Phase diagram of 4D SU(3) Yang-Mills theory at $\theta=\pi$ via imaginary theta simulations

TL;DR

This study investigates the phase diagram of 4D SU(3) Yang-Mills theory at $ heta=\pi$ by using imaginary theta simulations and analytic continuation, aiming to understand CP symmetry breaking and restoration.

Contribution

The paper introduces a novel simulation approach using imaginary theta and stout smearing to explore CP symmetry behavior in Yang-Mills theory.

Findings

Evidence of CP symmetry breaking at low temperatures.

Observation of symmetry restoration near the deconfining temperature.

Development of a scaling analysis for smearing-time dependence.

Abstract

It has been speculated that the CP symmetry of 4D SU(3) Yang-Mills theory at $\theta=\pi$ is spontaneously broken in the confined phase, and it is recovered precisely at the deconfining temperature. The direct simulation of the theory at $\theta=\pi$ is, however, difficult due to the sign problem. We therefore simulate the theory with an imaginary theta parameter and perform analytic continuation to the real theta to explore the phase diagram. We implement the stout smearing technique in the hybrid Monte Carlo simulation to recover the topological property of the gauge field. The smearing-time dependence of the observable is investigated using the reweighting method with respect to the smearing step parameters, and a clear scaling behavior is observed. The order parameter of the CP symmetry is then computed in the scaling region to detect symmetry breaking. We report preliminary results on the expected CP breaking and restoration temperature.