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

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.

Withdrawn due to an elementary error in Eq.(8). Physically, the single, purely chromoelectric part of the action is insensitive to rotation