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arXiv · 2510.03888

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

Yutong Li·Yiwen Pan·Wenbin Yan
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Abstract

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

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Yutong Li, Yiwen Pan, Wenbin Yan. 2025-10-04. Chiral algebra, Wilson lines, and mixed Hodge structure of Coulomb branch. https://arxiv.org/abs/2510.03888

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