Instantons, renormalons and the theta angle in integrable sigma models
Some sigma models which admit a theta angle are integrable at both $\vartheta=0$ and $\vartheta=\pi$. This includes the well-known $O(3)$ sigma model and two families of coset sigma models studied by Fendley. We consider the ground state energy of these models in the presence of a magnetic field, wh...
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| Format: | Article |
| Language: | English |
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SciPost
2023-11-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.15.5.184 |
| _version_ | 1797639356562800640 |
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| author | Marcos Mariño, Ramon Miravitllas, Tomas Reis |
| author_facet | Marcos Mariño, Ramon Miravitllas, Tomas Reis |
| author_sort | Marcos Mariño, Ramon Miravitllas, Tomas Reis |
| collection | DOAJ |
| description | Some sigma models which admit a theta angle are integrable at both $\vartheta=0$ and $\vartheta=\pi$. This includes the well-known $O(3)$ sigma model and two families of coset sigma models studied by Fendley. We consider the ground state energy of these models in the presence of a magnetic field, which can be computed with the Bethe Ansatz. We obtain explicit results for its non-perturbative corrections and we study the effect of the theta angle on them. We show that imaginary, exponentially small corrections due to renormalons remain unchanged, while instanton corrections change sign, as expected. We find in addition corrections due to renormalons which also change sign as we turn on the theta angle. Based on these results we present an explicit non-perturbative formula for the topological susceptibility of the $O(3)$ sigma model in the presence of a magnetic field, in the weak coupling limit. |
| first_indexed | 2024-03-11T13:15:40Z |
| format | Article |
| id | doaj.art-7a6d1e0c533a478495f781e9b5a320cf |
| institution | Directory Open Access Journal |
| issn | 2542-4653 |
| language | English |
| last_indexed | 2024-03-11T13:15:40Z |
| publishDate | 2023-11-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj.art-7a6d1e0c533a478495f781e9b5a320cf2023-11-03T12:20:00ZengSciPostSciPost Physics2542-46532023-11-0115518410.21468/SciPostPhys.15.5.184Instantons, renormalons and the theta angle in integrable sigma modelsMarcos Mariño, Ramon Miravitllas, Tomas ReisSome sigma models which admit a theta angle are integrable at both $\vartheta=0$ and $\vartheta=\pi$. This includes the well-known $O(3)$ sigma model and two families of coset sigma models studied by Fendley. We consider the ground state energy of these models in the presence of a magnetic field, which can be computed with the Bethe Ansatz. We obtain explicit results for its non-perturbative corrections and we study the effect of the theta angle on them. We show that imaginary, exponentially small corrections due to renormalons remain unchanged, while instanton corrections change sign, as expected. We find in addition corrections due to renormalons which also change sign as we turn on the theta angle. Based on these results we present an explicit non-perturbative formula for the topological susceptibility of the $O(3)$ sigma model in the presence of a magnetic field, in the weak coupling limit.https://scipost.org/SciPostPhys.15.5.184 |
| spellingShingle | Marcos Mariño, Ramon Miravitllas, Tomas Reis Instantons, renormalons and the theta angle in integrable sigma models SciPost Physics |
| title | Instantons, renormalons and the theta angle in integrable sigma models |
| title_full | Instantons, renormalons and the theta angle in integrable sigma models |
| title_fullStr | Instantons, renormalons and the theta angle in integrable sigma models |
| title_full_unstemmed | Instantons, renormalons and the theta angle in integrable sigma models |
| title_short | Instantons, renormalons and the theta angle in integrable sigma models |
| title_sort | instantons renormalons and the theta angle in integrable sigma models |
| url | https://scipost.org/SciPostPhys.15.5.184 |
| work_keys_str_mv | AT marcosmarinoramonmiravitllastomasreis instantonsrenormalonsandthethetaangleinintegrablesigmamodels |