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H 1 A string theorist view point on the genus-two Kawazumi-Zhang invariant

Auteurs : Pioline, Boris (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : The genus-two Kawazumi-Zhang (KZ) invariant is a real-analytic modular function on the Siegel upper half-plane of degree two, which plays an important role in arithmetic geometry. In String theory, it appears as part of the integrand in two-loop four-graviton scattering amplitudes. With hindsight from String theory, I will show that the KZ invariant can be obtained as a generalized Borcherds lift from a weak Jacobi form of index 1 and weight 2. This implies that the KZ invariant is an eigenmode of the quadratic and quartic Casimir operators, and gives access to the full asymptotic expansion in all possible degeneration limits. It also reveals a mock-type holomorphic Siegel modular form underlying the KZ invariant. String theory amplitudes involves modular integrals of the KZ invariant (times lattice partition functions) on the Siegel upper half-plane, which provide new examples of automorphic objects on orthogonal Grassmannians, beyond the usual Langlands-Eisenstein series.

    Note: this talk is based on the preprint "A Theta lift representation for the Kawazumi-Zhang and Faltings invariants of genus-two Riemann surfaces" available on arXiv:1504.04182. Following up on a question asked during the talk (which was answered very poorly), the author obtained shortly after a proof of the conjecture stated in this preprint and during the talk. The proof is available in the revised version arXiv:1504.04182v2.

    Codes MSC :
    81T30 - String and superstring theories; other extended objects (e.g., branes)
    83E30 - String and superstring theories

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 18/06/15
      Date de captation : 27/05/15
      Sous collection : Research talks
      Format : quicktime ; audio/x-aac
      arXiv category : High Energy Physics ; Dynamical Systems
      Domaine : Mathematical Physics ; Dynamical Systems & ODE
      Durée : 00:49:56
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2015-05-27_Pioline.mp4

    Informations sur la rencontre

    Nom de la rencontre : Automorphic forms: advances and applications / Formes automorphes: avancées et applications
    Organisateurs de la rencontre : Bringmann, Kathrin ; Lovejoy, Jérémy ; Richter, Olav
    Dates : 25/05/15 - 29/05/15
    Année de la rencontre : 2015
    URL Congrès : http://conferences.cirm-math.fr/1108.html

    Citation Data

    DOI : 10.24350/CIRM.V.18769203
    Cite this video as: Pioline, Boris (2015). A string theorist view point on the genus-two Kawazumi-Zhang invariant. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18769203
    URI : http://dx.doi.org/10.24350/CIRM.V.18769203


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