Chromomagnetic Condensate in Finite-Temperature SU(2) Yang-Mills Theory under Imaginary Rotation

TL;DR

This paper analyzes the finite-temperature SU(2) Savvidy model under an imaginary angular velocity $\Omega_I$, incorporating a constant chromomagnetic condensate $H$ and a Polyakov-loop background $\phi$. Using the background-field method, it computes the one-loop effective potential and disentangles its real and imaginary parts, finding that $\Omega_I$ modifies both $H$ and $\phi$ and can partially suppress the Nielsen–Olesen instability within a finite parameter window. A high-temperature expansion reveals that $g_{\text{eff}}$ grows with $\Omega_I$, signaling enhanced infrared interactions and a tendency toward confinement-like behavior, while the curvature with respect to $\Omega_I$ yields a negative contribution to the moment of inertia from the chromomagnetic condensate. The results provide insight into how magnetic gluon sectors influence rotating gauge theories and may help reconcile lattice findings on rotating gluonic matter; they also establish a framework for future extensions to SU(3) and quark degrees of freedom.

Abstract

We investigate the finite-temperature SU(2) Savvidy model under an imaginary angular velocity. Employing the background-field method, we derive the one-loop effective potential and analyze both its real and imaginary parts. We demonstrate that imaginary rotation modifies the chromomagnetic condensate and the Polyakov loop, and can partially suppress the Nielsen-Olesen instability of the chromomagnetic background. Moreover, a high-temperature expansion shows that imaginary rotation strengthens the effective coupling and that the chromomagnetic field induces a negative contribution to the moment of inertia.

Figures (5)

• Figure 1: Real part of the effective potential $V_R$ as a function of $\beta g\phi$ for several values of $\beta\sqrt{gH}$ at $\Omega_I=\pi/2$.
• Figure 2: Polyakov-loop phase $\beta g\phi$ as a function of the imaginary angular velocity $\Omega_I$ at high temperature $T=10\mu$. The black curve corresponds to the case with a chromomagnetic condensate $gH$, while the red curve shows the result without taking into account the condensate.
• Figure 3: Dependence of the chromomagnetic condensate on the imaginary angular velocity $\Omega_I$ at fixed temperature $T = 10\mu$.
• Figure 4: Imaginary part of the effective potential, $V_I$, as a function of the imaginary angular velocity $\Omega_I$ at temperature $T=10\mu$, evaluated at the corresponding minima of the real part $V_R$.
• Figure 5: Dependence of the chromomagnetic condensate on the imaginary angular velocity $\Omega_I$ at fixed temperature $T = 10\mu$, obtained from the high-temperature expansion Eq. \ref{['eq:VRexpansion']}.