Scaling and Goldstone effects in a QCD with two flavours of adjoint quarks

TL;DR

This paper investigates QCD with two Dirac fermions in the adjoint representation at finite temperature to disentangle deconfinement and chiral transitions and to test the universality class of the chiral transition. Using lattice simulations with staggered adjoint quarks, the authors locate the chiral critical point at $\beta_c=5.624(2)$ and demonstrate that the chiral condensate scales according to the three-dimensional $O(2)$ universality class, with partial agreement to $O(6)$. They confirm Goldstone-mode effects in the chirally broken phase and establish a first-order deconfinement transition at $\beta_d=5.236(3)$, yielding a ratio $T_c/T_d\approx7.8(2)$. The results provide a coherent picture of aQCD thermodynamics between the two transitions and validate the use of this model to study chiral criticality and Goldstone phenomena in a controlled setting, with implications for understanding universality in finite-temperature gauge theories.

Abstract

We study QCD with two Dirac fermions in the adjoint representation at finite temperature by Monte Carlo simulations.In such a theory the deconfinement and chiral phase transitions occur at different temperatures. We locate the second order chiral transition point at beta_c=5.624(2) and show that the scaling behaviour of the chiral condensate in the vicinity of beta_c is in full agreeement with that of the 3d O(2) universality class, and to a smaller extent comparable to the 3d O(6) class. From the previously determined first order deconfinement transition point beta_d=5.236(3) and the two-loop beta function we find the ratio T_c/T_d = 7.8(2). In the region between the two phase transitions we explicitly confirm the quark mass dependence of the chiral condensate which is expected due to the existence of Goldstone modes like in 3d O(N) spin models. At the deconfinement transition the condensate shows a gap, and below beta_d, it is nearly mass-independent for fixed beta.

Figures (12)

• Figure 1: The chiral condensate ${\langle \bar{\psi}\psi \rangle }$ (a) and the Polyakov loop $L_3$ (b) versus $\beta$ and $m_qa$ on the $8^3\times 4$ lattice (plot (b) has been rotated by $90^{\circ}$). The filled squares denote the new data, the empty ones are from Ref. Karsch:1998qj. The dotted lines indicate the height. The data points are connected by straight lines to guide the eye.
• Figure 2: The universal scaling function $f_G=Mh^{-1/\delta}$ versus the scaling variable $z=t h^{-1/\beta\delta}$ for $N=2$Engels:2000xw, $N=4$Engels:2003nq and $N=6$Holtmann:2003he. Parametrizations of the curves can be found in Refs. Engels:2000xwEngels:2003nqHoltmann:2003he.
• Figure 3: The susceptibility $\chi_{dis}$ as a function of $\beta$ for the three smallest masses $m_qa=0.005,\,0.01$ and 0.02 on the $8^3\times 4$ lattice. The solid lines are the results from reweighting, the dashed lines show the Jackknife error corridor.
• Figure 4: The parameter $d_c^1(\beta-\beta_c)$ as a function of $\beta$ for $O(2)$ (circles) and $O(6)$ exponents (triangles). The straight lines are fits to the values at $\beta= 5.6,5.65$ and $5.7\,$. The zeros of the fits are given by the numbers in the plot.
• Figure 5: The chiral condensate ${\langle \bar{\psi}\psi \rangle }$ as a function of $(m_qa)^{1/2}$ for all $\beta$-values between 5.3 (highest values) and 5.9 (lowest values) from $N_\sigma$N_σ$^3 \times 4$ lattices with $N_\sigma$N_σ$=8$ (circles), 12 (triangles) and 16 (diamonds). The lines are fits with the ansatz (\ref{['pbpgold']}), the filled circles denote the extrapolations to $m_qa =0$.