# Numerical stochastic perturbation theory applied to the twisted Eguchi-Kawai model

## TL;DR

This paper explores the application of numerical stochastic perturbation theory to the four-dimensional twisted Eguchi-Kawai model, achieving high-precision calculations of Wilson loop coefficients and analyzing their behavior as N increases.

## Contribution

It demonstrates the use of NSPT with a GHMD algorithm on the TEK model, computing perturbative expansions up to O(g^8) and analyzing large N behavior.

## Key findings

- High-precision coefficients up to O(g^4) match exact values.
- Coefficients tend to Gaussian distribution as N increases.
- Method can be extended to higher orders.

## Abstract

We present the results of an exploratory study of the numerical stochastic perturbation theory (NSPT) applied to the four dimensional twisted Eguchi-Kawai (TEK) model. We employ a Kramers type algorithm based on the Generalized Hybrid Molecular Dynamics (GHMD) algorithm. We have computed the perturbative expansion of square Wilson loops up to $O(g^8)$. The results of the first two coefficients (up to $O(g^4)$) have a high precision and match well with the exact values. The next two coefficients can be determined and even extrapolated to large $N$, where they should coincide with the corresponding coefficients for ordinary Yang-Mills theory on an infinite lattice. Our analysis shows the behaviour of the probability distribution for each coefficient tending to Gaussian for larger $N$. The results allow us to establish the requirements to extend this analysis to much higher order.