Juan Abranches: From complex to self-adjoint matrix and tensor models via intermediate fields

mercredi 20 mai 2026, 14:00 → 15:00 Europe/Paris

Random matrix and tensor models provide an analytic framework for studying ensembles of discretized geometries. When one attempts to incorporate geometric or causal constraints—such as those arising in causal dynamical triangulations—these models typically acquire technically involved structures. In this talk, I present a reformulation that applies to a broad class of complex matrix and tensor models. Using an intermediate field representation, I show that they can be rewritten as equivalent self-adjoint theories with linearly coupled auxiliary fields. In this reformulation, the intermediate field acquires a dually weighted logarithmic potential determined by the covariance of the original complex model. This construction extends and unifies several previously known results, which were restricted to trivial covariance or specific interaction choices, and clarifies how interaction and covariance data are reorganized in matrix and tensor models. This talk is based on arXiv:2512.16583.