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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.

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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)