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Mirror symmetry for circle compactified 4d mathcal{N}=2 SCFTs

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arxiv 2306.15214 v1 pith:C27ZDCG7 submitted 2023-06-27 hep-th math.QAmath.RT

Mirror symmetry for circle compactified 4d mathcal{N}=2 SCFTs

Peng Shan , Dan Xie , Wenbin Yan This is my paper
classification hep-th math.QAmath.RT
keywords mirrorpropertiessymmetrybranchcoulombalgebracirclecompactified
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We propose a mirror symmetry for 4d $\mathcal{N}=2$ superconformal field theories (SCFTs) compactified on a circle with finite size. The mirror symmetry involves vertex operator algebra (VOA) describing the Schur sector (containing Higgs branch) of 4d theory, and the Coulomb branch of the effective 3d theory. The basic feature of the mirror symmetry is that many representational properties of VOA are matched with geometric properties of the Coulomb branch moduli space. Our proposal is verified for a large class of Argyres-Douglas (AD) theories engineered from M5 branes, whose VOAs are W-algebras, and Coulomb branches are the Hitchin moduli spaces. VOA data such as simple modules, Zhu's algebra, and modular properties are matched with geometric properties like $\mathbb{C}^*$-fixed varieties in Hitchin fibers, cohomologies, and some DAHA representations. We also mention relationships to 3d symplectic duality.

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Cited by 2 Pith papers

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  1. R-Twisting, Fibered Knots, and Gauge Theories

    hep-th 2026-07 conditional novelty 6.0

    R-twisting scales the R-symmetry circle angle by mn/(m+n), turning Argyres–Douglas Seiberg–Witten curves into mapping tori of (m,n) torus knots that label 3d gauge theories.

  2. Bridging 4D QFTs and 2D VOAs via 3D high-temperature EFTs

    hep-th 2024-09 unverdicted novelty 6.0

    High-temperature limits on higher sheets of the superconformal index for (A1,A2n) Argyres-Douglas theories yield Gang-Kim-Stubbs 3d N=2 theories whose boundaries support Virasoro minimal model VOAs M(2,2n+3) and assoc...