Complex instantons in sigma models with chemical potential

TL;DR

This paper studies two-dimensional sigma models with nonzero chemical potential, revealing complex instanton solutions and their properties, including how they are affected by the imaginary part of the chemical potential and their topological characteristics.

Contribution

It introduces exact BPS-like solutions for sigma models with chemical potential, generalizing instantons to complex actions and analyzing their decay and topological charge distribution.

Findings

Exact BPS-like solutions in complex sigma models

Generalization of instantons to nonzero chemical potential

Decay behavior controlled by the imaginary part of mu

Abstract

We analyze two-dimensional nonlinear sigma models at nonzero chemical potentials, which are governed by a complex action. In the spirit of contour deformations (thimbles) we extend the fields into the complex plane, which allows to incorporate the chemical potentials mu as twisted boundary conditions. We write down the equations of motion and find exact BPS-like solutions in terms of pairs of (anti)holomorphic functions, in particular generalizations of unit charge and fractional instantons to generic mu. The decay of these solutions is controled by the imaginary part of mu and a vanishing imaginary part causes jumps in the action. We analyze how the total charge is distributed into localized objects and to what extent these are characterized by topology.