Renormalon structure in compactified spacetime

We point out that the location of renormalon singularities in theory on a circle-compactified spacetime R^d-1} × S¹ (with a small radius R Λ << 1) can differ from that on the non-compactified spacetime R^d. We argue this under the following assumptions, which are often realized in large N theories with twisted boundary conditions: (i) a loop integrand of a renormalon diagram is volume independent, i.e. it is not modified by the compactification, and (ii) the loop momentum variable along the S¹ direction is not associated with the twisted boundary conditions and takes the values n/R with integer n. We find that the Borel singularity is generally shifted by-1/2 in the Borel u-plane, where the renormalon ambiguity of O(Λ^k) is changed to O(Λ^k-1/R) due to the circle compactification R^d → Rd^-1 × S¹. The result is general for any dimension d and is independent of details of the quantities under consideration. As an example, we study the CP^N-1} model on R × S¹ with Z_N twisted boundary conditions in the large-N limit.