Associated variety equals Higgs branch for VOAs from 4d N=2 SCFTs

Establish that, for vertex operator algebras arising from four-dimensional N=2 superconformal field theories, the associated variety X_V is isomorphic to the Higgs branch of the SCFT.

Background

This conjecture, due to Beem and Rastelli, connects the algebraic geometry of VOAs with the moduli space of vacua of 4d N=2 SCFTs. It serves as motivation for analogous statements in lower-dimensional settings and for the present work’s focus on associated varieties in the 3d A-model context.

The authors restate this conjecture to motivate their verification of analogous phenomena for SQED[n] and L_1(psl_{n|n}), while acknowledging that the general 4d conjecture remains open.

References

In the more familiar context of VOAs arising form 4d $\mathcal{N}=2$ SCFTs, a fruitful conjecture of Beem and Rastelli states that the associated variety is isomorphic to the Higgs branch.

— $L_1(\mathfrak{psl}_{n|n})$ from BRST reductions, associated varieties and nilpotent orbits (2409.13028 - Ferrari et al., 19 Sep 2024) in Section 1 (Introduction)