We point out that the location of renormalon singularities in theory on a circle-compactified spacetime Rd-1} × S1 (with a small radius R Λ << 1) can differ from that on the non-compactified spacetime Rd. 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(Λk) is changed to O(Λk-1/R) due to the circle compactification Rd → 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 CPN-1} model on R × S1 with ZN twisted boundary conditions in the large-N limit.
All Science Journal Classification (ASJC) codes
- Physics and Astronomy(all)