Fractional instanton of the SU($3$) gauge theory in weak coupling regime

Abstract

Motivated by recent studies on the resurgence structure of quantum field theories, we numerically study the nonperturbative phenomena of the SU($3$) gauge theory in a weak coupling regime. We find that topological objects with a fractional charge emerge if the theory is regularized by an infrared (IR) cutoff via the twisted boundary conditions. Some configurations with nonzero instanton number are generated as a semi-classical configuration in the Monte Carlo simulation even in the weak coupling regime. Furthermore, some of them consist of multiple fractional-instantons. We also measure the Polyakov loop to investigate the center symmetry and confinement. The fractional-instanton corresponds to a solution linking two of degenerate ${\mathbb{Z}}_3$-broken vacua in the deconfinement phase.

Comments: 28 pages, 10 figures, (v2) improved presentation and added references, (v3) comments added