Correlators of Hopf Wilson loops in the AdS/CFT correspondence

Abstract:

The Wilson loop is one of the most important observables in gauge theories. It has long been suspected that its dynamics should have a natural description in terms of strings. The AdS/CFT correspondence is a realisation of this idea: the expectation value of Wilson loops in maximally supersymmetric Yang-Mills theory (MSYM) in four dimensions is captured by the partition function of type IIB superstring theory on AdS₅ x S⁵, satisfying suitable boundary conditions. Accordingly, the MSYM computation at strong coupling is equivalent to a semiclassical approximation on the string theory side, and amounts to finding certain minimal area surfaces in AdS₅ x S⁵.

In this talk, we deal with the correlator of two (supersymmetric) Wilson loops with contours lying on Hopf fibers of S³. A connected classical string surface, linking two different fibers, is presented. This string theory solution describes oppositely oriented fibers, and it is able to interpolate between a supersymmetric and non-supersymmetric configuration according to the fiber position on the Hopf base. We show that the system can be thought of as a deformation of the ordinary anti-parallel lines describing the static quark-antiquark potential, which is indeed correctly reproduced, at weak and strong coupling, as the fibers approach one another.