  We introduce a notion of holonomy in twistor space and construct a holonomy
operator by use of a spinor-momenta formalism in twistor space. The holonomy
operator gives a monodromy representation of the Knizhnik-Zamolodchikov (KZ)
equation, which is mathematically equivalent to a linear representation of a
braid group. We show that an S-matrix functional for gluon amplitudes can be
expressed in terms of a supersymmetric version of the holonomy operator. A
variety of mathematical and physical concepts, such as integrability, general
covariance, Lorentz invariance and Yangian symmetry, are knit together by the
holonomy operator. These results shed a new light on gauge theories in
four-dimensional spacetime.
