)}$ at boundary admissible level $k=-3/2$, and ${\mathrm{BP}}^k$-algebra with special value $k=-9/4$. We also derive characters of some non-vacuum modules for affine VOA of type $D_4$ at non-admissible level $-2$ from spectral flow automorphism.

v2 some statements are corrected