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Register a new userInfrared properties of propagators in Landau-gauge pure Yang-Mills theory at finite temperature
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The finite-temperature behavior of gluon and of Faddeev-Popov-ghost propagators is investigated for pure SU(2) Yang-Mills theory in Landau gauge. We present nonperturbative results, obtained using lattice simulations and Dyson-Schwinger equations. Possible limitations of these two approaches, such as finite-volume effects and truncation artifacts, are extensively discussed. Both methods suggest a very different temperature dependence for the magnetic sector when compared to the electric one. In particular, a clear thermodynamic transition seems to affect only the electric sector. These results imply in particular the confinement of transverse gluons at all temperatures and they can be understood inside the framework of the so-called Gribov-Zwanziger scenario of confinement.
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Greens functions are a central element in the attempt to understand non-perturbative phenomena in Yang-Mills theory. Besides the propagators, 3-point Greens functions play a significant role, since they permit access to the running coupling constant and are an important input in functional methods. Here we present numerical results for the two non-vanishing 3-point Greens functions in 3d pure SU(2) Yang-Mills theory in (minimal) Landau gauge, i.e. the three-gluon vertex and the ghost-gluon vertex, considering various kinematical regimes. In this exploratory investigation the lattice volumes are limited to 20^3 and 30^3 at beta=4.2 and beta=6.0. We also present results for the gluon and the ghost propagators, as well as for the eigenvalue spectrum of the Faddeev-Popov operator. Finally, we compare two different numerical methods for the evaluation of the inverse of the Faddeev-Popov matrix, the point-source and the plane-wave-source methods.
We study the pressure anisotropy in anisotropic finite-size systems in SU(3) Yang-Mills theory at nonzero temperature. Lattice simulations are performed on lattices with anisotropic spatial volumes with periodic boundary conditions. The energy-momentum tensor defined through the gradient flow is used for the analysis of the stress tensor on the lattice. We find that a clear finite-size effect in the pressure anisotropy is observed only at a significantly shorter spatial extent compared with the free scalar theory, even when accounting for a rather large mass in the latter.
Euclidean strong coupling expansion of the partition function is applied to lattice Yang-Mills theory at finite temperature, i.e. for lattices with a compactified temporal direction. The expansions have a finite radius of convergence and thus are valid only for $beta<beta_c$, where $beta_c$ denotes the nearest singularity of the free energy on the real axis. The accessible temperature range is thus the confined regime up to the deconfinement transition. We have calculated the first few orders of these expansions of the free energy density as well as the screening masses for the gauge groups SU(2) and SU(3). The resulting free energy series can be summed up and corresponds to a glueball gas of the lowest mass glueballs up to the calculated order. Our result can be used to fix the lower integration constant for Monte Carlo calculations of the thermodynamic pressure via the integral method, and shows from first principles that in the confined phase this constant is indeed exponentially small. Similarly, our results also explain the weak temperature dependence of glueball screening masses below $T_c$, as observed in Monte Carlo simulations. Possibilities and difficulties in extracting $beta_c$ from the series are discussed.
The authors of ref. Phys.Rev. D94 (2016) no.1, 014502 reported about a careful analysis of the impact of lattice artifacts on the $SU(3)$ gauge-field propagators. In particular, they found that the low-momentum behavior of the renormalized propagators depends on the lattice bare coupling and interpreted this fact as the result of it being affected by finite lattice spacing artifacts. We do not share this interpretation and present here a different and more suitable explanation for these results.
Euclidean two-point correlators of the energy-momentum tensor (EMT) in SU(3) gauge theory on the lattice are studied on the basis of the Yang-Mills gradient flow. The entropy density and the specific heat obtained from the two-point correlators are shown to be in good agreement with those from the one-point functions of EMT. These results constitute a first step toward the first principle simulations of the transport coefficients with the gradient flow.
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