Renormalon structure in compactified spacetime
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 \to {R}^{d-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 {C} P^{N-1} model on {R} × S^1 with {Z}_N twisted boundary conditions in the large-N limit.
- Publication:
-
Progress of Theoretical and Experimental Physics
- Pub Date:
- January 2020
- DOI:
- 10.1093/ptep/ptz147
- arXiv:
- arXiv:1909.09579
- Bibcode:
- 2020PTEP.2020a3B01I
- Keywords:
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- High Energy Physics - Theory;
- High Energy Physics - Lattice;
- High Energy Physics - Phenomenology
- E-Print:
- 15 pages, 1 figure, version to appear in PTEP