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

A bstract 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 2 × 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 v -expansion with $$ v=\sqrt{q_1{q}_2} $$ v = q 1 q 2 , similar to the Hilbert-series structure of instanton partitions in pure gauge theories.