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 \U0001d4ac introduced in [1] which computes observables in the \U0001d4ac- cohomology. We classify general defects of different codimensions in the mathcal{N} = 4 SYM that belong to the \U0001d4ac-cohomology, which form 1 -BPS defect networks. By performing the \U0001d4ac- 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 AdS5× S5.
Highlights
The N = 4 super-Yang-Mills (SYM) theory in four spacetime dimensions is one of the most well-studied quantum field theories in recent decades
By performing the localization of the N = 4 SYM on the four-dimensional hemisphere, we discover a novel defect-Yang-Mills theory on a submanifold given by the two-dimensional hemisphere and described by two-dimensional Yang-Mills coupled to topological quantum mechanics on the boundary circle
As a simple application of the dYM setup, we show such defect correlators are computed by standard matrix model techniques in the leading strong coupling limit, and in perfect match with results from IIB string theory on AdS5 ×S5 [38]
Summary
We extend the 4d/2d setup of [1, 18, 19] by classifying general conformal defects of the 4d N = 4 SYM in the Q-cohomology, which include, in addition to the Wilson loops and ’t Hooft loops, interfaces (or boundaries) and surface operators. When the interface hosts a local 3d N = 4 SCFT, this includes a 1d protected subsector of the full 3d operator algebra, known as the 1d topological quantum mechanics (TQM) on this S1 [29,30,31] For this reason, we refer to the equator (boundary) S1 as ST1 QM.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
