Algebro-geometric bootstrapping from OPE decoupling

Monica Jinwoo Kang; Craig Lawrie; Jaewon Song

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arXiv · 2602.04946

Algebro-geometric bootstrapping from OPE decoupling

Monica Jinwoo Kang·Craig Lawrie·Jaewon Song

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Abstract

We conjecture that decoupling relations in the operator product expansion of a 4d $\mathcal{N}=2$ superconformal field theory (SCFT) are encoded by an algebro-geometric object: a bifiltered affine scheme. We demonstrate how this scheme reproduces the Macdonald index (thus the Schur index) as well as the Higgs branch. Although the associated scheme typically admits continuous deformations, we find that a geometric extremization principle uniquely fixes these moduli, thereby providing a possible geometric route toward a classification of 4d $\mathcal{N}=2$ SCFTs.

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Monica Jinwoo Kang, Craig Lawrie, Jaewon Song. 2026-02-04. Algebro-geometric bootstrapping from OPE decoupling. https://arxiv.org/abs/2602.04946

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