Taming defects in N = 4 super-Yang-Mills

Abstract

We study correlation functions involving extended defect operators in the four- dimensional N = 4 super-Yang-Mills (SYM). The main tool is supersymmetric localization with respect to the supercharge introduced in [1] which computes observables in the - cohomology. We classify general defects of different codimensions in the N = 4 SYM that belong to the -cohomology, which form 1 -BPS defect networks. By performing the - localization of the 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 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 116 -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 AdS5× S5.