Infrared renormalon in the supersymmetric ℂP^N-1 model on ℝ × S¹

In the leading order of the large-N approximation, we study the renormalon ambiguity in the gluon (or, more appropriately, photon) condensate in the 2D supersymmetric ℂP^N-1 model on ℝ × S¹ with the ℤ_N twisted boundary conditions. In our large-N limit, the combination ΛR, where Λ is the dynamical scale and R is the S¹ radius, is kept fixed (we set ΛR ≪ 1 so that the perturbative expansion with respect to the coupling constant at the mass scale 1/R is meaningful). We extract the perturbative part from the large-N expression of the gluon condensate and obtain the corresponding Borel transform B(u). For ℝ × S¹, we find that the Borel singularity at u = 2, which exists in the system on the uncompactified ℝ² and corresponds to twice the minimal bion action, disappears. Instead, an unfamiliar renormalon singularity emerges at u = 3/2 for the compactified space ℝ × S¹. The semi-classical interpretation of this peculiar singularity is not clear because u = 3/2 is not dividable by the minimal bion action. It appears that our observation for the system on ℝ × S¹ prompts reconsideration on the semi-classical bion picture of the infrared renormalon.