Séminaires : Séminaire d'Analyse et Géométrie

Equipe(s) :
Responsables :O. Biquard, A. Deruelle, I. Itenberg, X. Ma
Email des responsables : {olivier.biquard, alix.deruelle, ilia.itenberg, xiaonan.ma}@imj-prg.fr
Salle : 15–25.502
Adresse :Jussieu

Orateur(s) Vincent Vargas - ENS Paris,
Titre Path integral for quantum Mabuchi K-energy
Horaire14:00 à 15:00
RésumeI will present the probabilistic construction of a path integral based on the coupling of the Liouville action and the Mabuchi K-energy on a one-dimensional complex manifold. Both functionals play an important role respectively in Riemannian geometry (in the case of surfaces) and Kähler geometry. Motivations come from theoretical physics where these type of path integrals arise as a model for fluctuating metrics on surfaces when coupling (small) massive perturbations of conformal field theories to quantum gravity as advocated by A. Bilal, F. Ferrari, S. Klevtsov and S. Zelditch. Interestingly, our computations show that quantum corrections perturb the classical Mabuchi K-energy and produce a quantum Mabuchi K-energy: these type of corrections are reminiscent of the quantum Liouville theory