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Mirror symmetry for circle compactified 4d $A_1$ class-$S$ theories

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arxiv 2410.15695 v1 pith:VHVNW5PS submitted 2024-10-21 hep-th math-phmath.MPmath.RT

Yiwen Pan , Wenbin Yan This is my paper
classification hep-thmath-phmath.MPmath.RT
keywords branchrepresentationtheoriestheoryclass-correspondencecoulombhiggs
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abstract

In this letter, we propose a 4d mirror symmetry for the class-$\mathcal{S}$ theories which relates the representation theory of the chiral quantization of the Higgs branch and the geometry of the Coulomb branch. We study the representation theory by using the 4d/VOA correspondence, (defect) Schur indices and (flavor) modular differential equations, and match the data with the fixed manifolds of the Hitchin moduli spaces. This correspondence extends the connection between Higgs and Coulomb branch of Argyres-Douglas theories, and can provide systematic guidance for the study of the representation theory of vertex operator algebras by exploiting results from Hitchin systems.

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  1. Generalized Schur partition functions and RG flows

    hep-th 2025-06 conditional novelty 6.0 of 10

    The generalized Schur partition function of SU(2) N_f=4 SQCD, evaluated at alpha = h^vee_g / 6, reproduces the Schur indices of every SCFT in the Deligne-Cvitanovic rank-one series.

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