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Motivated by the sign problem, we calculate the effective Polyakov lineaction corresponding to certain SU(3) lattice gauge theories on a ${16^3 \times6}$ lattice via the "relative weights" method introduced in our previousarticles. The calculation is carried out at $\beta=5.6,5.7$ for the pure gaugetheory, and at $\beta=5.6$ for the gauge field coupled to a relatively lightscalar particle. In the latter example we determine the effective theory alsoat finite chemical potential, and show how observables relevant to phasestructure can be computed in the effective theory via mean field methods. Inall cases a comparison of Polyakov line correlators in the effective theory andthe underlying lattice gauge theory, computed numerically at zero chemicalpotential, shows accurate agreement down to correlator magnitudes of order$10^{-5}$. We also derive the effective Polyakov line action corresponding to agauge theory with heavy quarks and large chemical potential, and apply meanfield methods to extract observables.

Finding the effective Polyakov line action for SU(3) gauge theories at finite chemical potential