ASPECTS OF WILSON LOOPS AND MINIMAL SURFACES IN ADS/CFT

Abstract

With an eye towards better understanding the AdS/CFT correspondence, in this thesis we study the 1d defect conformal field theory (CFT) living on the half-BPS Wilson line in N=4 Super Yang-Mills and its dual description via the AdS2 string in AdS5xS5. The first half of the thesis, based on work with Simone Giombi, Shota Komatsu and Jieru Shan, develops the formalism for computing boundary correlators on the AdS2 string in conformal gauge and explores its consequences. A key role is played by the boundary reparameterization mode that maps the worldsheet boundary coordinate to the target space coordinate along the Wilson line and whose practical effect is to mediate interactions between transverse fluctuations of the string. We determine its effective action to cubic order in a saddle point expansion and compute the tree-level four- and six-point boundary correlators, which match results in static gauge. We also use the reparameterization mode to study the out-of-time-order correlators (OTOCs), both at leading order via analytic continuation and to all orders in a double-scaling limit by resumming a relevant subset of diagrams. These methods nicely complement analyses of the OTOCs in terms of scattering processes on the worldsheet or geodesics on the worldsheet with shockwaves. The second half of the thesis, based on work with Simone Giombi and Shota Komatsu, examines a large charge sector of the Wilson line defect CFT. We analyze defect correlators of two large charge insertions and several light insertions using both supersymmetric localization and their dual description as expectation values of light vertex operators on a classical string spinning in S5. We also study quantum fluctuations of the spinning string and compute the correlation function of two large charge and two light insertions in terms of Green's functions on the worldsheet, which we use to extract CFT data for a tower of operators on the defect.