ABSTRACT: In a celebrated paper in 1989, E. Witten discovered a beautiful
connection between knot invariants (such as the Jones polynomial) and
the three-dimensional Chern-Simons theory. Since there are similarities
between knot theory and integrable models, it is natural to ask if
there is also a gauge-theory explanation for integrable models.
The answer to this long-standing question was given only recently by
K. Costello in 2013,
who wrote down a Chern-Simons-like partially-topological gauge theory
in four dimensions.
In this talk I will describe my forthcoming papers with K. Costello
and E. Witten,
which explains many results in integrable models from standard perturbative
quantum field theory analysis of Costello’s theory.