The potential of the effective Polyakov line action from the underlying lattice gauge theory

Abstract

I adapt a numerical method, previously applied to investigate the Yang-Mills vacuum wavefunctional, to the problem of extracting the effective Polyakov line action from SU(N) lattice gauge theories, with or without matter fields. The method can be used to find the variation of the effective Polyakov line action along any trajectory in field configuration space; this information is sufficient to determine the potential term in the action, and strongly constrains the possible form of the kinetic term. The technique is illustrated for both pure and gauge-Higgs SU(2) lattice gauge theory at finite temperature. A surprise, in the pure gauge theory, is that the potential of the corresponding Polyakov line action contains a non-analytic (yet center-symmetric) term proportional to |P|^3, where P is the trace of the Polyakov line at a given point, in addition to the expected analytic terms proportional to even powers of P.

24 pages, 12 figures

References in corpus (4)

• Monte Carlo simulation of the SU(3) spin model with chemical potential in a flux representation
• Testing Proposals for the Yang-Mills Vacuum Wavefunctional by Measurement of the Vacuum
• Inverse Monte-Carlo determination of effective lattice models for SU(3) Yang-Mills theory at finite temperature
• Mean field theory of effective spin models as a baryon fugacity expansion

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• Comparison of complex Langevin and mean field methods applied to effective Polyakov line models
• (S)QCD on R^3 x S^1: Screening of Polyakov loop by fundamental quarks and the demise of semi-classics
• Two-colour QCD with heavy quarks at finite densities
• Holonomy potential and confinement from a simple model of the gauge topology
• Effective potential for SU(2) Polyakov loops and Wilson loop eigenvalues
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• Gauge turbulence, topological defect dynamics, and condensation in Higgs models
• Perturbative aspects of the deconfinement transition -- Physics beyond the Faddeev-Popov model
• $\xi /{\xi }_{2nd}$ ratio as a tool to refine Effective Polyakov Loop models
• A window on infrared QCD with small expansion parameters