NSPT on the twisted Eguchi-Kawai model yields gradient flow coupling coefficients whose flow-time dependence reproduces the universal one-loop beta function and, with large errors, a two-loop value.
Numerical stochastic perturbation theory applied to the twisted Eguchi-Kawai model
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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.
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The perturbative computation of the gradient flow coupling for the twisted Eguchi-Kawai model with the numerical stochastic perturbation theory
NSPT on the twisted Eguchi-Kawai model yields gradient flow coupling coefficients whose flow-time dependence reproduces the universal one-loop beta function and, with large errors, a two-loop value.