18 | IHES Annual Report 2020
Slava RYCHKOV Theoretical Physics, permanent professor since 2017.
With D. J. Binder Deligne Categories in Lattice Models and Quantum Field Theory, or Making Sense of O(N) Symmetry with Non-integer N J. High Energ. Phys. 2020, 117 (2020), pre publication arXiv:1911.07895.
With A. Kaviraj and E. Trevisani Random Field Ising Model and Parisi-Sourlas Supersymmetry I. Supersymmetric CFT J. High Energ. Phys. 2020, 90 (2020), pre publication arXiv:1912.01617.
Random Field Ising Model and Parisi-Sourlas Supersymmetry II. Renormalization Group Pre publication arXiv:2009.10087.
With A. Giuliani and V. Mastropietro Gentle Introduction to Rigorous Renormalization Group: a Worked Fermionic Example Pre publication arXiv:2008.04361.
3D Ising Model: a View from the Conformal Bootstrap Island C. R. Physique 21 (2020)2, pre publication arXiv:2007.14315.
With P. Kravchuk and J. Qiao Distributions in CFT, Part I. Cross-Ratio Space J. High Energ. Phys. 2020, 137 (2020), pre publication arXiv:2001.14315
New Horizons Prize in Physics (2014) Institut Universitaire de France, junior member (2012-2017) Grand prix Mergier Bourdeix, Académie des sciences de Paris (2019)
Editor of: SciPost Physics Communications in Mathematical Physics
SLAVA RYCHKOV, in collaboration with postdocs Apratim Kaviraj and Emilio Trevisani, resolved a long-standing puzzle concerning phase transition in lattice models with magnetic impurities (random field Ising model). Their work explained why, from the renormalization group theory point of view, an old and famous conjecture by Giorgio Parisi and Nicolas Sourlas only holds above a certain critical dimension. The conjecture was that the transition in d dimensions must exhibit a form of supersymmetry and the same critical exponents as the ordinary Ising model in d-2 dimensions. His project concerned the renormalization group. In collaboration with mathematical
physicists Prof. Alessandro Giuliani (University of Rome) and Prof. Vieri Mastropietro (University of Milan), he developed a rigorous renormalization group theory of non-Gaussian fixed points in models containing only fermionic fields, establishing the analytic dependence of critical indices on these models parameters. This work is an example of historical continuity and relates to articles from the 1980s written by the late IHES professor Oscar E. Lanford III, and Krzysztof Gawędzki, then CNRS researcher at IHES. Slava Rychkov is also continuing his collaboration with his PhD student Jiaxin Qiao and postdoc Petr Kravchuk (IAS Princeton) on the analytic continuation of Euclidean conformal field theories towards the Lorentzian signature. Preliminary results were reported in his Cours de l'IHES in 2019, and in an online seminar Analysis, Quantum Fields, and Probability in 2020. The first article on this project has now appeared in JHEP, and three more are in preparation. In addition, he has recently started a collaboration with PhD student Benoit Sirois, postdoc Marten Reehorst, and Prof. Balt van Rees (École polytechnique) to develop a new numerical conformal bootstrap algorithm. Preliminary results are encouraging.