Nonlinear sigma models at nonzero chemical potential: breaking up instantons and the phase diagram

Abstract

We consider asymptotically free nonlinear sigma models in two dimensions which, due to their internal symmetries, allow for a conserved charge. Introducing nonzero chemical potential for the SO(2) subgroup of the symmetry group, we discuss two expected phase transitions, which are related to charge condensation and percolation of merons, respectively. The latter are topological objects with half integer charge similar to vortices in the abelianized \emph{O(2)} theory, that emerge for large chemical potentials due to the suppression of the complementary field components. We conjecture a particular ordering of these transitions supported by large N calculations, and discuss dualities helpful for the understanding of these systems in the continuum and on the lattice. In conclusion we suggest that similar behavior is to be expected in QCD at finite density.

12 pages, 3 figures. References and minor changes updated in this version

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Cited by in corpus (6)

• Classifying bions in Grassmann sigma models and non-Abelian gauge theories by D-branes
• Fractional instantons and bions in the O(N) model with twisted boundary conditions
• Relations among topological solitons
• The two-dimensional O(3) model at nonzero density: from dual lattice simulations to repulsive bosons
• Resurgence and Dynamics of O(N) and Grassmannian Sigma Models
• One-loop effective action of the $\mathbb{C}{P}^{N-1}$ model at large $\mu \beta$