Effective lattice Polyakov loop theory vs. full SU(3) Yang-Mills at finite temperature

Abstract

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.

Heavy dense QCD and nuclear matter from an effective lattice theory

“…The drawback is that the effective action is only valid in parameter ranges where the expansion converges, which is currently restricted to the heavy mass region and the confined phase. Even there, the effective theory is unsuitable for long range correlation functions, but it gives accurate results for bulk thermodynamic quantities and phase transitions [12]. In particular, it has already provided predictions with better than 10% accuracy for the critical couplings of SU (2), SU(3) Yang-Mills [8], the critical quark masses where the deconfinement transition changes to a crossover [9] and the tricritical point of the deconfinement transition at imaginary chemical potential [13].…”

Numerical corrections to the strong coupling effective Polyakov-line action for finite T Yang-Mills theory

“…This already vastly improves over direct strong coupling calculations of thermodynamic observables [13][14][15]. On the other hand, the missing higher order couplings and long range interactions hamper the applicability of the effective theory to correlation functions and the string tension, where non-local contributions play an increasing role as lattices get finer [12]. The same observation was made with a non-perturbatively determined form of the effective action [9,10].…”

“…This is illustrated in figure 3. In [12] we observed that the mis-match of the correlator remains when additional couplings are added in the strong coupling approach, since their leading order contributions are too small. The situation is different with the numerically determined effective couplings.…”

“…Svetitsky and Yaffe conjectured that the short range Polyakov interactions are the relevant terms for the phase transition [5]. This is based on the fact that these are the dominant contributions both in the strong and weak coupling limit, while for all couplings interactions are screened by the mass gap of the theory (see also the discussion in [12]). In [7] the integration of the spatial links was performed by means of a strong coupling expansion, where interaction terms are parametrically suppressed with increasing distance and n-points.…”

“…The relation between effective couplings corresponding to different character expansion schemes is then established perturbatively in terms of a rapidly converging power series. This allows us to check the range of applicability of the strong coupling approach [7,12] and significantly improve on the results. This paper is organised as follows.…”