Quasi-lisse Vertex Algebras and Modular Linear Differential Equations

  • Tomoyuki ArakawaEmail author
  • Kazuya Kawasetsu
Part of the Progress in Mathematics book series (PM, volume 326)


We introduce the notion of quasi-lisse vertex algebras, which generalizes admissible affine vertex algebras. We show that the normalized character of an ordinary module over a quasi-lisse vertex operator algebra has a modular invariance property, in the sense that it satisfies amodular linear differential equation. As an application we obtain the explicit character formulas of simple affine vertex algebras associated with the Deligne exceptional series at level −h−/6−1, which express the homogeneous Schur indices of 4d SCFTs studied by Beem, Lemos, Liendo, Peelaers, Rastelli and van Rees, as quasimodular forms.


Vertex algebras Modular linear differential equations Quasimodular forms Affine Kac-Moody algebras Affine W-algebras Associated varieties Deligne exceptional series Schur limit of superconformal index 

Mathematics Subject Classification (2010):

17B69 17B67 11F22 81R10 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Research Institute for Mathematical SciencesKyoto UniversityKyotoJapan
  2. 2.Department of Mathematics, MITCambridgeUSA
  3. 3.School of Mathematics and StatisticsThe University of MelbourneMelbourneAustralia

Personalised recommendations