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

Abstract

We study correlation functions involving extended defect operators in the four-dimensional $\mathcal{N}=4$ super-Yang-Mills (SYM). The main tool is supersymmetric localization with respect to the supercharge $\mathcal{Q}$ introduced in \cite{Pestun:2009nn} which computes observables in the $\mathcal{Q}$-cohomology. We classify general defects of different codimensions in the $\mathcal{N}=4$ SYM that belong to the $\mathcal{Q}$-cohomology, which form $\frac{1}{16}$-BPS defect networks. By performing the $\mathcal{Q}$-localization of the $\mathcal{N}=4$ 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. This also generalizes to interface defects in $\mathcal{N}=4$ SYM by the folding trick. We provide explicit dictionary between defect observables in the SYM and those in the dYM, which enables extraction of general $\frac{1}{16}$-BPS defect network observables of the SYM from two-dimensional gauge theory and matrix model techniques. Applied to the D5 brane interface in the $SU(N)$ SYM, we explicitly determine a set of defect correlation functions in the large $N$ limit and obtain precise matching with strong coupling results from IIB supergravity on $Ad{S}_5\times S^5$.

arXiv comment91 pages, 2 figures; v3: minor corrections and more references added

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