[Seminar] Matrix Bootstrap Approximation without Positivity Constraint | Reishi Maeta (Hiroshima University / McGill University)

The speaker:Reishi Maeta (Hiroshima University / McGill University)

Title: Matrix Bootstrap Approximation without Positivity Constraint

Abstract:Recent proposals of bootstrap methods for matrix models have opened a new avenue for the numerical analysis of matrix models in the large-N limit.  However, the notion of positivity is meaningful only for Euclidean-type theories and it cannot be directly applied to Minkowski-type theories. In this work, we propose a bootstrap approximation method that does not rely on positivity. Instead, our approach combines the Schwinger–Dyson equations with a function called the eigenvalue distribution ρ(λ). While conventional methods derive inequalities from the requirement that positivity constraints be satisfied, our method is based on the assumption that an eigenvalue distribution exists. Under this assumption, the values of physical observables, as well as the eigenvalue distribution itself, are determined approximately in a self-consistent manner. In this talk, we will first briefly explain the motivation for analyzing Minkowski-type large-N matrix models, then explain the method with a few simple equations, and finally present numerical results.

Date and time: 28th April Tuesday at 9:00