Chiral algebra, Wilson lines, and mixed Hodge structure of Coulomb branch
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| Format: | Preprint |
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2025
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| _version_ | 1866911249829199872 |
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| author | Li, Yutong Pan, Yiwen Yan, Wenbin |
| author_facet | Li, Yutong Pan, Yiwen Yan, Wenbin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_03888 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Chiral algebra, Wilson lines, and mixed Hodge structure of Coulomb branch Li, Yutong Pan, Yiwen Yan, Wenbin High Energy Physics - Theory Mathematical Physics Representation Theory 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. |
| title | Chiral algebra, Wilson lines, and mixed Hodge structure of Coulomb branch |
| topic | High Energy Physics - Theory Mathematical Physics Representation Theory |
| url | https://arxiv.org/abs/2510.03888 |