# Freddy Cachazo

Deputy Faculty Chair

Gluskin Sheff/Onex Freeman Dyson Chair in Theoretical Physics

Perimeter Institute for Theoretical Physics

Areas of research:

### Teaching Affiliations

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

### Research Interests

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.

### Positions Held

- 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

### Awards

- 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

### Recent Publications

- 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

### Seminars

- 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
- Worldsheet Approaches to Field Theory Amplitudes, Discussion Session. Strings 2021, ICTP-SAIFR (virtual), 2021/06/01