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.
Highlights
This paper is devoted to a study of the systematics of a three-dimensional effective lattice action for Yang-Mills theory derived from the four-dimensional Wilson action by the strong coupling expansion [3]
A local effective action with the correct symmetries is capable to provide a good description of bulk thermodynamic quantities as well as phase transitions, even though it might be inaccurate for specific correlation functions or the spectrum of the theory
We have systematically studied the predictive power of a three-dimensional effective Polyakov loop theory for Yang-Mills on the lattice, which has been derived previously by means of a strong coupling expansion
Summary
The effective lattice Polyakov loop theory is defined starting from Wilson’s lattice YangMills action on a Ns3 × Nτ lattice by splitting the link integrations into a spatial and temporal part,. Since all spatial links, which are originally coupled by nearest neighbour interactions, were integrated over, the effective action is of long-range type, irrespective of the way it is determined. It contains interactions of Polyakov lines at all distances, even a non-local form is allowed. Note that in eq (2.2) we have resummed higher powers of nearest neighbour interactions and nextto-nearest neighbours into a logarithm We investigate the predictive power of the effective theory for correlation functions and bulk thermodynamic quantities
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