Non-perturbative Field Theory

In this talk we review recent developments which enable us to use techniques of integrable twodimensional quantum field theories to solve exactly four dimensional N=4 gauge theory through the use of the AdS/CFT correspondence. By ‘solve’ we mean here to find all anomalous dimensions of all operators of the theory for any value of the gauge coupling. We illustrate the methods with the case of the Konishi operator, the simplest operator not protected by supersymmetry, whose perturbative anomalous dimension can be computed from the string side of the AdS/CFT correspondence and is in exact agreement with a direct gauge theory perturbative computation.