Freddy Cachazo

Massless particles are the backbone of our best theory of nature; the Standard Model of particle physics and gravity. In 2003, Witten combined twistor theory and string theory to produce a new formulation for the scattering matrix of gauge bosons - massless particles of helicity plus or minus one. Finding a similar formulation for gravitons - particles with helicity plus or minus two - remained an important open problem until 2012 when in collaboration with Y. Geyer (a PSI student), I found one such formulation. Not long after this first formulation was found, I found a second one with D. Skinner (a PI postdoctoral fellow). All these constructions are based on four dimensional kinematics. A natural question is the existence of similar constructions in other dimensions. In 2013 and in collaboration with S. He (a PI postdoctoral fellow) and E. Yuan (a PI graduate student), I found a construction for scalars, gluons and gravitons in arbitrary dimensions. This is now known as the CHY construction and it gives tree-level scattering matrices of a large variety of theories, including gluons and gravitons, in any dimension as integrals over the space of n-points on a one-dimensional complex projective space. In the spring of 2019 and in collaboration A. Guevara, S. Mizera (both my graduate students) and N. Early (a postdoc at MIT) I found a generalization of the CHY formulation to n-points on higher dimensional projective spaces. This has deep connections to tropical geometry and is giving a natural framework for exploring ways of going beyond standard quantum field theory.