Abstract
We derive dual representations for O(N) and 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.
Highlights
A very visible shortcoming of lattice QCD is the current inability to properly deal with QCD at finite density
The complex action problem of the conventional formulation is overcome and using the dual variables Monte Carlo simulations are possible at arbitrary chemical potential
As a matter of fact, the complex action problem appears in most field theories at finite chemical potential, both on the lattice and in the continuum, and for fermionic as well as for bosonic degrees of freedom
Summary
A very visible shortcoming of lattice QCD is the current inability to properly deal with QCD at finite density. In terms of the dual variables the partition sums have only real and positive contributions at finite chemical potential. The complex action problem of the conventional formulation is overcome and using the dual variables Monte Carlo simulations are possible at arbitrary chemical potential.
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