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Register a new userFinite-temperature study of eight-flavor SU(3) gauge theory
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We present new lattice investigations of finite-temperature transitions for SU(3) gauge theory with Nf=8 light flavors. Using nHYP-smeared staggered fermions we are able to explore renormalized couplings $g^2 lesssim 20$ on lattice volumes as large as $48^3 times 24$. Finite-temperature transitions at non-zero fermion mass do not persist in the chiral limit, instead running into a strongly coupled lattice phase as the mass decreases. That is, finite-temperature studies with this lattice action require even larger $N_T > 24$ to directly confirm spontaneous chiral symmetry breaking.
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We study the discrete beta function of SU(3) gauge theory with Nf=12 massless fermions in the fundamental representation. Using an nHYP-smeared staggered lattice action and an improved gradient flow running coupling $tilde g_c^2(L)$ we determine the continuum-extrapolated discrete beta function up to $g_c^2 approx 8.2$. We observe an IR fixed point at $g_{star}^2 = 7.3left(_{-2}^{+8}right)$ in the $c = sqrt{8t} / L = 0.25$ scheme, and $g_{star}^2 = 7.3left(_{-3}^{+6}right)$ with c=0.3, combining statistical and systematic uncertainties in quadrature. The systematic effects we investigate include the stability of the $(a / L) to 0$ extrapolations, the interpolation of $tilde g_c^2(L)$ as a function of the bare coupling, the improvement of the gradient flow running coupling, and the discretization of the energy density. In an appendix we observe that the resulting systematic errors increase dramatically upon combining smaller $c lesssim 0.2$ with smaller $L leq 12$, leading to an IR fixed point at $g_{star}^2 = 5.9(1.9)$ in the c=0.2 scheme, which resolves to $g_{star}^2 = 6.9left(_{-1}^{+6}right)$ upon considering only $L geq 16$. At the IR fixed point we measure the leading irrelevant critical exponent to be $gamma_g^{star} = 0.26(2)$, comparable to perturbative estimates.
We study an SU(3) gauge theory with Nf=8 degenerate flavors of light fermions in the fundamental representation. Using the domain wall fermion formulation, we investigate the light hadron spectrum, chiral condensate and electroweak S parameter. We consider a range of light fermion masses on two lattice volumes at a single gauge coupling chosen so that IR scales approximately match those from our previous studies of the two- and six-flavor systems. Our results for the Nf=8 spectrum suggest spontaneous chiral symmetry breaking, though fits to the fermion mass dependence of spectral quantities do not strongly disfavor the hypothesis of mass-deformed infrared conformality. Compared to Nf=2 we observe a significant enhancement of the chiral condensate relative to the symmetry breaking scale F, similar to the situation for Nf=6. The reduction of the S parameter, related to parity doubling in the vector and axial-vector channels, is also comparable to our six-flavor results.
We show that the nature of the topological fluctuations in $SU(3)$ gauge theory changes drastically at the finite temperature phase transition. Starting from temperatures right above the phase transition topological fluctuations come in well separated lumps of unit charge that form a non-interacting ideal gas. Our analysis is based on a novel method to count not only the net topological charge, but also separately the number of positively and negatively charged lumps in lattice configurations using the spectrum of the overlap Dirac operator. This enables us to determine the joint distribution of the number of positively and negatively charged topological objects, and we find this distribution to be consistent with that of an ideal gas of unit charged topological objects.
Using a standard cooling method for SU(3) lattice gauge fields constant Abelian magnetic field configurations are extracted after dyon-antidyon constituents forming metastable Q=0 configurations have annihilated. These so-called Dirac sheets, standard and non-standard ones, corresponding to the two U(1) subgroups of the SU(3) group, have been found to be stable if emerging from the confined phase, close to the deconfinement phase transition, with sufficiently nontrivial Polyakov loop values. On a finite lattice we find a nice agreement of the numerical observations with the analytic predictions concerning the stability of Dirac sheets depending on the value of the Polyakov loop.
A novel method to study the bulk thermodynamics in lattice gauge theory is proposed on the basis of the Yang-Mills gradient flow with a fictitious time t. The energy density (epsilon) and the pressure (P) of SU(3) gauge theory at fixed temperature are calculated directly on 32^3 x (6,8,10) lattices from the thermal average of the well-defined energy-momentum tensor (T_{mu nu}^R(x)) obtained by the gradient flow. It is demonstrated that the continuum limit can be taken in a controlled manner from the t-dependence of the flowed data.
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