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  • Letter
  • Open Access

Chiral algebra, Wilson lines, and mixed Hodge structure of Coulomb branch

Yutong Li and Yiwen Pan

Wenbin Yan

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Phys. Rev. D 114, L061703 – Published 28 September, 2026

DOI: https://doi.org/10.1103/ly16-93ts

Abstract

We find an intriguing relation between the chiral algebra and the mixed Hodge structure of the Coulomb branch of four dimensional N=2 superconformal field theories. We identify the space of irreducible characters of the N=4 SU(N) chiral algebra V[TSU(N)] by analytically computing the Wilson line Schur index, and imposing modular invariance. We further establish a map from the V[TSU(N)] characters to the characters of the Tp,N chiral algebra. We extract the pure part of the mixed Hodge polynomial PHc of the Coulomb branch compactified on a circle, and prove that PHc encodes the representation theory of V[TSU(N)]. We expect this to be a new entry of the 4D mirror symmetry framework.

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Phys. Rev. D 114, L061703– Published 28 September, 2026
  • Received 8 December 2025
  • Accepted 24 August 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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