Infrared renormalon in the supersymmetric $\mathbb{C}{P}^{N-1}$ model on $\mathbb{R}\times S^1$

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 $\Lambda R\ll 1$ 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 \emph{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.

26 pages, 1 figure, the final version to appear in PTEP

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Cited by in corpus (12)

• Lattice $\mathbb{C}{P}^{N-1}$ model with ${\mathbb{Z}}_N$ twisted boundary condition: bions, adiabatic continuity and pseudo-entropy
• Treating Divergent Perturbation Theory: Lessons from Exactly Solvable 2D Models at Large $N$
• Quantum phase transition and Resurgence: Lessons from 3d $\mathcal{N}=4$ SQED
• Identification of perturbative ambiguity canceled against bion
• Renormalons beyond the Borel plane
• Strongly coupled QFT dynamics via TQFT coupling
• TQFT at work for IR-renormalons, resurgence and Lefschetz decomposition
• Confinement as Analytic Continuation Beyond Infinity
• Remarks on the large-$N$ $\mathbb{C}{P}^{N-1}$ model
• Renormalon Subtraction in OPE by Dual Space Approach: Nonlinear Sigma Model and QCD
• More on the infrared renormalon in $SU(N)$ QCD(adj.) on ${\mathbb{R}}^3\times S^1$
• The UV sensitivity of the Higgs potential in Gauge-Higgs Unification