  In this letter we explore different representations of the SU(2) principal
chiral model on the lattice. We couple chemical potentials to two of the
conserved charges to induce finite density. This leads to a complex action such
that the conventional field representation cannot be used for a Monte Carlo
simulation. Using the recently developed Abelian color flux approach we derive
a new worldline representation where the partition sum has only real and
positive weights, such that a Monte Carlo simulation is possible. In a second
step we transform the model to new dual variables in the Kramers-Wannier (KW)
sense, such that the constraints are automatically fulfilled, and we obtain a
second representation free of the complex action problem. We implement
exploratory Monte Carlo simulations for both, the worldline, as well as the
KW-dual form, for cross-checking the two dualizations and a first assessment of
their potential for dual simulations.
