Perturbative Gauge Theory As A String Theory In Twistor Space

TL;DR

This paper demonstrates that perturbative scattering amplitudes in Yang-Mills theory can be interpreted as string theory in twistor space, revealing deep geometric structures and connections to topological string models.

Contribution

It establishes a link between ${ m N}=4$ super Yang-Mills perturbation theory and a topological string theory in twistor space, providing a geometric interpretation of scattering amplitudes.

Findings

Amplitudes are supported on holomorphic curves in twistor space.

The equivalence relates Yang-Mills perturbation expansion to D-instanton expansion of a topological B model.

Supports the idea of a string theory description underlying gauge theory amplitudes.

Abstract

Perturbative scattering amplitudes in Yang-Mills theory have many unexpected properties, such as holomorphy of the maximally helicity violating amplitudes. To interpret these results, we Fourier transform the scattering amplitudes from momentum space to twistor space, and argue that the transformed amplitudes are supported on certain holomorphic curves. This in turn is apparently a consequence of an equivalence between the perturbative expansion of ${\cal N}=4$ super Yang-Mills theory and the $D$-instanton expansion of a certain string theory, namely the topological $B$ model whose target space is the Calabi-Yau supermanifold $\Bbb{CP}^{3|4}$.