Fractional instantons and bions in the O(N) model with twisted boundary conditions

Abstract

Recently, multiple fractional instanton configurations with zero instanton charge, called bions, have been revealed to play important roles in quantum field theories on compactified spacetime. In two dimensions, fractional instantons and bions have been extensively studied in the $\mathbb{C}{P}^{N-1}$ model and the Grassmann sigma model on ${\mathbb{R}}^1\times S^1$ with the ${\mathbb{Z}}_N$ symmetric twisted boundary condition. Fractional instantons in these models are domain walls with a localized $U(1)$ modulus twisted half along their world volume. In this paper, we classify fractional instantons and bions in the $O(N)$ nonlinear sigma model on ${\mathbb{R}}^{N-2}\times S^1$ with more general twisted boundary conditions in which arbitrary number of fields change sign. We find that fractional instantons have more general composite structures, that is, a global vortex with an Ising spin (or a half-lump vortex), a half sine-Gordon kink on a domain wall, or a half lump on a "space-filling brane" in the $O(3)$ model ($\mathbb{C}{P}^1$ model) on ${\mathbb{R}}^1\times S^1$, and a global monopole with an Ising spin (or a half-Skyrmion monopole), a half sine-Gordon kink on a global vortex, a half lump on a domain wall, or a half Skyrmion on a "space-filling brane" in the $O(4)$ model (principal chiral model or Skyrme model) on ${\mathbb{R}}^2\times S^1$. We also construct bion configurations in these models.

43 pages, 16 figures, v2: a reference added, published version

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• Non-perturbative Contributions from Complexified Solutions in $\mathbb{C}{P}^{N-1}$ Models
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• Fractional Skyrmions and their molecules
• Topological solitons in the supersymmetric Skyrme model
• Lattice $\mathbb{C}{P}^{N-1}$ model with ${\mathbb{Z}}_N$ twisted boundary condition: bions, adiabatic continuity and pseudo-entropy
• Quantum phase transition and Resurgence: Lessons from 3d $\mathcal{N}=4$ SQED
• Resurgence and semiclassical expansion in two-dimensional large-$N$ sigma models
• Resurgence of one-point functions in a matrix model for 2D type IIA superstrings
• Resurgence and Dynamics of O(N) and Grassmannian Sigma Models
• Two-point functions at arbitrary genus and its resurgence structure in a matrix model for 2D type IIA superstrings