Wiener-Hopf solution of the free energy TBA problem and instanton sectors in the O(3) sigma model
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| Auteurs principaux: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866913598441259008 |
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| author | Bajnok, Zoltán Balog, János Vona, István |
| author_facet | Bajnok, Zoltán Balog, János Vona, István |
| contents | Perturbation theory in asymptotically free quantum field theories is asymptotic. The factorially growing perturbative coefficients carry information about non-perturbative corrections, which can be related to renormalons and instantons. Using the Wiener-Hopf technique we determine the full analytic solution for the free energy density in the two dimensional $O(N)$ sigma models. For $N>3$ there are no instantons, and we found that the perturbative series carries all the information about the non-perturbative corrections. However, in the $O(3)$ case, we identify several non-perturbative sectors that are not related to the asymptotics of the perturbative series. The number of sectors depends on the observables: for the ground-state energy density we identify three sectors, which we attribute to instantons. For the free energy density in the running perturbative coupling we found infinitely many sectors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_07621 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Wiener-Hopf solution of the free energy TBA problem and instanton sectors in the O(3) sigma model Bajnok, Zoltán Balog, János Vona, István High Energy Physics - Theory Mathematical Physics Perturbation theory in asymptotically free quantum field theories is asymptotic. The factorially growing perturbative coefficients carry information about non-perturbative corrections, which can be related to renormalons and instantons. Using the Wiener-Hopf technique we determine the full analytic solution for the free energy density in the two dimensional $O(N)$ sigma models. For $N>3$ there are no instantons, and we found that the perturbative series carries all the information about the non-perturbative corrections. However, in the $O(3)$ case, we identify several non-perturbative sectors that are not related to the asymptotics of the perturbative series. The number of sectors depends on the observables: for the ground-state energy density we identify three sectors, which we attribute to instantons. For the free energy density in the running perturbative coupling we found infinitely many sectors. |
| title | Wiener-Hopf solution of the free energy TBA problem and instanton sectors in the O(3) sigma model |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2404.07621 |