Clustering and decomposition for non BPS solutions of the ${\mathbb{CP}}^{N-1}$ models

Abstract

We look at solutions (both BPS and non-BPS) of the ${\mathbb{CP}}^{N-1}$ model on $\mathbb{R}\times S^1$ (with twisted boundary conditions), in particular by using a conformal mapping technique, and we show how to interpret these solutions by decomposing them into expressions describing constituent solitons. We point out the problems that may arise (for non-BPS solutions) when one naively looks at the clustering properties of these solutions. This could lead to misunderstandings when studying extrapolations between small and large compactification radii.

21 pages, 4 figures; v2: published version

References in corpus (3)

• Resurgence in QFT: Unitons, Fractons and Renormalons in the Principal Chiral Model
• Resurgence theory, ghost-instantons, and analytic continuation of path integrals
• Instanton constituents in the O(3) model at finite temperature

Cited by in corpus (10)

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• Fractional instantons and bions in the O(N) model with twisted boundary conditions
• Non-BPS exact solutions and their relation to bions in $\mathbb{C}{P}^{N-1}$ models
• Josephson instantons and Josephson monopoles in a non-Abelian Josephson junction
• Decoding perturbation theory using resurgence: Stokes phenomena, new saddle points and Lefschetz thimbles
• BPS Sphalerons in the $F_2$ Non-Linear Sigma Model
• Resurgence and Dynamics of O(N) and Grassmannian Sigma Models
• Fermion scattering on topological solitons in the ${\mathbb{CP}}^{N-1}$ model