Upgrade quasi-lisse VOAs to full 2d CFTs

Develop a concrete, general method to upgrade quasi-lisse vertex operator algebras—especially those arising from four-dimensional N=2 superconformal field theories via the SCFT/VOA correspondence—into full non-chiral two-dimensional conformal field theories.

Background

Many VOAs associated to 4d N=2 SCFTs are non-rational but are expected to be quasi-lisse; a central conjecture identifies their associated varieties with Higgs branches of the parent SCFT. Constructing a full non-chiral 2d CFT for these VOAs is a major challenge in both physics and mathematics.

The paper proposes a 2d/2d correspondence that, in favorable rational cases, immediately identifies the full CFT, and provides GLSM realizations for specific reductions. However, a general procedure for quasi-lisse VOAs remains an open problem.