  Yang Mills theory in 2+1 dimensions can be expressed as an array of coupled
(1+1)-dimensional principal chiral sigma models. The $SU(N)\times SU(N)$
principal chiral sigma model in 1+1 dimensions is integrable, asymptotically
free and has massive excitations. We calculate all the form factors and
two-point correlation functions of the Noether current and energy-momentum
tensor, in 't~Hooft's large-$N$ limit (some form factors can be found even at
finite $N$). We use these new form factors to calculate physical quantities in
(2+1)-dimensional Yang-Mills theory, generalizing previous $SU(2)$ results from
Orland to $SU(N)$. The anisotropic gauge theory is related to standard
isotropic one by a Wilsonian renormalization group with ellipsoidal cutoffs in
momentum. We calculate quantum corrections to the effective action of QED and
QCD, as the theory flows from isotropic to anisotropic. The exact principal
chiral sigma model S-matrix is also used to examine the spectrum of
(1+1)-dimensional massive Yang Mills theory.
