## Abstract

We point out that the location of renormalon singularities in theory on a circle-compactified spacetime R^{d-1}} × S^{1} (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 S^{1} 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} × S^{1}. 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 × S^{1} with Z_{N} twisted boundary conditions in the large-N limit.

Original language | English |
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Article number | 013B01 |

Journal | Progress of Theoretical and Experimental Physics |

Volume | 2020 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 8 2020 |

## All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)