  We study two-dimensional integrable field theories from the viewpoint of the
four-dimensional Chern-Simons-type gauge theory introduced recently. The
integrable field theories are realized as effective theories for the
four-dimensional theory coupled with two-dimensional surface defects, and we
can systematically compute their Lagrangians and the Lax operators satisfying
the zero-curvature condition. Our construction includes many known integrable
field theories, such as Gross-Neveu models, principal chiral models with
Wess-Zumino terms and symmetric-space coset sigma models. Moreover we obtain
various generalization these models in a number of different directions, such
as trigonometric/elliptic deformations, multi-defect generalizations and models
associated with higher-genus spectral curves, many of which seem to be new.
