  We study the infrared renormalon in the gluon condensate in the $SU(N)$ gauge
theory with $n_W$-flavor adjoint Weyl fermions (QCD(adj.))
on~$\mathbb{R}^3\times S^1$ with the $\mathbb{Z}_N$ twisted boundary
conditions. We rely on the so-called large-$\beta_0$ approximation as a
conventional tool to analyze the renormalon, in which only Feynman diagrams
that dominate in the large-$n_W$ limit are considered while the coefficient of
the vacuum polarization is set by hand to the one-loop beta
function~$\beta_0=11/3-2n_W/3$. In the large~$N$ limit within the
large-$\beta_0$ approximation, the W-boson, which acquires the twisted
Kaluza--Klein momentum, produces the renormalon ambiguity corresponding to the
Borel singularity at~$u=2$. This provides an example that the system in the
compactified space~$\mathbb{R}^3\times S^1$ possesses the renormalon ambiguity
identical to that in the uncompactified space~$\mathbb{R}^4$. We also discuss
the subtle issue that the location of the Borel singularity can change
depending on the order of two necessary operations.

High Energy Physics - Theory;High Energy Physics - Lattice;High Energy Physics - Phenomenology