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

TL;DR

This paper investigates two-dimensional nonlinear sigma models at finite chemical potential, exploring phase transitions related to charge condensation and topological objects called merons, with implications for understanding QCD at finite density.

Contribution

It introduces a detailed analysis of phase transitions in nonlinear sigma models at nonzero chemical potential, including the role of merons and dualities, and conjectures their ordering based on large N calculations.

Findings

Identification of charge condensation and meron percolation transitions

Large N calculations support the ordering of phase transitions

Discussion of dualities aids understanding of continuum and lattice systems

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.