Freddy Cachazo

Freddy Cachazo (PhD Harvard University, 2002) has been a faculty member at Perimeter Institute since 2005. Cachazo is one of the world’s leading experts in the study and computation of scattering amplitudes in gauge theories, such as quantum chromodynamics and N=4 super Yang-Mills, and in Einstein’s gravity theory. He was a member of the School of Natural Sciences at the Institute for Advanced Study in Princeton from 2002 until 2005. His many honors include the Gribov Medal of the European Physical Society (2009), the Rutherford Memorial Medal in Physics from the Royal Society of Canada (2011), the Herzberg Medal from the Canadian Association of Physicists (2012), a New Horizons in Physics Prize from the Fundamental Physics Prize Foundation (2014), and the CAP-CRM Prize in Theoretical and Mathematical Physics from the Canadian Association of Physicists and the Centre de recherches mathématiques (2016). In 2018, he was selected to inaugurate Harvard’s Center of Mathematical Sciences and Applications lecture series on mathematical physics in honor of Raoul Bott.

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.