Spatially inhomogeneous confinement-deconfinement phase transition in accelerated gluodynamics

Abstract

This study explores confinement-deconfinement transition properties of SU($3$) Yang--Mills theory under weak accelerations at finite temperatures, using first-principles lattice simulations. The system is formulated in the Rindler spacetime, and the properties are studied from the perspective of a co-accelerating observer situated at the center of the lattice. We found that spatially separated confinement and deconfinement phases can coexist in the Rindler spacetime within certain intervals of temperature and acceleration. The position of the boundary between the phases is calculated as a function of temperature for several accelerations, and it is in accordance with the TE prediction, although a small deviation is observed. Moreover, in the weak acceleration regime, the critical temperature of the system is found to coincide with that of non-accelerated gluodynamics.

Figures (4)

• Figure 1: (Left) Renormalized local Polyakov loop as a function of coordinate $z$. (Right) The critical distances as a function of temperature.
• Figure 2: (Left) Difference between $z_c$ and $z_c^{\rm TE}$ as a function of temperature. (Right) Continuum limit extrapolation of the fit parameters $k_0, k_1$, and $T_c$ for the critical distance obtained from the inflection point of the local Polyakov loop.
• Figure 3: (Left) Renormalized Polyakov loop susceptibility as a function of the coordinate $z$. (Right) Continuum limit extrapolation of the fit parameters $k_0, k_1$, and $T_c$ for the critical distance obtained from the peak position of the local susceptibility.
• Figure 4: Continuum limit values of the fit parameters $k_0, k_1, T_c$ obtained from the Polyakov loop inflection point (left) and susceptibility peak (right) as a function the thickness $\delta z$.