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A three-dimensional effective theory of Polyakov loops has recently been derived from Wilson's Yang-Mills lattice action by means of a strong coupling expansion. It is valid in the confined phase up to the deconfinement phase transition, for which it predicts the correct order and gives quantitative estimates for the critical coupling. In this work we study its predictive power for further observables like correlation functions and the equation of state. We find that the effective theory correctly reproduces qualitative features and symmetries of the full theory as the continuum is approached. Regarding quantitative predictions, we identify two classes of observables by numerical comparison as well as analytic calculations: correlation functions and their associated mass scales cannot be described accurately from a truncated effective theory, due to its inherently non-local nature involving long-range couplings. On the other hand, phase transitions and bulk thermodynamic quantities are accurately reproduced by the leading local part of the effective theory. In particular, the effective theory description is numerically superior when computing the equation of state at low temperatures or the properties of the phase transition. [ABSTRACT FROM AUTHOR]

The non-perturbative properties of supersymmetric theories are of interest for elementary particle physics beyond the Standard Model. Numerical simulations of these theories are associated with theoretical and technical challenges. The minimal supersymmetric model containing gauge fields is the $ \mathcal{N}=1 $ supersymmetric Yang-Mills theory. We present the results of our investigations of the masses of the lightest particles of this model on a lattice. The central question is, whether a continuum limit exists with unbroken supersymmetry. In this case the bound states would form mass-degenerate supermultiplets. We have obtained the masses of the gluino-glue particle, mesonic states, and the scalar glueball at a fine lattice spacing. The statistical accuracy as well as the control of finite size effects and lattice artefacts are significantly better than in all previous investigations. Taking the statistical and systematic uncertainties into account, the masses of the fermionic and bosonic states in our present calculations are consistent with the formation of degenerate supermultiplets, indicating that in the continuum limit there is no spontaneous supersymmetry breaking. This new finding is in contrast to previous results. [ABSTRACT FROM AUTHOR]