Inhomogeneity of rotating gluon plasma and Tolman-Ehrenfest law in imaginary time: lattice results for fast imaginary rotation

TL;DR

This paper uses lattice simulations to explore how a rotating gluon plasma exhibits inhomogeneous phase transitions due to the Tolman-Ehrenfest effect, revealing new insights into confinement and deconfinement phases in rotating systems.

Contribution

It introduces a novel lattice approach to study rotating gluon plasma and derives the Euclidean Tolman-Ehrenfest law, connecting imaginary time formalism with inhomogeneous phase behavior.

Findings

Inhomogeneous confining-deconfining crossover observed in Euclidean simulations.

Rotating gluon plasma likely forms inhomogeneous phases with confinement near the axis.

The Euclidean Tolman-Ehrenfest law is derived and discussed in the context of imaginary rotation.

Abstract

We present the results of first-principle numerical simulations of Euclidean SU(3) Yang-Mills plasma rotating with a high imaginary angular frequency. The rigid Euclidean rotation is introduced via ``rotwisted'' boundary conditions along imaginary time direction. The Polyakov loop in the co-rotating Euclidean reference frame shows the emergence of a spatially inhomogeneous confining-deconfining phase through a broad crossover transition. A continuation of our numerical results to Minkowski spacetime suggests that the gluon plasma, rotating at real angular frequencies, produces a new inhomogeneous phase possessing the confining phase near the rotation axis and the deconfinement phase in the outer regions. The inhomogeneous phase structure has a purely kinematic origin, rooted in the Tolman-Ehrenfest effect in a rotating medium. We also derive the Euclidean version of the Tolman-Ehrenfest law in imaginary time formalism and discuss two definitions of temperature at imaginary Euclidean rotation.