Spin chains from gauge theories

Abstract: The large N limit of t’Hooft relates certain gauge theories to string theory. The limit states that the two formulations can be dual to each other. A natural question then arises: how can one see the string dynamics directly from the gauge theory? This is important beacuse QCD confinement is supposed to be produced by flux tubes stretching between quarks and these flux tubes are governed by an effective string dynamics. I will argue that in many setups, the string dynamics can be reduced to a type of Hamiltonian lattice theory on a spin chain, where perturbative methods on the gauge theory side produce a list of effective Hamiltonians on the spin chain. At leading order the Hamiltonian is nearest neighbor and to higher orders there appear next to nearest neighbor interactions and so on. I will describe two such applications. The first applucation is the (perturbative) computation of anomalous dimensions in the maximally sipersymmetric field theory. The second application is to the study of the Hamiltonian formulation of pure QCD on a lattice by doing a strong coupling expansion. I will describe what the future of this second program for QCD looks like and what one would hope to obtain from such a formulation.