Chromomagnetic condensation and perturbative confinement induced by imaginary rotation in SU(2) Yang-Mills Theory

TL;DR

This work investigates SU(2) Yang–Mills theory under imaginary rotation in the presence of a chromomagnetic background, deriving a one-loop Polyakov-loop potential and decomposing it into chromomagnetic-favoring and -suppressing components. The imaginary rotation shifts the potential via $\phi+(l-s)\tilde{\Omega}$, leading to explicit $\mathbb{Z}(2)$ breaking and a perturbative confinement mechanism that emerges at high $T$ with a first-order transition. The phase diagram on the $\tilde{\Omega}$–$T$ plane shows an expanded deconfined region at large $\tilde{\Omega}$ and an asymptotic boundary $\tilde{\Omega}_c \to \pi/\sqrt{3}$, while real rotation introduces a cusp in the Polyakov potential and reduces the chromomagnetic condensate. The study also discusses analytic continuation challenges, causality-bound boundary conditions, and potential extensions to include dynamical quarks and SU(3), offering concrete targets for lattice validation of rotating gauge theories.

Abstract

We perturbatively investigate the rotation effect on the Polyakov loop potential in SU(2) gauge theroy within a chromomagnetic background. It is observed that the imaginary rotation spontaneously induces both confinement and chromomagnetic condensation at high temperatures, thereby provides a perturbative window to explore non-perturbative dynamics. Compared to the case without including the induced chromomagnetic field, the perturbative confinement transition becomes first-order, with a temperature-dependent phase boundary that asymptotically approaches $\tildeΩ_c = π/\sqrt{3}$ at high temperatures. This leads to a significantly enriched $\tildeΩ$-$T$ phase diagram characterized by an expanded deconfined region. For real angular velocities, we find that the chromomagnetic condensate decreases with increasing rotation, and that the coupling between rotation, spin, and the chromomagnetic background leads to a cusp in the Polyakov loop potential, suggesting that the underlying dynamics could be more intricate.

Figures (10)

• Figure 1: Evolution of the dimensionless Polyakov loop potential $\beta^4 V$ (left) and the corresponding scaled variable $\beta \sqrt{\langle gH \rangle}$ (right) as functions of $\phi$ at several temperatures, for $\Omega = 0$ and $r=0$.
• Figure 2: Three-dimensional plots of the dimensionless potentials $\beta^4 V_{\text{nonH}}$ (left) and $\beta^4 V_H$ (right) as functions of $\phi$ and $\beta\sqrt{gH}$ for $\tilde{\Omega}=0$.
• Figure 3: Evolution of the dimensionless $\beta^4 V_{\text{nonH}}$ chromomagnetic-suppressing potential with $\phi$ for $\tilde{\Omega}=0, \pi/4, 3\pi/8, \pi/2$ at $H\rightarrow0$ and $r=0$.
• Figure 4: Evolution of the dimensionless Polyakov loop potential $\beta^4 V$ (left) and the corresponding scaled variable $\beta \sqrt{\langle gH \rangle}$ (right) with $\phi$ for several values of $\tilde{\Omega}$ at $T=10\Lambda$ and $r=0$.
• Figure 5: The expectation value of the fundamental Polyakov loop $|L|$ (left) and the scaled chromomagnetic condensate $\beta\sqrt{gH}$ (right) as functions of $\tilde{\Omega}$ at different temperatures.