Resurgence and fractional instanton of the SU($3$) gauge theory in weak coupling regime

TL;DR

This paper provides numerical evidence for fractional instantons in SU(3) gauge theory under weak coupling, highlighting their role in resurgence and confinement phenomena with implications for topological objects in quantum field theories.

Contribution

It demonstrates the existence of fractional instantons in SU(3) gauge theory using numerical methods with IR cutoff and twisted boundary conditions, advancing understanding of resurgence in gauge theories.

Findings

Fractional instantons appear in weak coupling regimes.

Fractional instantons connect degenerate vacua in the deconfinement phase.

Polyakov loop measurements relate to center symmetry and confinement.

Abstract

According to recent studies on resurgence scenario of quantum systems, some topological objects with fractional charges play an important role to see the resurgence structure. In this talk, we report a numerical evidence of the fractional-instantons of the SU($3$) gauge theory. The fractional-instanton appears in a weak coupling regime, if the theory is regularized by an infrared (IR) cutoff via the $1$-form twisted boundary conditions. The Polyakov loop is also measured 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. This talk is based on the paper[1].