Deconfinement and Chiral Symmetry Restoration in an SU(3) Gauge Theory with Adjoint Fermions

TL;DR

This work probes whether confinement and chiral symmetry restoration in an SU(3) gauge theory with adjoint fermions can occur at separate temperatures. Using lattice simulations with four Majorana fermions, the authors find that deconfinement at $T_d$ is a strongly first-order transition, while chiral symmetry restoration occurs at a higher temperature $T_c \,\approx\,8\,T_d$ and appears continuous in the chiral limit. Bulk thermodynamics are dominated by the deconfinement transition, with a sizable latent heat and rapid screening of static charges above $T_d$, whereas bulk observables show little change at $T_c$ despite the vanishing chiral condensate. The results demonstrate a clear decoupling of confinement and chiral restoration in aQCD and provide quantitative estimates for $T_c/T_d$ and the associated thermodynamic signatures, including Goldstone-mode effects in the intermediate phase.

Abstract

We analyze the finite temperature phase diagram of$QC$ with fermions in the adjoint representation. The simulations performed with four dynamical Majorana fermions show that the deconfinement and chiral phase transitions occur at two distinct temperatures. While the deconfinement transition is first order at T_d we find evidence for a continuous chiral transition at a higher temperature $T_c ~ 8 T_d. We observe a rapid change of bulk thermodynamic observables at T_d which reflects the increase in the number of degrees of freedom. However, these show little variation at T_c, where the fermion condensate vanishes. We also analyze the potential between static fundamental and adjoint charges in all three phases and extract the corresponding screening masses above T_d.

Figures (6)

• Figure 1: Expectation value of the absolute value of the Polyakov loop for the fundamental representation, $L_3$, versus coupling, $\beta=6/g^2$, calculated on lattices of size $8^3\times 4$ (a). Shown are results from simulations with different fermion masses and a result from simulations in the pure gauge sector ($m\rightarrow \infty$). Figure 1b gives a comparison of results from two different lattice sizes for $m=0.02$ and in addition also shows the adjoint Polyakov loop $L_8$.
• Figure 2: Static potentials for fundamental and adjoint charges calculated below (a) and above (b) $T_{\rm d}$ on lattices of size $16^3\times 4$ at $\beta=5.25$ and $5.4$, respectively. Calculations have been performed with fermion mass $m=0.02$. The lines show fits as discussed in the text. For $\beta=5.25$ the potentials have been normalized at $R=1$. Also note the different scales in (a) and (b).
• Figure 3: Fermion condensate (a) and fermionic susceptibility (b) calculated on lattices of size $8^3 \times 4$ for several values of the fermion mass. In Figure 3a we also show the result of an extrapolation to $m=0$ (see text). Also shown in Figure 3b are interpolating curves with the corresponding error band obtained with the help of the Ferrenberg-Swendsen reweighting method.
• Figure 4: Chiral susceptibility versus $1/\sqrt{m}$ at three values of the gauge coupling in the intermediate phase, i.e. for $T_{\rm d} < T < T_{\rm c}$.
• Figure 5: Normalized expectation values of the gluon action defined by Eq. 18 (plaquette expectation value) for different fermion masses on lattices of size $8^3 \times 4$. Also shown is the corresponding result obtained in the pure gauge sector ($m\rightarrow \infty$) on a $16^3\times 4$ lattice.