Correlation functions in maximally supersymmetric Yang-Mills theory

• Main Author: Sikorowski, Jakub
• Other Authors: Alday, Luis ; Starinets, Andrei
• Published: University of Oxford 2015
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.730501

In this thesis we consider the planar maximally supersymmetric Yang-Mills theory. First, we look at the correlation function of a null Wilson loop with four edges and a local operator at weak coupling. We use the Lagrangian insertion technique to find the integral representation up to two loops. Performing the integrals with a method closely linked to the dual space formalism for the scattering amplitudes, we explicitly compute the two loop result. We demonstrate the connection between the calculated observable and the cusp anomalous dimension by recovering the three loop value of the cusp anomalous dimension. We also explore the advantages of expressing the loop integrand in twistor variables. The second observable we look at is the four point correlation function of the BMN operators on a line at strong coupling. In order to access this regime we perform a semi-classical computation in the classical string theory. Considering area of an extended minimal surface stretched between the four operators, we find two different saddle points. We show that the extended minimal surface is sub-dominant to the saddle point composed of three geodesic strings joining the four operators in a sequence. The result is that, to the leading order at strong coupling, the considered correlation function is equal to its tree-level value when all operators are on a line.