More on the infrared renormalon in SU (N) QCD(adj.) on $\mathbb{R}^3\times S^1$

We present additional observations to previous studies on the infrared (IR) renormalon in $SU(N)$ QCD(adj.), the $SU(N)$ gauge theory with $n_W$-flavor adjoint Weyl fermions on $\mathbb{R}^3\times S^1$ with the $\mathbb{Z}_N$ twisted boundary condition. First, we show that, for arbitrary finite $N$, a logarithmic factor in the vacuum polarization of the “photon” (the gauge boson associated with the Cartan generators of $SU(N)$) disappears under the $S^1$ compactification. Since the IR renormalon is attributed to the presence of this logarithmic factor, it is concluded that there is no IR renormalon in this system with finite $N$. This result generalizes the observation made by Anber and Sulejmanpasic [J. High Energy Phys. 1501, 139 (2015)] for $N=2$ and $3$ to arbitrary finite $N$. Next, we point out that, although renormalon ambiguities do not appear through the Borel procedure in this system, an ambiguity appears in an alternative resummation procedure in which a resummed quantity is given by a momentum integration where the inverse of the vacuum polarization is included as the integrand. Such an ambiguity is caused by a simple zero at non-zero momentum of the vacuum polarization. Under the decompactification $R\to\infty$, where $R$ is the radius of the $S^1$, this ambiguity in the momentum integration smoothly reduces to the IR renormalon ambiguity in $\mathbb{R}^4$. We term this ambiguity in the momentum integration “renormalon precursor”. The emergence of the IR renormalon ambiguity in $\mathbb{R}^4$ under the decompactification can be naturally understood with this notion.

Nontrivial center dominance in high temperature QCD

We investigate the properties of quarks and gluons above the chiral phase transition temperature [Formula: see text], using the renormalization group (RG) improved gauge action and the Wilson quark action with two degenerate quarks mainly on a [Formula: see text] lattice. In the one-loop perturbation theory, the thermal ensemble is dominated by the gauge configurations with effectively [Formula: see text] center twisted boundary conditions, making the thermal expectation value of the spatial Polyakov loop take a nontrivial [Formula: see text] center. This is in agreement with our lattice simulation of high temperature quantum chromodynamics (QCD). We further observe that the temporal propagator of massless quarks at extremely high temperature [Formula: see text] remarkably agrees with the temporal propagator of free quarks with the [Formula: see text] twisted boundary condition for [Formula: see text], but differs from that with the [Formula: see text] trivial boundary condition. As we increase the mass of quarks [Formula: see text], we find that the thermal ensemble continues to be dominated by the [Formula: see text] twisted gauge field configurations as long as [Formula: see text] and above that the [Formula: see text] trivial configurations come in. The transition is similar to what we found in the departure from the conformal region in the zero-temperature many-flavor conformal QCD on a finite lattice by increasing the mass of quarks.