Centre symmetric 3d effective actions for thermal SU(N) Yang-Mills from strong coupling series

Abstract

We derive three-dimensional, Z(N)-symmetric effective actions in terms of Polyakov loops by means of strong coupling expansions, starting from thermal SU(N) Yang-Mills theory in four dimensions on the lattice. An earlier action in the literature, corresponding to the (spatial) strong coupling limit, is thus extended by several higher orders, as well as by additional interaction terms. We provide analytic mappings between the couplings of the effective theory and the parameters $N_{\tau },\beta$ of the original thermal lattice theory, which can be systematically improved. We then investigate the deconfinement transition for the cases SU(2) and SU(3) by means of Monte Carlo simulations of the effective theory. Our effective models correctly reproduce second order 3d Ising and first order phase transitions, respectively. Furthermore, we calculate the critical couplings ${\beta }_c(N_{\tau })$ and find agreement with results from simulations of the 4d theory at the few percent level for $N_{\tau }=4-16$.

27 pages, 21 figures; final version published in JHEP; attached the corresponding Erratum (ref. JHEP 1107:014,2011, DOI 10.1007/JHEP07(2011)014) for ease of consultation

References in corpus (8)

• Effective Theory of Wilson Lines and Deconfinement
• Z(3)-symmetric effective theory for SU(3) Yang-Mills theory at high temperature
• Centre symmetric 3d effective actions for thermal SU(N) Yang-Mills from strong coupling series
• Center-Symmetric Effective Theory for High-Temperature SU(2) Yang-Mills Theory
• Inverse Monte-Carlo determination of effective lattice models for SU(3) Yang-Mills theory at finite temperature
• Phase Structure of Z(3)-Polyakov-Loop Models
• Chiral and deconfinement transitions in strong coupling lattice QCD with finite coupling and Polyakov loop effects
• Finite temperature SU(2) gauge theory: critical coupling and universality class

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