Description du projet
De nouvelles connaissances sur les mathématiques des cordes vibrantes qui pourraient constituer notre Univers
La théorie des cordes soutient l’idée que les particules fondamentales de notre Univers ne sont pas vraiment des particules, mais de minuscules cordes qui vibrent. Les amplitudes de diffusion des supercordes décrivent l’interaction des états physiques et sont essentielles à la caractérisation des observables physiques. L’étude des amplitudes de diffusion des supercordes fait appel aux mathématiques de pointe et a conduit à la découverte de nouvelles structures mathématiques. Le projet HIPSAM, financé par l’UE, fera avancer notre compréhension des amplitudes des supercordes avec des applications potentielles aussi bien dans le domaine général des mathématiques que dans la théorie quantique des champs et les expériences menées avec les accélérateurs de particules.
Objectif
In this interdisciplinary project we will describe the mathematical structure of superstring amplitudes in genus one and two, generalizing recent beautiful progress made at genus zero. This will enable us to present original ideas for advancing in the study of higher-genus polylogarithms, and at the same time to obtain new information on string theory predictions for fundamental interactions. To reach our goal, we will focus on three main research directions, and we will collaborate with some of the world-leading experts on the subject, among which my host supervisor P. Vanhove. In particular, we will complete the description of genus-one superstring amplitudes in terms of elliptic polylogarithms, we will begin a systematic analysis of the special functions involved at genus two and we will push the computation of the low-energy expansion of closed-string amplitudes. Parts of this project will require advanced tools from algebraic geometry, which we plan to discuss with the secondment supervisor F. Brown at University of Oxford. The Theoretical Physics Institute (IPhT, Saclay) of CEA (host institution) is one of the few places in Europe hosting international experts in all branches of mathematical physics related to the topic of this proposal. The results obtained will point towards new directions in many fields of mathematics, such as mixed motives and moduli spaces of curves, opening new research gates completely inspired by physics. On the other side, the techniques developed will allow to attack similar nowadays intractable computations of amplitudes in quantum field theory, which can be compared with the experimental data produced by particle accelerators.
Champ scientifique
- natural sciencesphysical sciencestheoretical physicsparticle physicsparticle accelerator
- natural sciencesmathematicsapplied mathematicsmathematical physics
- natural sciencesphysical sciencesquantum physicsquantum field theory
- natural sciencesphysical sciencestheoretical physicsstring theory
- natural sciencesmathematicspure mathematicsalgebraalgebraic geometry
Mots‑clés
Programme(s)
Régime de financement
MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF)Coordinateur
75015 PARIS 15
France