Taming Defects in $\mathcal{N}=4$ Super-Yang-Mills

Understand

We study correlation functions involving extended defect operators in the four-dimensional ${\cal N}=4$ super-Yang-Mills (SYM).

• The main tool is supersymmetric localization with respect to the supercharge $\cal Q$ introduced in \cite{Pestun:2009nn} which computes observables in the $\cal Q$-cohomology.
• We classify general defects of different codimensions in the ${\cal N}=4$ SYM that belong to the $\cal Q$-cohomology, which form ${1\over 16}$-BPS defect networks.
• By performing the $\cal Q$-localization of the ${\cal N}=4$ SYM on the four-dimensional hemisphere, we discover a novel defect-Yang-Mills (dYM) theory on a submanifold given by the two-dimensional hemisphere and described by (constrained) two-dimensional Yang-Mills coupled to topological quantum mechanics on the boundary circle.