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

TL;DR

This paper advances the understanding of Wilson loop computations in higher-rank 5d gauge theories, introducing systematic blowup equations and analyzing instanton contributions, including cases with exceptional gauge groups.

Contribution

It proposes a systematic method for deriving blowup equations for Wilson loops using one-form symmetry constraints and instanton data, extending computations to exceptional gauge groups.

Findings

Explicit computation of Wilson loops via Chern-character and qq-characters.

Systematic formulation of blowup equations for Wilson loops.

Observation of q_1q_2-expansion in one-instanton contributions.

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.