Phase structure of SU(3) gauge theory with two flavors of symmetric-representation fermions

TL;DR

This study investigates the phase structure of SU(3) gauge theory with $N_f=2$ fermions in the symmetric (sextet) representation to test for an infrared fixed point and the possibility of scale separation between confinement and chiral dynamics. Using tadpole-improved clover Wilson fermions on lattices with temporal extents $N_t=6,8,12$, the authors map the deconfinement line, extract hadron spectra, and analyze the heavy-quark potential to assess chiral restoration and confinement. They find no evidence of scale separation: the deconfinement transition coincides with chiral symmetry restoration, and the movement of the deconfinement lines with increasing $N_t$ is consistent with the existence of an IRFP basin in the massless theory. These results place important constraints on candidate walking technicolor scenarios and motivate using improved lattice actions and lighter quark masses to further probe the massless limit and IR conformality in this theory.

Abstract

We have performed numerical simulations of SU(3) gauge theory coupled to Nf=2 flavors of symmetric representation fermions. The fermions are discretized with the tadpole-improved clover action. Our simulations are done on lattices of length L=6, 8, and 12. In all simulation volumes we observe a crossover from a strongly coupled confined phase to a weak coupling deconfined phase. Degeneracies in screening masses, plus the behavior of the pseudoscalar decay constant, indicate that the deconfined phase is also a phase in which chiral symmetry is restored. The movement of the confinement transition as the volume is changed is consistent with avoidance of the basin of attraction of an infrared fixed point of the massless theory.

Figures (11)

• Figure 1: Phase diagram in the $(\beta,\kappa)$ plane. The solid curve is $\kappa_c(\beta)$, where $m_q$ vanishes; the dashed curves are $\kappa_\text{th}(\beta)$, the thermal confinement transition, for three values of $N_t$: short dashes for $N_t=6$, long dashes for $N_t=8$ (lower curve) and $N_t=12$ (upper curve). The star on the $\kappa_c$ curve marks the approximate location of the IR fixed point found in Ref. Shamir:2008pb. The uncertainty in $\kappa_\text{th}$ is in the neighborhood of 0.001.
• Figure 2: Scatter plots of real and imaginary parts of the Polyakov loop from simulations at $\beta=5.5$, volume $8^4$ lattices. Top: $\kappa=0.140$, in the confined phase. Bottom: $\kappa=0.150$, in the deconfined phase.
• Figure 3: Screening masses and $f_P$ for $\beta=5.5$ on volume $(12\times 8^2)\times 8$. In (a) we plot the squares of the quantities, while in (b) we plot the quantities themselves. Crosses show $f_{P}$, pseudoscalars are diamonds, vectors are squares, octagons are axial vectors and bursts are scalars.
• Figure 4: Map of our runs in the $(\beta,\kappa)$ plane. The upper set of points parallels the $\kappa_c$ line in the deconfined phase. The lower set of points populates the regions of $\kappa_\text{th}$ lines.
• Figure 5: AWI quark mass from $(12\times 8^2)\times 8$ lattices. Curves are for (right to left) $\beta=5.1$, 5.2, 5.5, 5.7, 6.0, and 7.0.