We study the infrared (IR) renormalon in the gluon condensate in the SU (N) gauge theory with nW -flavor adjoint Weyl fermions (QCD(adj.)) on R3 × S1 with the ZN twisted boundary conditions. We rely on the so-called large-β0 approximation as a conventional tool to analyze the renormalon, in which only Feynman diagrams that dominate in the large nW limit are considered while the coefficient of the vacuum polarization is set by hand to the one-loop beta function β0 = 11/3 − 2nW /3. In the large N limit within the large-β0 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 R3 × S1 possesses the renormalon ambiguity identical to that in the un-compactified space R4. We also discuss a subtle issue that the location of the Borel singularity can change depending on the order we take two necessary operations.
|Publication status||Published - Sep 12 2019|
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