Higher-Loop amplitudes on the sphere: a new approach to the perturbative expansion of quantum field theories
Almost all we know about particle physics and the Standard Model comes
from scattering experiments and our ability to predict them via
scattering amplitudes (these measure probabilities of scattering
processes). To meet the impressive technological advances of particle
colliders like the Large Hadron Collider at CERN, new tools and
concepts have emerged over the last 25 years. More than giving
methods, they have triggered a revolution in our understanding of the
formal microscopic structure of particle physics, a subject people
thought they knew everything about.

My program is based on a set of formulæ due to Cachazo, He & Yuan
(CHY), that challenge the way we think about scattering
amplitudes. They relate to 'twistor' ideas and string theory. The
former aims at manifesting the geometry of field theories, but failed
so far to grasp their quantum-ness. The latter, in spite of its
mathematical beauty, has the drawback of having additional
contributions that are hard to decouple from the field theory
ones. The CHY formulæ retain the advantages of both methods, and lead
to a variety of remarkable expressions for scattering amplitudes in a
increasing number of theories, including gauge, gravity and scalar
theories.

In a crucial work, I showed that these methods actually carry over to
the first quantum correction: this was the first time ever that
twistor methods were shown to work at the quantum level. My project
aims to extend this and reformulate the full pertubative quantum
expansion of field theories in the CHY language. This would be a major
conceptual advance. I explain that to do so will require to understand
a more fundamental object called Null String, whose quantization will
shed light on my 'quantum CHY formalism'. I also propose applications
of the formalism of interest for LHC physic, like a third order
calculation for the 2 to 3 gluon scattering in gauge theory,  that
all other existing methods have failed to determine so far.