Holonomies of gauge fields in twistor space 1: bialgebra, supersymmetry, and gluon amplitudes

Understand

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.