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<p>In this article, we further explore the construction and computation of expectation values for Wilson loops in higher-rank 5d 𝒩 = 1 gauge theories on ℂ<sup>2</sup> × <i>S</i><sup>1</sup>, by explicitly computing the Wilson loops via Chern-character insertion and qq-characters, including cases with the exceptional gauge group <i>G</i><sub>2</sub>. 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 <i>v</i>-expansion with <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <mi>v</mi> <mo>=</mo> <msqrt> <mrow> <msub> <mi>q</mi> <mn>1</mn> </msub> <msub> <mi>q</mi> <mn>2</mn> </msub> </mrow> </msqrt> </math></EquationSource> <EquationSource Format="TEX">\( v=\sqrt{q_1{q}_2} \)</EquationSource> </InlineEquation>, similar to the Hilbert-series structure of instanton partitions in pure gauge theories.</p>

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More on 5d Wilson loops in higher-rank theories and blowup equations

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月29日

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  • Minhao Liu,
  • Xin Wang,
  • Rui-Dong Zhu

摘要

In this article, we further explore the construction and computation of expectation values for Wilson loops in higher-rank 5d 𝒩 = 1 gauge theories on ℂ2 × S1, by explicitly computing the Wilson loops via Chern-character insertion and qq-characters, including cases with the exceptional gauge group G2. 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 v-expansion with v = q 1 q 2 \( v=\sqrt{q_1{q}_2} \) , similar to the Hilbert-series structure of instanton partitions in pure gauge theories.