Complex instantons in sigma models with chemical potential

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.

14 pages, 8 figures

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Cited by in corpus (8)

• Bion non-perturbative contributions versus infrared renormalons in two-dimensional $\mathbb{C}{P}^{N-1}$ models
• O(3) nonlinear sigma model in 1+1 dimensions with matrix product states
• Infrared renormalon in the supersymmetric $\mathbb{C}{P}^{N-1}$ model on $\mathbb{R}\times S^1$
• Confinement-Deconfinement Crossover in the Lattice $\mathbb{C}{P}^{N-1}$ Model
• Lattice $\mathbb{C}{P}^{N-1}$ model with ${\mathbb{Z}}_N$ twisted boundary condition: bions, adiabatic continuity and pseudo-entropy
• Exploring instantons with spin-lattice systems
• Infrared renormalon in $SU(N)$ QCD(adj.) on ${\mathbb{R}}^3\times S^1$
• Vacuum energy of the supersymmetric $\mathbb{C}{P}^{N-1}$ model on $\mathbb{R}\times S^1$ in the $1/N$ expansion