Resurgence and semiclassical expansion in two-dimensional large-$N$ sigma models
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2021
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915314097192960 |
|---|---|
| author | Nishimura, Hiromichi Fujimori, Toshiaki Misumi, Tatsuhiro Nitta, Muneto Sakai, Norisuke |
| author_facet | Nishimura, Hiromichi Fujimori, Toshiaki Misumi, Tatsuhiro Nitta, Muneto Sakai, Norisuke |
| contents | The resurgence structure of the 2d $O(N)$ sigma model at large $N$ is studied with a focus on an IR momentum cutoff scale $a$ that regularizes IR singularities in the semiclassical expansion. Transseries expressions for condensates and correlators are derived as series of the dynamical scale $Λ$ (nonperturbative exponential) and coupling $λ_μ$ renormalized at the momentum scale $μ$. While there is no ambiguity when $a > Λ$, we find for $a < Λ$ that the nonperturbative sectors have new imaginary ambiguities besides the well-known renormalon ambiguity in the perturbative sector. These ambiguities arise as a result of an analytic continuation of transseries coefficients to small values of the IR cutoff $a$ below the dynamical scale $Λ$. We find that the imaginary ambiguities are cancelled each other when we take all of them into account. By comparing the semiclassical expansion with the transseries for the exact large-$N$ result, we find that some ambiguities vanish in the $a \rightarrow 0$ limit and hence the resurgence structure changes when going from the semiclassical expansion to the exact result with no IR cutoff. An application of our approach to the ${\mathbb C}P^{N-1}$ sigma model is also discussed. We find in the compactified model with the ${\mathbb Z}_N$ twisted boundary condition that the resurgence structure changes discontinuously as the compactification radius is varied. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_13999 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Resurgence and semiclassical expansion in two-dimensional large-$N$ sigma models Nishimura, Hiromichi Fujimori, Toshiaki Misumi, Tatsuhiro Nitta, Muneto Sakai, Norisuke High Energy Physics - Theory The resurgence structure of the 2d $O(N)$ sigma model at large $N$ is studied with a focus on an IR momentum cutoff scale $a$ that regularizes IR singularities in the semiclassical expansion. Transseries expressions for condensates and correlators are derived as series of the dynamical scale $Λ$ (nonperturbative exponential) and coupling $λ_μ$ renormalized at the momentum scale $μ$. While there is no ambiguity when $a > Λ$, we find for $a < Λ$ that the nonperturbative sectors have new imaginary ambiguities besides the well-known renormalon ambiguity in the perturbative sector. These ambiguities arise as a result of an analytic continuation of transseries coefficients to small values of the IR cutoff $a$ below the dynamical scale $Λ$. We find that the imaginary ambiguities are cancelled each other when we take all of them into account. By comparing the semiclassical expansion with the transseries for the exact large-$N$ result, we find that some ambiguities vanish in the $a \rightarrow 0$ limit and hence the resurgence structure changes when going from the semiclassical expansion to the exact result with no IR cutoff. An application of our approach to the ${\mathbb C}P^{N-1}$ sigma model is also discussed. We find in the compactified model with the ${\mathbb Z}_N$ twisted boundary condition that the resurgence structure changes discontinuously as the compactification radius is varied. |
| title | Resurgence and semiclassical expansion in two-dimensional large-$N$ sigma models |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2112.13999 |