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Register a new userEguchi-Kawai model with dynamical adjoint fermions
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It is believed that fermions in adjoint representation on single site lattice will restore the center symmetry, which is a crucial requirement for the volume independence of large-N lattice gauge theories. We present a perturbative analysis which supports the assumption for overlap fermions, but shows that center symmetry is broken for naive fermions.
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The motivation and construction of the original Quenched Eguchi-Kawai model are reviewed, providing much greater detail than in the first, 1982 QEK paper. A 2008 article announced that QEK fails as a reduced model because the average over permutations of eigenvalues stays annealed. It is shown here that the original quenching logic naturally leads to a formulation with no annealed average over permutations.
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.
We have evaluated perturbation coefficients of Wilson loops up to $O(g^8)$ for the four-dimensional twisted Eguchi-Kawai model using the numerical stochastic perturbation theory (NSPT) in arXiv:1902.09847. In this talk we present a progress report on the higher order calculation up to $O(g^{63})$, for which we apply a fast Fourier transformation (FFT) based convolution algorithm to the multiplication of polynomial matrices in the NSPT aiming for higher order calculation. We compare two implementations with the CPU-only version and the GPU version of the FFT based convolution algorithm, and find a factor 9 improvement on the computational speed of the NSPT algorithm with SU($N=225$) at $O(g^{31})$. The perturbation order dependence of the computational time, we investigate it up to $O(g^{63})$, shows a mild scaling behavior on the truncation order.
We present simulation results for the 2-flavour Schwinger model with dynamical overlap fermions. In particular we apply the overlap hypercube operator at seven light fermion masses. In each case we collect sizable statistics in the topological sectors 0 and 1. Since the chiral condensate Sigma vanishes in the chiral limit, we observe densities for the microscopic Dirac spectrum, which have not been addressed yet by Random Matrix Theory (RMT). Nevertheless, by confronting the averages of the lowest eigenvalues in different topological sectors with chiral RMT in unitary ensemble we obtain -- for the very light fermion masses -- values for Sigma that follow closely the analytical predictions in the continuum.
Taming finite-volume effects is a crucial ingredient in order to identify the existence of IR fixed points. We present the latest results from our numerical simulations of SU(2) gauge theory with 2 Dirac fermions in the adjoint representation on large volumes. We compare with previous results, and extrapolate to thermodynamic limit when possible.
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