Abstract

 
We study in depth the (1+1)-dimensional principal chiral sigma model. This is an asymptotically-free  N\times N matrix-valued field with massive excitations. We compute all the form factors of several operators combining the integrable bootstrap program and 't Hooft's large-N limit. These results are used to compute finite volume/temperature expectation values at large N. The matrix structure leads to nontrivial thermodynamics that are not captured by the trivial large-N thermodynamic Bethe ansatz. We also study different Yang-Mills theories in 1+1 and 2+1 dimensions as nonintegrable deformations of the sigma model. We address the problems of quark confinement and the glueball spectrum using ideas of form factor perturbation theory.