Effects of imaginary and real rotations on QCD matters

TL;DR

This paper investigates how imaginary and real rotations influence Polyakov loop potentials in pure SU(3) gauge theories, revealing differences in phase transition behavior and implications for the phase diagram's analytic continuation.

Contribution

It introduces a variable transformation approach to incorporate rotation effects into Polyakov loop potentials and compares their impacts on deconfinement and chiral symmetry in a unified framework.

Findings

Imaginary rotation suppresses Polyakov loop at all temperatures with first-order deconfinement transition.

Real rotation enhances Polyakov loop at low temperatures and decreases the pseudo-critical temperature.

Analytic continuation from imaginary to real rotation may not be valid in the non-perturbative region.

Abstract

Inspired from perturbative calculations, this work introduces imaginary ($\Omega_{\rm I}$) and real ($\Omega$) rotation effects to the pure $SU(3)$ gauge potentials simply through variable transformations: The empirical Polyakov loop (PL) potentials can be rewritten as functions of the imaginary chemical potentials of gluons and ghosts $(q_{\rm ij})$, and the transformations are taken as $q_{\rm ij}\rightarrow q_{\rm ij}\pm\Omega_{\rm I}/T$ and $q_{\rm ij}\rightarrow q_{\rm ij}\pm i\,\Omega/T$, respectively. For the PL potential of Fukushima $(V_1)$, a smaller imaginary rotation $\Omega_{\rm I}$ tends to suppress PL at all temperature and the deconfinement transition keeps of first order. However, for the PL potential of Munich group $(V_2)$, $\Omega_{\rm I}$ tends to enhance PL at low temperature $T$, consistent with lattice simulations; but suppress PL at high $T$, consistent with perturbative calculations. Moreover, the deconfinement alters from first order to crossover with increasing $\Omega_{\rm I}$ as is expected from lattice simulations. On the other hand, the real rotation $\Omega$ tends to enhance PL at relatively low $T$ for both potentials, and the (pseudo-)critical temperature decreases with $\Omega$ as expected. Therefore, we find that analytic continuation of the phase diagram from imaginary to real rotation is not necessarily valid in the non-perturbative region. Finally, we apply the more successful PL potential $V_2$ to the Polyakov--Nambu-Jona-Lasinio (PNJL) model and discover that $\Omega_{\rm I}$ tends to break chiral symmetry while $\Omega$ tends to restore it. Especially, the modified model is even able to qualitatively explain the lattice result that a larger $T$ would catalyze chiral symmetry breaking for a large $\Omega_{\rm I}$.