Exploring Partially Confined Phases

TL;DR

This work extends high-temperature analyses of $SU(N)$ gauge theories by adding a center-symmetric external potential depending on Polyakov-loop traces, enabling partially confining phases where $Z(N)$ breaks to $Z(L)$. By analyzing the high-$T$ effective action $S_{eff}$, the authors map phase diagrams and compute thermodynamic quantities, string tensions $\sigma_k$, Debye masses $m_D$, and 't Hooft loop surface tensions $\rho_k$ for general $SU(N)$, with explicit results for $SU(4)$ and $SU(6)$. They show that the phase structure is rich and tunable via the couplings $\lambda_k$, with Casimir-scaling results for a broad class of kink-driven surface tensions. The results provide analytic benchmarks for lattice studies and offer insight into caloron-driven nonperturbative effects in confining gauge theories at high temperature.

Abstract

Phases of SU(N) gauge theories in which the global Z(N) symmetry breaks spontaneously to a subgroup Z(L) can be realized by adding appropriate Wilson line terms to the gauge action. These phases are partially confining, in the sense that quarks are confined but bound states of L quarks are not. At temperatures large compared to the normal deconfinement temperature, the phase diagram, pressure, string tensions, and 't Hooft loop surface tensions can be calculated analytically. Approximate scaling laws emerge naturally for both string tensions and surface tensions.

Figures (3)

• Figure 1: Phase diagram for $SU(4)$.
• Figure 2: $SU(6)$ phases for $\lambda_1>0$.
• Figure 3: $SU(6)$ phases for $\lambda_1<0$.