Euclidean Wilson Loops and Riemann Theta Functions

          @misc{ scivideos_PIRSA:11080043,
            doi = {10.48660/11080043},
            url = {https://pirsa.org/11080043},
            author = {Kruczenski, Martin},
            keywords = {},
            language = {en},
            title = {Euclidean Wilson Loops and Riemann Theta Functions},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2011},
            month = {aug},
            note = {PIRSA:11080043 see, \url{https://scivideos.org/pirsa/11080043}}
          }
          

Abstract

For N=4 super Yang-Mills theory, in the large-N limit and at strong coupling, Wilson loops can be computed using the AdS/CFT correspondence. In the case of flat Euclidean loops the dual computation consists in finding minimal area surfaces in Euclidean AdS3 space. In such case very few solutions were known. In this talk I will describe an infinite parameter family of minimal area surfaces that can be described analytically using Riemann Theta functions. Furthermore, for each Wilson loop a one parameter family of deformations that preserve the area can be exhibited explicitly. The area is given by a one dimensional integral over the world-sheet boundary.