• DOI:10.1007/JHEP08(2022)207
• Corpus ID: 248524812

Topological strings and Wilson loops

@article{Huang2022TopologicalSA,
  title={Topological strings and Wilson loops},
  author={Min-xin Huang and Kimyeong M. Lee and Xin Wang},
  journal={Journal of High Energy Physics},
  year={2022},
  volume={2022}
}

• Min-xin Huang, Kimyeong M. Lee, Xin Wang
• Published 4 May 2022
• Mathematics
• Journal of High Energy Physics

We propose the refined topological string correspondence to the expectation values of half-BPS Wilson loop operators in 5d N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N} $$\end{document} = 1 gauge theory partition function on the Omega-deformed background ℝϵ1,24\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\mathbb{R}}_{\upepsilon_{1,2}}^4 $$\end{document}× S1. We provide the refined topological vertex method and the refined holomorphic anomaly equation method in the topological string theory, from which we have exact computations on the 5d Wilson loops partition functions in both A- and B-models. Finally, with the exact results we have in B-model, we recover the quantum periods of local ℙ1 × ℙ1 model and local ℙ2 model in the study of quantum geometry and we further give a refined generalization of A-period.