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Spatially inhomogeneous confinement-deconfinement phase transition in rotating QGP

V. V. Braguta, M. N. Chernodub, Ya. A. Gershtein, A. A. Roenko

Abstract

Using first-principles numerical simulations, we find a new spatially inhomogeneous phase in a rotating gluon plasma. This mixed phase simultaneously contains regions of both confining and deconfining states in thermal equilibrium, separated by a spatial transition. The position of the boundary between the two phases is determined by the local critical temperature. We calculate the critical temperature of the local transition as a function of angular velocity and radius for a full (imaginary) rotating system and within a local thermalization approximation, and find an excellent agreement between these approaches. An analytic continuation of the results to the domain of real angular frequencies indicates that the confinement phase localizes at the periphery of the rotating system and the deconfinement phase appears closer to the rotation axis. We argue that the anisotropy of the gluon action in the curved co-rotating background can quantitatively explain the remarkable property that the spatial structure of this inhomogeneous phase disobeys the picture based on a straightforward implementation of the Tolman-Ehrenfest law. We also perform the first lattice simulation of rotating $N_f=2$ QCD which confirms that a similar picture is expected for theory with dynamical quarks.

Spatially inhomogeneous confinement-deconfinement phase transition in rotating QGP

Abstract

Using first-principles numerical simulations, we find a new spatially inhomogeneous phase in a rotating gluon plasma. This mixed phase simultaneously contains regions of both confining and deconfining states in thermal equilibrium, separated by a spatial transition. The position of the boundary between the two phases is determined by the local critical temperature. We calculate the critical temperature of the local transition as a function of angular velocity and radius for a full (imaginary) rotating system and within a local thermalization approximation, and find an excellent agreement between these approaches. An analytic continuation of the results to the domain of real angular frequencies indicates that the confinement phase localizes at the periphery of the rotating system and the deconfinement phase appears closer to the rotation axis. We argue that the anisotropy of the gluon action in the curved co-rotating background can quantitatively explain the remarkable property that the spatial structure of this inhomogeneous phase disobeys the picture based on a straightforward implementation of the Tolman-Ehrenfest law. We also perform the first lattice simulation of rotating QCD which confirms that a similar picture is expected for theory with dynamical quarks.
Paper Structure (7 sections, 9 equations, 6 figures)

This paper contains 7 sections, 9 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Lattice formulation of rotating QCD
  3. Mixed phase in rotating gluodynamics
  4. Action decomposition and analytic continuation
  5. Approximation of local thermalization
  6. Mixed phase in rotating QCD
  7. Conclusions

Figures (6)

  • Figure 1: (top) The distribution of the local Polyakov loop in the $x,y$-plane at the temperature $T/T_{c0} = 0.95$ and several values of the angular velocity (also shown in units of $v_I = \Omega_I R$ with $R=13.5$ fm) for a lattice of size $5\times 30\times 181^2$ with open boundary conditions. (bottom) The Polyakov loop at the $x$-axis. The vertical lines mark the phase boundaries with shaded uncertainties. The violet (blue) data points correspond to periodic (open) boundary conditions.
  • Figure 2: The critical temperature $T_c(r)$ of the local transition as a function of radius $r$ at $v_I^2 = 0.16$ for open and periodic boundary conditions (left) and at various velocities $v_I$ for open boundary conditions (right).
  • Figure 3: (left) The local Polyakov loop as a function of $x$ coordinate for lattice of size $5\times 30\times 181^2$ with OBC/PBC for the regimes Im2 and Re2. Data are shown, respectively, for $|v^2| = 0.16$ at $T/T_{c0} = 0.95$ with imaginary angular velocity (Im2) and at $T/T_{c0} = 1.05$ with real angular velocity (Re2). (right) The critical temperature $T_c(r)$ of the local transition as a function of radius for different regimes of rotation. Hatched bands represent the analytic continuation of the Im2 results to the domain of real $\Omega$ using Eq. \ref{['eq:Tc_r']}.
  • Figure 4: The mixed inhomogeneous phase for imaginary and real rotations.
  • Figure 5: (left) The critical temperature in the purely gluon system with local action \ref{['eq:S_local']} (filled points) as a function of $u_I$. The dotted (dashed) lines represent the best fit of the data by the polynomial (rational) function \ref{['eq:fit_u']}. In addition, we show the critical temperatures calculated for the rotating system with the original action \ref{['eq:S_structure']} (empty points) at $v_I = 0.48$. (right) The fitting functions \ref{['eq:fit_u']} in the continuum limit.
  • ...and 1 more figures