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We apply the relative weights method to extract an effective Polyakov line action, at finite chemical potential, from an underlying $SU(3)$ lattice gauge theory with dynamical fermions. The center-symmetry breaking terms in the effective theory are fit to a form suggested by the hopping-parameter expansion, and the effective action is solved at finite chemical potential by a mean field approach. We present preliminary results for one-link staggered fermions with mass $ma=1.0$ and Wilson gauge action at $\beta=5.4$ on $L^3\times4$ lattices with $L=16$.

Polyakov line actions from SU(3) lattice gauge theory with dynamical fermions: first results via relative weights