Abstract
We discuss a hydrodynamical description of the eigenvalues of the Polyakov line at large but finite Nc for Yang–Mills theory in even and odd space-time dimensions. The hydro-static solutions for the eigenvalue densities are shown to interpolate between a uniform distribution in the confined phase and a localized distribution in the de-confined phase. The resulting critical temperatures are in overall agreement with those measured on the lattice over a broad range of Nc, and are consistent with the string model results at Nc=∞. The stochastic relaxation of the eigenvalues of the Polyakov line out of equilibrium is captured by a hydrodynamical instanton. An estimate of the probability of formation of a Z(Nc) bubble using a piece-wise sound wave is suggested.
Highlights
Lattice simulations of Yang-Mills theory in even and odd dimensions show that the confined phase is center symmetric [1, 2]
The Yang-Mills theory is simplified to the eigenvalues of the Polyakov line and an effective potential is used with parameters fitted to the bulk pressure to study such a transition [8, 9], in the spirit of the strong coupling transition in the Gross-Witten model [10]
In this letter we develop a hydrodynamical description of the gauge invariant eigenvalues of the Polyakov line for an SU(Nc) Yang-Mills theory at large but finite Nc
Summary
Lattice simulations of Yang-Mills theory in even and odd dimensions show that the confined phase is center symmetric [1, 2]. The Yang-Mills theory is simplified to the eigenvalues of the Polyakov line and an effective potential is used with parameters fitted to the bulk pressure to study such a transition [8, 9], in the spirit of the strong coupling transition in the Gross-Witten model [10]. The matrix model partition function for the eigenvalues of the Polyakov line for SU(Nc) in 1 + 2 dimensions was discussed in [8]. Since ρ(θ) = ρ0 + Re G+(z = eiθ), careful considerations of the singularity structures of the quadratic solutions to (13) yield (Θ is a step function).
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