Wilson surfaces in M5-branes

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 $\mathcal{N}=1^{\ast }$ 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.

arXiv comment30 pages, 6 figures, 4 tables

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• Fiber-base duality from the algebraic perspective
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• Web Construction of ABCDEFG and Affine Quiver Gauge Theories
• Elliptic Quantum Curves of 6d SO(N) theories
• Elliptic Quantum Curves of Class ${\mathcal{S}}_k$
• Topological strings and Wilson loops
• Blowup Equations for Little Strings
• R-matrices and Miura operators in 5d Chern-Simons theory
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• Surface Operators in Superspace
• D-type Minimal Conformal Matter: Quantum Curves, Elliptic Garnier Systems, and the 5d Descendants
• OPE of line defects in 5d $E_n$ SCFT