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arXiv · 2605.21159

Mirror Symmetry of the Affine Toda Systems

Xin Jin·Zhiwei Yun
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Abstract

For a complex reductive group $G$, we prove a homological mirror symmetry between the wrapped Fukaya category of the affine Toda system for $G$ and coherent sheaves on the regular centralizer group scheme for the Langlands dual group $G^\vee$. This can be interpreted as a geometric Langlands equivalence for $\mathbb{P}^1$ with mildest wild ramification at $0$ and $\infty$.

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Xin Jin, Zhiwei Yun. 2026-05-20. Mirror Symmetry of the Affine Toda Systems. https://arxiv.org/abs/2605.21159

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