2025/07/16 by Kang, Monica Jinwoo, Lawrie, Craig, Song, Jaewon · 2 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2507.12510
We propose an algebro-geometric interpretation of the Schur and Macdonald indices of four-dimensional N=2 superconformal field theories (SCFTs). We conjecture that there exists an affine scheme X such that the Hilbert series of the (appropriately-graded) arc space of its polynomial ring J_∞(ℂ[X]) encodes the indices. Distinct local descriptions of a (singular) point correspond to distinct choices of X, giving rise to a family of N=2 SCFTs each without a Higgs branch. These local descriptions directly translate into nilpotency relations in the operator product expansions. We test our conjecture across a variety of (generalized) Argyres-Douglas (AD) theories.