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- Title
Infrared renormalon in the supersymmetric |$\mathbb{C}P^{N-1}$| model on |$\mathbb{R}\times S^1$|.
- Authors
Ishikawa, Kosuke; Morikawa, Okuto; Nakayama, Akira; Shibata, Kazuya; Suzuki, Hiroshi; Takaura, Hiromasa
- Abstract
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 |$\mathbb{C}P^{N-1}$| model on |$\mathbb{R}\times S^1$| with the |$\mathbb{Z}_N$| twisted boundary conditions. In our large- |$N$| limit, the combination |$\Lambda R$| , where |$\Lambda$| is the dynamical scale and |$R$| is the |$S^1$| radius, is kept fixed (we set |$\Lambda R\ll1$| 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 |$\mathbb{R}\times S^1$| , we find that the Borel singularity at |$u=2$| , which exists in the system on the uncompactified |$\mathbb{R}^2$| and corresponds to twice the minimal bion action, disappears. Instead, an unfamiliar renormalon singularity emerges at |$u=3/2$| for the compactified space |$\mathbb{R}\times S^1$|. 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 |$\mathbb{R}\times S^1$| prompts reconsideration on the semi-classical bion picture of the infrared renormalon.
- Subjects
SEMI-classical model (Atomic physics); PERTURBATION theory; VACUUM energy (Astronomy); PARTICLES (Nuclear physics); STANDARD model (Nuclear physics)
- Publication
Progress of Theoretical & Experimental Physics: PTEP, 2020, Vol 2020, Issue 2, pN.PAG
- ISSN
2050-3911
- Publication type
Article
- DOI
10.1093/ptep/ptaa002