Wilson surfaces in M5-branes

TL;DR

This paper investigates Wilson surface defects in 6d superconformal theories via two methods—instanton partition functions and elliptic genera—finding precise agreement for minuscule representations and partial for others, advancing understanding of these defects.

Contribution

It introduces two independent approaches to compute Wilson surface observables in 6d theories and compares their results, highlighting exact matches for minuscule representations.

Findings

Exact agreement for minuscule representations.

Partial agreement for non-minuscule representations.

Provides new insights into Wilson surface defect computations.

Abstract

We study Wilson surface defects in 6d $\mathcal{N}=(2,0)$ 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 $T^2$ inside Omega-deformed $\mathbf{R}^4 \times T^2$. One approach is to compute 5d $\mathcal{N}=1^*$ 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 $\mathcal{N}=(0,4)$ 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.