Spatial confinement-deconfinement transition in accelerated gluodynamics within lattice simulation

Abstract

In this work we investigate the influence of weak acceleration on the confinement-deconfinement phase transition in gluodynamics. Our study is carried out within lattice simulation in the comoving reference frame of accelerated observer which is parameterized by the Rindler coordinates. We find that finite temperature confinement-deconfinement phase transition turns into spatial crossover in the Rindler spacetime. In other words, spatially separated confinement and deconfinement phases can coexist in the Rindler spacetime within certain intervals of temperature and acceleration. We determine the position of the boundary between the phases as a function of temperature for several accelerations and find that it can be described by the Tolman-Ehrenfest law with rather good accuracy although a minor deviation takes place. Moreover, the critical temperature of the system in the weak acceleration regime is found to remain unchanged as that of the standard homogeneous gluodynamics. Our results imply that the spatial confinement-deconfinement transition might take place in the vicinity of the Schwarzschild black hole horizon.

Figures (16)

• Figure 1: Comparison of characteristic values of gravitational acceleration near various astrophysical objects and in heavy-ion collision experiments (HIC). In particular, as an example of such objects we chose the stars: Vega, Fomalhaut, Sun and the neutron stars: PSR J1614-2230, PSR B1919+21, PSR J0952-0607. For the accelerations which can be reached in HIC experiments we shade the region from 100 MeV to 1 GeV Prokhorov:2025vakKharzeev:2005iz. Classically arbitrary large acceleration can be achieved in the vicinity of black hole horizon.
• Figure 2: The coordinate system of a uniformly accelerated observer in Minkowski spacetime (see formulas (\ref{['eq:coord_transformation']})). The hypersurfaces $\eta^1=const$ are depicted by the black solid hyperbolas $(\xi^1)^2-(\xi^0)^2=e^{2\alpha\eta^1}/\alpha^2$. The trajectory of the observer is represented by the blue hyperbola $(\xi^1)^2-(\xi^0)^2=1/\alpha^2$. The hypersurfaces $\eta^0=const$ are depicted by black dotted rays $\xi^0/\xi^1 = \tanh \alpha \eta^0$. The red dashed lines show the lightcone and boundary for the space which can be parameterized by the coordinates (\ref{['eq:coord_transformation']}).
• Figure 3: The renormalized local Polyakov loop (left) and its susceptibility (right) as a function of coordinate $z$ for different temperatures. The results were calculated on the lattice $5\times 40^2\times 121$ for $\alpha = 6$ MeV.
• Figure 4: The critical distance $z_c$ as a function of temperature for various accelerations $\alpha$. These results were obtained on the lattices $4\times 32^2 \times 97$, $5\times 40^2 \times 121$, $6\times 48^2 \times 145$, $8\times 64^2 \times 193$. The solid black lines represent the TE-prediction \ref{['eq:zc_TE']}.
• Figure 5: (left) The critical distance normalized by acceleration, $\alpha z_c$, as a function of temperature for various accelerations $\alpha$. The results were obtained on the lattice $5\times 40^2 \times 121$. Dashed lines represent the fit of the data by quadratic function \ref{['eq:zc_fit']}, and black solid line shows the TE-prediction, $z_c^{\rm TE}$ from Eq. \ref{['eq:zc_TE']}. (right) The difference between $z_c$ and $z_c^{\text{TE}}$ as a function of temperature. The horizontal error bars represent the uncertainty in temperature, which propagates from the fit parameter $T_c$.