Title:  Character preservation property of matrix model

Presenter:  Pedram Karimi (Warsaw University)

Time & Date: 14:00 IRST - 18 December 2023

Location:  Ferdowsi University, Faculty of Science, Physics Department, Administration Room

Abstract:  Our intention of solving a quantum field theory generally aims to find multi-point functions. In rare cases, we can solve the theory exactly. In all these cases, theories with exact solutions have sets of additional symmetries. The theory of random matrices, as a zero-dimensional field theory, can be solved precisely because of such symmetries. The theory of random matrices is not only solvable, but the solution can be rewritten in a compact form based on special functions, and characters. Such relations, which are known as superintegrability, have their roots in representation theory.
In this lecture, after reviewing the theory of random matrices and symmetric polynomials, a summary of the proof of the character preservation property for Gaussian transformed theorems is presented. Finally, we look at why such relationships exist.

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