New Phases of SU(3) and SU(4) at Finite Temperature

TL;DR

The paper investigates finite-temperature $SU(N)$ gauge theories augmented by an adjoint Polyakov loop term, showing that negative $h_A$ induces new phases: a novel skewed phase in $SU(3)$ and a partially confined phase with $Z(4)\to Z(2)$ in $SU(4)$. A perturbative one-loop plus classical $-h_A Tr_A P$ effective potential $V_{eff}$ explains the observed phase structure and thermodynamics, aligning with lattice results in key respects while revealing new symmetry-breaking patterns. The work highlights a rich high-temperature phase diagram controlled by $h_A/T^3$, offering predictions for pressures and order-parameter behavior and suggesting broader implications for confinement mechanisms, calorons, and extensions to larger gauge groups. It also discusses limitations due to neglecting fluctuations and low-temperature physics, framing future tests and cross-checks with lattice experiments and potential connections to spin-system universality.

Abstract

The addition of an adjoint Polyakov loop term to the action of a pure gauge theory at finite temperature leads to new phases of SU(N) gauge theories. For SU(3), a new phase is found which breaks Z(3) symmetry in a novel way; for SU(4), the new phase exhibits spontaneous symmetry breaking of Z(4) to Z(2), representing a partially confined phase in which quarks are confined, but diquarks are not. The overall phase structure and thermodynamics is consistent with a theoretical model of the effective potential for the Polyakov loop based on perturbation theory.

Figures (12)

• Figure 1: $SU(3)$ phase diagram in the $\beta-H_A$ plane. The dotted line represents a plausible extrapolation.
• Figure 2: $SU(3)$ Polyakov loop histogram at $\beta=6.5$, $H_A=-0.05$.
• Figure 5: $SU(3)$ Polyakov loop histogram at $\beta=6.5$, $H_A=-0.1$.
• Figure 7: Projected $Tr_{F}P$ for $\beta=6.5$.
• Figure 8: Adjoint susceptibility $\chi_{M}$ for $\beta=6.5$.