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

TL;DR

This paper introduces a holonomy operator in twistor space that represents gluon amplitudes and connects various mathematical and physical concepts like integrability and Yangian symmetry, offering new insights into gauge theories.

Contribution

It constructs a supersymmetric holonomy operator in twistor space that encodes gluon scattering amplitudes and relates to the KZ equation and braid group representations.

Findings

Holonomy operator provides a monodromy representation of the KZ equation.

Gluon amplitudes are expressed via a supersymmetric holonomy operator.

Connections between gauge theories, integrability, and symmetries are established.

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.