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 |$mathbb{R}^3imes S^1$| with the |$mathbb{Z}_N$| twisted boundary conditions. We rely on the so-called large-|$eta_0$| 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 |$eta_0=11/3-2n_W/3$|?. In the large |$N$| limit within the large-|$eta_0$| 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 |$mathbb{R}^3imes S^1$| 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.
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