  It has recently pointed out that a four-dimensional analog of Chern-Simons
theory provides an elegant framework for understanding integrable models with
spectral parameters. The goal of this short note is to better understand the
relation of this theory to the more standard three-dimensional Chern-Simons
theory. We point out that two Chern-Simons theories, in four dimensions and
three dimensions, are related by a novel T-duality in field theory. We then
discuss this T-duality in string theory. Our T-duality prescription applies to
a more general class of topological quantum field theories, producing mixed
topological/holomorphic theories. This paper is motivated by the observation by
C. Vafa.
