Dual lattice representations for O(N)O(N) and CP(N−1)CP(N−1) models with a chemical potential

We derive dual representations for O(N)O(N) and CP(N−1)CP(N−1) models on the lattice. In terms of the dual variables the partition sums have only real and positive contributions also at finite chemical potential. Thus the complex action problem of the conventional formulation is overcome and using the dual variables Monte Carlo simulations are possible at arbitrary chemical potential.