Instanton constituents and fermionic zero modes in twisted CP(n) models

TL;DR

This paper constructs twisted instanton solutions in CP(n) models, revealing that charge-k instantons split into fractional constituents with specific properties, and studies their fermionic zero modes, linking analytical results with lattice simulations.

Contribution

It introduces explicit twisted instanton solutions in CP(n) models and analyzes their fractional constituents and fermionic zero modes, connecting theory with lattice data.

Findings

Instantons split into well-separated fractional constituents.

Fermionic zero modes hop between constituents, tracing their positions.

Analytical results match lattice simulations, confirming zero modes as filters.

Abstract

We construct twisted instanton solutions of CP(n) models. Generically a charge-k instanton splits into k(n+1) well-separated and almost static constituents carrying fractional topological charges and being ordered along the noncompact direction. The locations, sizes and charges of the constituents are related to the moduli parameters of the instantons. We sketch how solutions with fractional total charge can be obtained. We also calculate the fermionic zero modes with quasi-periodic boundary conditions in the background of twisted instantons for minimally and supersymmetrically coupled fermions. The zero modes are tracers for the constituents and show a characteristic hopping. The analytical findings are compared to results extracted from Monte-Carlo generated and cooled configurations of the corresponding lattice models. Analytical and numerical results are in full agreement and it is demonstrated that the fermionic zero modes are excellent filters for constituents hidden in fluctuating lattice configurations.