von Neumann algebras from large N matrix models | BIMSA-Tsinghua String Seminar

Abstract

I will show the emergence of type III_1 von Neumann algebras from large N quantum mechanical models. These are effective models constructed from gauge theories on a circle. Their partition functions are matrix models that are explicitly solved in the large N limit. The spectral densities underlying the algebras are computed in closed form, and expressed in terms of the eigenvalue densities of the matrix models. Furthermore, I will explain how to systematically promote these systems to have a 1st order phase transition with emergence of type III_1 algebras above the critical temperature, compatible with the Hawking-Page transition. A relation between the quantum mechanics and Calabi-Yau is also discussed. Based on 2402.10262