Regularized Master-Field Approximation for Large-$N$ Reduced Matrix Models

TL;DR

This paper introduces a numerical method for large-N reduced matrix models based on regularizing the master field, effectively reproducing known solutions and enabling computations without sign problems.

Contribution

The authors develop a finite-dimensional regularization of the master field approach, allowing practical numerical analysis of large-N matrix models in both Euclidean and Minkowski settings.

Findings

Exact solutions are well reproduced in Euclidean models.

Perturbative results are accurately captured in Minkowski models.

The method demonstrates the existence of a regularized master-field description.

Abstract

We propose a numerical method based on the master field for large-$N$ reduced matrix models. While the master field is originally an infinite-dimensional matrix, in this method it is regularized to a finite dimension, with the requirement that it satisfies the loop equations as much as possible. This formulation can be directly implemented for numerical computation, and since there is no sign problem at the fundamental level, the method can be applied regardless of whether the model is of Euclidean or Minkowski type. In numerical calculations for one- and two-matrix models, the exact solution is well reproduced in the Euclidean case, while perturbative results are well reproduced in the Minkowski case. This demonstrates the effectiveness of the method and supports the idea that the matrix models studied in this paper admit a regularized master-field description.