# Freddy Cachazo

Gluskin Sheff/Onex Freeman Dyson Chair in Theoretical Physics

Perimeter Institute for Theoretical Physics

Areas of research:

### 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

- September 2009 - June 2010 School of Natural Sciences. Institute for Advanced Study. Princeton NJ. Member.
- 2005-present. University of Waterloo. Adjunct professor.
- 2005-present. Perimeter Institute. Faculty Member
- 2002-2005 School of Natural Sciences. Institute for Advanced Study. Princeton NJ. Postdoctoral Member.

### Awards

- 2016 CAP-CRM Prize in Theoretical and Mathematical Physics.
- 2014 New Horizons Prize (FPP).
- 2012 Herzberg Medal (CAP).
- 2011 Rutherford Medal, Royal Society of Canada (RSC).
- 2009 Gribov Medal, European Physical Society (EPS)
- Early Reseach Award of Ontario (ERA).

### Recent Publications

- F. Cachazo, S. Mizera and G. Zhang, Scattering Equations: Real Solutions and Particles on a Line, JHEP 1703, 151 (2017) [arXiv: 1609.00008 [hep-th]].
- F. Cachazo, P. Cha and S. Mizera, Extensions of Theories from Soft Limits, JHEP 1606, 170 (2016) [arXiv: 1604.03893 [hep-th]].
- F. Cachazo, S. He and E. Y. Yuan, One-Loop Corrections from Higher Dimensional Tree Amplitudes, JHEP 1608, 008 (2016) [arXiv: 1512.05001 [hep-th]].
- N. Arkani-Hamed, J. L. Bourjaily, F. Cachazo, A. Postnikov and J. Trnka, On-Shell Structures of MHV Amplitudes Beyond the Planar Limit, JHEP 1506, 179 (2015) [arXiv: 1412.8475 [hep-th]].
- F. Cachazo, S. He and E. Y. Yuan, Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM, JHEP 1507, 149 (2015) [arXiv: 1412.3479 [hep-th]].
- N. Arkani-Hamed, J. L. Bourjaily, F. Cachazo and J. Trnka, Singularity Structure of Maximally Supersymmetric Scattering Amplitudes, Phys. Rev. Lett. 113, no. 26, 261603 (2014) [arXiv: 1410.0354 [hep-th]].
- F. Cachazo, S. He and E. Y. Yuan, Einstein-Yang-Mills Scattering Amplitudes From Scattering Equations, JHEP 1501 (2015) 121 [arXiv: 1409.8256 [hep-th]].
- F. Cachazo, S. He and E. Y. Yuan, Scattering of Massless Particles: Scalars, Gluons and Gravitons, JHEP 1407, 033 (2014) [arXiv: 1309.0885 [hep-th]].
- F. Cachazo, S. He and E. Y. Yuan, Scattering of Massless Particles in Arbitrary Dimensions, Phys. Rev. Lett. 113, no. 17, 171601 (2014) [arXiv: 1307.2199 [hep-th]].
- F. Cachazo, S. He and E. Y. Yuan, Scattering equations and Kawai-Lewellen-Tye orthogonality, Phys. Rev. D 90, no. 6, 065001 (2014) [arXiv: 1306.6575 [hep-th]].
- F. Cachazo, S. He and E. Y. Yuan, Scattering in Three Dimensions from Rational Maps, JHEP 1310, 141 (2013) [arXiv: 1306.2962 [hep-th]].
- F. Cachazo, L. Mason and D. Skinner, Gravity in Twistor Space and its Grassmannian Formulation, SIGMA 10, 051 (2014) [arXiv: 1207.4712 [hep-th]].
- F. Cachazo and D. Skinner, Gravity from Rational Curves, Phys. Rev. Lett. 110, 161301 (2013) [arXiv: 1207.0741 [hep-th]].
- Connecting Scalar Amplitudes using The Positive Tropical Grassmannian, Freddy Cachazo and Bruno Umbert, arXiv: 2205.02722
- Biadjoint Scalars and Associahedra from Residues of Generalized Amplitudes, Freddy Cachazo, and Nick Early, arXiv: 2204.01743
- Smoothly Splitting Amplitudes and Semi-Locality, Freddy Cachazo, Nick Early, and Bruno Umbert, arXiv: 2112.14191
- Freddy Cachazo, Diagonally Embedded Sets of ${\rm Trop}^+G(2,n)$'s in ${\rm Trop}\, G(2,n)$: Is There a Critical Value of $n$? arXiv: 2104.10628
- Freddy Cachazo and Nicholas Early, Planar Kinematics: Cyclic Fixed Points, Mirror Superpotential, k-Dimensional Catalan Numbers, and Root Polytopes, arXiv: 2010.09708
- F. Cachazo and N. Early, Minimal Kinematics: An all $k$ and $n$ peek into ${\rm Trop}^+G(k,n)$, arXiv: 2003.07958
- F. Cachazo, A. Guevara, B. Umbert, and Y. Zhang, Planar Matrices and Arrays of Feynman Diagrams, arXiv: 1912.09422
- F. Cachazo, B. Umbert, and Y. Zhang, Singular Solutions in Soft Limits, JHEP05(2020)148, [arXiv: 1911.02594]
- F. Borges and F. Cachazo, Generalized Planar Feynman Diagrams: Collections, arXiv: 1910.10674 [hep-th].
- F. Cachazo, K. Yeats and S. Yusim, Compatible Cycles and CHY Integrals, arXiv: 1907.12661 [math-ph].
- F. Cachazo and J. M. Rojas, Notes on Biadjoint Amplitudes, Trop G(3,7) and X(3,7) Scattering Equations, arXiv: 1906.05979 [hep-th].
- F. Cachazo, N. Early, A. Guevara and S. Mizera, Scattering Equations: From Projective Spaces to Tropical Grassmannians, JHEP 1906, 039 (2019) [arXiv: 1903.08904 [hep-th]].
- F. Cachazo, N. Early, A. Guevara and S. Mizera, Delta-algebra and scattering amplitudes, JHEP 1902 (2019) 005 [arXiv: 1812.01168 [hep-th]].
- F. Cachazo, A. Guevara, M. Heydeman, S. Mizera, J. H. Schwarz and C. Wen, The S Matrix of 6D Super Yang-Mills and Maximal Supergravity from Rational Maps, arXiv: 1805.11111 [hep-th].
- F. Cachazo, Combinatorial Factorization, arXiv: 1710.04558 [hep-th].
- F. Cachazo and A. Guevara, Leading Singularities and Classical Gravitational Scattering, arXiv: 1705.10262 [hep-th].
- Grassmannian Geometry of Scattering Amplitudes, N. Arkani-Hamed, J. Bourjaily, F. Cachazo, A. Goncharov, A. Postnikov, J. Trnka, Cambridge University Press, 2016

### Seminars

- Worldsheet Approaches to Field Theory Amplitudes. Discussion Session. Strings 2021. ICTP-SAIFR (virtual). June 2021
- Amplitudes 2020. Plenary talk. On-line conference hosted by Brown University, Rhode Island, USA, May 2020
- Quantum Theory and Symmetries 2019. Plenary talk. CRM, Montreal, Canada, July 2019
- Invited talk at the Annual Canadian Association of Physicists (CAP) Congress. "From the NLSM to the Probe M5-brane". Dalhousie University. Halifax, NS, June 2018
- Tutte Colloquium: "Combinatorics in Scattering Amplitudes", Department of Combinatorics and Optimization. University of Waterloo. May 2018
- Inaugural Math Science Lectures in Honor of Raoul Bott: "Geometry and Combinatorics in Particle Interactions". Series of two lectures at the Harvard University Center of Mathematical Sciences and Applications (CMSA). April 2018
- Series of four lectures at the CERN Winter School on Supergravity, Strings and Gauge Theory 2018. CERN, Geneva, Switzerland. February 2018.
- Series of five lectures at the Kavli Asian Winter School on Strings, Particles and Cosmology 2018. International Centre for Theoretical Sciences (ICTS), Bangalore, India. January 2018.
- Plenary talk on ``Amplitudes from Riemann Spheres", LoopFest XV, University of Buffalo, NY, USA, August 2016.
- Plenary talk on ``S-Matrix Theory", Canadian Association of Physicist Congress, University of Ottawa, Canada, June 2016.
- Plenary talk on ``Unification and Extension", Theory CANADA 11, Carleton University, Ottawa, Canada, June 2016.
- Plenary talk on "Developments in String and Field Theory" at the European Physical Society 2015 meeting in Vienna, Austria, July 2015.
- Five lectures at TASI 2015 "New Frontiers in Fields and Strings", University of Colorado, Colorado, USA, June 2015
- Plenary talk at Amplitudes 2015, EHT, Zurich, Switzerland, June 2015
- Plenary talk at PASCOS 2015, Abdus Salam ICTP, Trieste, Italy, June 2015
- Series of three lectures given at the Spring School on Superstring Theory and Related Topics. Abdus Salam ICTP, Trieste, Italy, March 2015
- Colloquium. Department of Physics, University of Toronto, Toronto, Canada, March 2015
- Plenary talk at STRINGS 2014 in Princeton USA.
- Plenary talk at Quantum Gravity in Paris 2014. Paris. March 2014.
- PIRSA:18040049, PSI 2017/2018 - Scattering Amplitudes in QFT & String Theory - Lecture 17, 2018-04-27, PSI 2017/2018 - Scattering Amplitudes in QFT & String Theory (Cachazo)
- PIRSA:18040048, PSI 2017/2018 - Scattering Amplitudes in QFT & String Theory - Lecture 16, 2018-04-26, PSI 2017/2018 - Scattering Amplitudes in QFT & String Theory (Cachazo)
- PIRSA:18040047, PSI 2017/2018 - Scattering Amplitudes in QFT & String Theory - Lecture 15, 2018-04-25, PSI 2017/2018 - Scattering Amplitudes in QFT & String Theory (Cachazo)
- PIRSA:18040046, PSI 2017/2018 - Scattering Amplitudes in QFT & String Theory - Lecture 14, 2018-04-24, PSI 2017/2018 - Scattering Amplitudes in QFT & String Theory (Cachazo)
- PIRSA:18040045, PSI 2017/2018 - Scattering Amplitudes in QFT & String Theory - Lecture 13, 2018-04-23, PSI 2017/2018 - Scattering Amplitudes in QFT & String Theory (Cachazo)
- PIRSA:18040044, PSI 2017/2018 - Scattering Amplitudes in QFT & String Theory - Lecture 12, 2018-04-20, PSI 2017/2018 - Scattering Amplitudes in QFT & String Theory (Cachazo)
- PIRSA:18040133, Welcome and Opening Remarks, 2018-04-16, New Directions in Conventional and Ambitwistor String Theories
- PIRSA:18040040, PSI 2017/2018 - Scattering Amplitudes in QFT & String Theory - Lecture 6, 2018-04-16, PSI 2017/2018 - Scattering Amplitudes in QFT & String Theory (Cachazo)
- PIRSA:18040039, PSI 2017/2018 - Scattering Amplitudes in QFT & String Theory - Lecture 5, 2018-04-13, PSI 2017/2018 - Scattering Amplitudes in QFT & String Theory (Cachazo)
- PIRSA:18040038, PSI 2017/2018 - Scattering Amplitudes in QFT & String Theory - Lecture 4, 2018-04-12, PSI 2017/2018 - Scattering Amplitudes in QFT & String Theory (Cachazo)
- PIRSA:18040037, PSI 2017/2018 - Scattering Amplitudes in QFT & String Theory - Lecture 3, 2018-04-11, PSI 2017/2018 - Scattering Amplitudes in QFT & String Theory (Cachazo)
- PIRSA:18040036, PSI 2017/2018 - Scattering Amplitudes in QFT & String Theory - Lecture 2, 2018-04-10, PSI 2017/2018 - Scattering Amplitudes in QFT & String Theory (Cachazo)
- PIRSA:18040035, PSI 2017/2018 - Scattering Amplitudes in QFT & String Theory - Lecture 1, 2018-04-09, PSI 2017/2018 - Scattering Amplitudes in QFT & String Theory (Cachazo)
- Academics Program Department Presentation to the Scientific Advisory Committee, October 2015.
- PIRSA:15060045, Welcome to Convergence - Opening Panel: Physics Today, 2015-06-22, Convergence
- PIRSA:15050055, Scattering Amplitudes and Riemann Surfaces, 2015-05-27, Geometry and Physics 2015
- PIRSA:15050063, Scattering Amplitudes and Riemann Surfaces, 2015-05-26, Geometry and Physics 2015
- PIRSA:15050047, Scattering Amplitudes and Riemann Surfaces, 2015-05-25, Geometry and Physics 2015
- PIRSA:14100026, 14/15 PSI - Conformal Field Theory - Lecture 14, 2014-10-24, 14/15 PSI - Conformal Field Theory
- PIRSA:14100025, 14/15 PSI - Conformal Field Theory - Lecture 13 , 2014-10-23, 14/15 PSI - Conformal Field Theory
- PIRSA:14100024, 14/15 PSI - Conformal Field Theory - Lecture 12 , 2014-10-22, 14/15 PSI - Conformal Field Theory
- PIRSA:14100023, 14/15 PSI - Conformal Field Theory - Lecture 11 , 2014-10-21, 14/15 PSI - Conformal Field Theory
- PIRSA:14100022, 14/15 PSI - Conformal Field Theory - Lecture 10, 2014-10-20, 14/15 PSI - Conformal Field Theory
- Quantum Gravity Group Meeting. Resultants and Gravity Amplitudes.