Matrices and moduli (Alessandro GIACCHETTO, ETH Zurich)

27.03.2026 14:00

Matrix models provide one of the oldest examples of a genus expansion suggestive of an underlying string theory, yet the identification of the corresponding worldsheet description has remained subtle. In this talk, I will explain how every Hermitian matrix model admits a dual closed-string description, mathematically formalised as a cohomological field theory on the moduli space of curves and explicitly governed by thimble integrals. This cohomological field theory is a mathematical incarnation of a B-twisted Landau–Ginzburg model coupled to 2d gravity. The key ingredient is the spectral curve emerging from the large-N loop equations. In this framework, the ramification points of the spectral curve correspond to the critical points of the Landau–Ginzburg superpotential, while expectation values in random matrix theory are identified with integrals of tautological classes on the moduli space of curves. From a physics perspective, this provides a concrete and fully controlled example of gauge/string duality. Based on joint work with R. Gopakumar and E. A. Mazenc.

Lieu

Conseil Général 7-9, Room 8-02, Séminaire de Physique mathématique

entrée libre