Freddy Cachazo

Freddy Cachazo profile picture
Deputy Faculty Chair
Gluskin Sheff/Onex Freeman Dyson Chair in Theoretical Physics
Perimeter Institute for Theoretical Physics
If you are interested in pursuing a MSc degree, please apply to the Perimeter Scholars International (PSI) masters program. If you are interested in working with me as a PhD student, please submit an application directly to my department at the University of Waterloo and indicate that you would like to be supervised by me
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.
  • Member, School of Natural Sciences. Institute for Advanced Study. Princeton, 2009-2010
  • Adjunct professor, University of Waterloo, 2005-present
  • Postdoctoral Member, School of Natural Sciences. Institute for Advanced Study. Princeton, 2002-2005
  • Discovery Grant, Natural Sciences and Engineering Research Council of Canada (NSERC), 2022
  • CAP-CRM Prize in Theoretical and Mathematical Physics, Canadian Association of Physicists, 2016
  • New Horizons in Physics Prize, Breakthrough Prize Foundation, 2014
  • Herzberg Medal, Canadian Association of Physicists (CAP), 2012
  • Rutherford Medal, Royal Society of Canada (RSC), 2011
  • Gribov Medal, European Physical Society, 2009
  • Early Research Award, Province of Ontario, 2007
  • Cachazo, F., Early, N., & Zhang, Y. (2024). Generalized color orderings: CEGM integrands and decoupling identities. Nuclear Physics B, 1004, 116552. doi:10.1016/j.nuclphysb.2024.116552
  • Cachazo, F., Guevara, A., Umbert, B., & Zhang, Y. (2024). Planar matrices and arrays of Feynman diagrams. Communications in Theoretical Physics, 76(3), 035002. doi:10.1088/1572-9494/ad102d
  • Cachazo, F., Early, N., & Zhang, Y. (n.d.). Color-Dressed Generalized Biadjoint Scalar Amplitudes: Local Planarity. Symmetry Integrability and Geometry Methods and Applications. doi:10.3842/sigma.2024.016
  • Cachazo, F., & Early, N. (2024). Planar kinematics: cyclic fixed points, mirror superpotential, $k$-dimensional Catalan numbers, and root polytopes. Annales de l’Institut Henri Poincaré D. doi:10.4171/aihpd/185
  • Cachazo, F., & Early, N. (n.d.). Biadjoint scalars and associahedra from residues of generalized amplitudes. Journal of High Energy Physics, 2023(10), 15. doi:10.1007/jhep10(2023)015
  • Cachazo, F., Early, N., & Umbert, B. G. (n.d.). Smoothly splitting amplitudes and semi-locality. Journal of High Energy Physics, 2022(8), 252. doi:10.1007/jhep08(2022)252
  • Cachazo, F., & Umbert, B. G. (2022). Connecting Scalar Amplitudes using The Positive Tropical Grassmannian. doi:10.48550/arxiv.2205.02722
  • Cachazo, F., & Early, N. (2022). Biadjoint Scalars and Associahedra from Residues of Generalized Amplitudes. doi:10.48550/arxiv.2204.01743
  • Cachazo, F., & Early, N. (n.d.). Minimal Kinematics: An All k and n Peek into Trop+G(k,n). Symmetry Integrability and Geometry Methods and Applications. doi:10.3842/sigma.2021.078
  • Cachazo, F. (2021). Diagonally Embedded Sets of ${\rm Trop}^+G(2,n)$'s in ${\rm Trop}\, G(2,n)$: Is There a Critical Value of $n$?. arxiv:2104.10628v1
  • Arrangements of Pseudolines, Tropical Grassmannians, and Generalized Scattering Amplitudes, University of Waterloo, Department of Combinatorics and Optimization, 200 University Ave., Waterloo, Ontario, ON N2L 3G1, Canada, 2023/03/30