Holonomies of gauge fields in twistor space 1: bialgebra, supersymmetry, and gluon amplitudes
arXiv:0906.2524 · doi:10.1016/j.nuclphysb.2009.09.026
Abstract
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.
30 pages; v2,3. references added + minor changes; v4. published version
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