N=4 Super Yang-Mills: the harmonic oscillator of interacting quantum field theories

Full text: In this talk I discuss progress over the last ten years in solving N=4 Super Yang-Mills in the planar limit, where the number of colors is taken to infinity. The key to the solution is mapping the theory to an integrable one-dimensional spin chain. At the leading perturbative level the spin-chain in question is the Heisenberg chain which was solved by Bethe in 1931. We discuss how the analysis of spin-chains ultimately allows to compute the spectrum of observables in the theory for any value of the coupling constant. I then discuss ongoing work to find the so-called three-point functions, which when combined with the spectrum would completely solve the theory in the planar limit. (author)