Negative moment of inertia of large-$N_c$ gluons on a ring

TL;DR

This paper demonstrates that the moment of inertia of a large-$N_c$ gluon plasma on a rotating ring is negative, providing a theoretical explanation consistent with recent numerical simulations and explaining several observed phenomena in vortexed QCD.

Contribution

It reveals the negative moment of inertia of large-$N_c$ gluons on a ring and offers a qualitative explanation for related lattice QCD observations.

Findings

Negative moment of inertia of gluon plasma confirmed.

Rotation effectively rescales the gauge coupling.

Qualitative explanation for inhomogeneous phases and deconfinement temperature enhancement.

Abstract

We study SU($N_c$) Yang-Mills theory in $1+1$ dimensions at finite temperature on a spatial ring that rotates uniformly in a plane. We show that the effect of rotation results only in a simple kinematic enhancement of the gauge coupling $g$, which becomes rescaled by a Lorentz factor corresponding to the tangential rotational velocity of the ring. Using well-established analytic results in Yang-Mills theory in the 't Hooft limit of an infinite number of colors, we demonstrate that the moment of inertia of the large-$N_c$ gluon plasma on the ring is negative. This counterintuitive conclusion is, however, in agreement with recent first-principle numerical simulations of hot $3+1$ dimensional SU(3) Yang-Mills theory that also reported a negative moment of inertia for gluon plasma in an experimentally relevant window of temperatures above the deconfinement transition. Furthermore, we argue that our picture provides a qualitative explanation for three other intriguing features observed in lattice simulations of vortical QCD: the emergence of a spatially inhomogeneous mixed phase, the inconsistency of its spatial structure with a standard picture dictated by the Tolman-Ehrenfest law, and the enhancement of the critical deconfining temperature by rotation.