Supersymmetric Wilson loops

TL;DR

The paper investigates Wilson loops in ${\cal N}=4$ SYM that preserve 1/16, 1/8, or 1/4 of the supersymmetry, examining both weak-coupling perturbative cancellations and strong-coupling AdS/CFT descriptions. It demonstrates that 1/4 BPS planar loops are not renormalized at the perturbative level and, at strong coupling, correspond to degenerate minimal surfaces in $AdS_5\times S^5$ whose moduli cancel the classical area, yielding $\langle W_s(C)\rangle=1$ for planar contours like the circle. Non-planar, less-supersymmetric loops retain coupling dependence through zero-mode counting in the string partition function. The results illuminate non-renormalization mechanisms, reflect the geometry of $S^5$ moduli in holography, and extend considerations to ${\cal N}=2$ theories, offering tests of AdS/CFT via Wilson loop observables.

Abstract

I construct 1/16, 1/8 and 1/4 BPS Wilson loops in N=4 supersymmetric Yang-Mills theory and argue that expectation values of 1/4 BPS loops do not receive quantum corrections. At strong coupling, non-renormalization of supersymmetric Wilson loops implies subtle cancellations in the partition function of the AdS string with special boundary conditions. The cancellations are shown to occur in the semiclassical approximation.

Figures (1)

• Figure 1: Feynman diagrams of leading and next-to-leading orders.