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arXiv · 2602.09807

More on 5d Wilson Loops in Higher-Rank Theories and Blowup Equations

Minhao Liu·Xin Wang·Rui-Dong Zhu
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Abstract

In this article, we further explore the construction and computation of expectation values for Wilson loops in higher-rank 5d $\mathcal{N} = 1$ gauge theories on $\mathbb{C}_2 \times S_1$, by explicitly computing the Wilson loops via Chern-character insertion and qq-characters, including cases with the exceptional gauge group $G_2$. In particular, we propose a systematic way to write down the general blowup equations for Wilson loops by using the constraints from the one-form symmetry and low-instanton data from the instanton partition function. In addition, for one-instanton contributions in a large family of Wilson loop representations, we observe that they admit a $q_1q_2$-expansion, similar to the Hilbert-series structure of instanton partitions in pure gauge theories.

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Minhao Liu, Xin Wang, Rui-Dong Zhu. 2026-02-10. More on 5d Wilson Loops in Higher-Rank Theories and Blowup Equations. https://doi.org/10.1007/jhep07(2026)268

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