Wilson surfaces in M5-branes

We study Wilson surface defects in 6d N=20\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N}=\left(2,0\right) $$\end{document} superconformal field theories, engineered by semi-infinite M2-branes intersecting M5-branes. Two independent approaches are used to obtain the Wilson surface observables on the T2 inside Ω-deformed R4 × T2. One approach is to compute 5d N=1*\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N}={1}^{*} $$\end{document} instanton partition functions in the presence of Wilson lines, where the instanton corrections capture the 6d Kaluza-Klein momentum modes. The other approach is to study the elliptic genera of 2d N=04\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N}=\left(0,4\right) $$\end{document} gauge theories, which we propose as describing 6d self-dual strings in the presence of Wilson surface defects. We make a detailed comparison between these two independent computations, which precisely agree for Wilson surfaces in minuscule representations; for non-minuscule representations instead we only find partial agreement, due to technical problems which we comment about.