KEK Theory workshop 2019

Infrared renormalon in the supersymmetric CPN−1 model on R×S1

5 Dec 2019, 15:00

3h

In front of Kobayashi Hall, Kenkyu-Honkan bldg. 1F (KEK)

Poster

Speaker

Mr Okuto Morikawa

Description

In the leading order of the large $N$ approximation, we study the renormalon ambiguity in the gluon (or more appropriately, photon) condensate in the two-dimensional 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 $\mathrm{\Lambda }R$, where $\mathrm{\Lambda }$ is the dynamical scale and $R$ is the $S^1$ radius, is kept fixed (we set $\mathrm{\Lambda }R\ll 1$ 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 un-compactified ${\mathbb{R}}^2$ 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.