arXiv subjects

Reishi Maeta

Publications and source records attributed to Reishi Maeta.

3 recordsLinked to original sources

arXiv2026

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

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.

hep-th↗

arXiv2026

Matrix Bootstrap Approximation without Positivity Constraint

We propose a bootstrap approximation method for the Hermitian one-matrix model that does not rely on positivity constraints. The theoretical foundation of this method is that the one-matrix model admits an eigenvalue distribution $ρ(λ)$, and that the moments $w_n$ generated from it satisfy the loop equations. Our framework is designed to numerically determine a self-consistent pair of $ρ(λ)$ and $w_n$ that simultaneously satisfies these two requirements. In the concrete implementation the least-squares method is employed, and since the sign problem is absent in this formulation, the method can be formally applied to the Minkowski one-matrix model as well, provided that the one-cut structure of the resolvent is assumed. Actual numerical calculations show that this bootstrap approximation reproduces, with very high accuracy, the exact solutions for Euclidean-type models and the perturbative results for Minkowski-type models.

hep-th↗

arXiv2025

A New Type of Saddle in the Euclidean IKKT Matrix Model and Its Emergent Geometry

We study the equation of motion of the Euclidean IKKT matrix model, and realize a new type of classical saddle that only exists in $N\rightarrow\infty$ limit. Under the assumption that the matrices are the generators of $\mathfrak{so}(n,m)$, we identify a unique solution, that is, $\mathfrak{so}(1,3)$. Even though it has $6$ generators and thus $6$ non-zero matrices, they are not independent due to the $2$ Casimir constraints in $\mathfrak{so}(1,3)$. Exploiting the Lie-algebraic structure and the Casimir constraints, we derive a four-dimensional space that a test scalar propagates on. The associated metric possesses $\mathrm{SU}(2)$ isometry, which is closely related to the Taub NUT/Bolt geometry and, more broadly, to black hole physics.

hep-th↗