Wilson loops in Gauge theory and holography

Abstract

Wilson loops are among the most interesting observables one can consider in any gaune theory. They are non-local operators associated to the phase acquired by a charged particle propagating in a gauge field. Being non-local, they capture global informations about the theory they probe and, among other things, can serve as order parameters for confinement/deconfinemont phase transitions and can give information about the energy radiated by accelerated particles. In 3-dimensional Chern-Simons theory, their expectation value computes knot invariants. In supersymmetric theories, Wilson loops are particularly interesting, as they can sometimes be computed exactly in the parameters of the theory, thanks to supersymmetric localization. These exact results are then useful to test non-perturbative dualities, most notably S-duality and gauge/ string dualities. In the former case, a Wilson loop can be mapped to its dual’t Hooft operator, while in the latter case; it can be mapped - at strong coupling - to certain minimal surfaces in the bulk of the AdS space. This proposal aims to push forward our understanding of Wilson loops in both gauge theories and their holographic duals. We will combine new and old techniques to address current problems in this subject. We plan to understand generic deformations of the circular 1/2 BPS Wilson loop, including the relation between Wilson loops and the conformal bootstrap. On the holographic side, we will use coincident giant Wilson loops to resolve long-standing problems in non-Abelian DSI theory, and we will generalize results known for Wilson loops in 4-dimensional theories to 3-dimensions. (AU)