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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| Online-Zugang: | https://arxiv.org/abs/2312.05221 |
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| _version_ | 1866910480522543104 |
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| author | Bianchi, Lorenzo Bonomi, Davide de Sabbata, Elia Gimenez-Grau, Aleix |
| author_facet | Bianchi, Lorenzo Bonomi, Davide de Sabbata, Elia Gimenez-Grau, Aleix |
| contents | We study the $O(3)$ critical model and the free theory of a scalar triplet in the presence of a magnetic impurity. We use analytic bootstrap techniques to extract results in the $\varepsilon$-expansion. First, we extend by one order in perturbation theory the computation of the beta function for the defect coupling in the free theory. Then, we analyze in detail the low-lying spectrum of defect operators, focusing on their perturbative realization when the defect is constructed as a path-ordered exponential. After this, we consider two different bulk two-point functions and we compute them using the defect dispersion relation. For a free bulk theory, we are able to fix the form of the correlator at all orders in $\varepsilon$. In particular, taking $\varepsilon\to1$, we can show that in $d=3$ one does not have a consistent and non-trivial defect CFT. For an interacting bulk, we compute the correlator up to second order in $\varepsilon$. Expanding these results in the bulk and defect block expansions, we are able to extract an infinite set of defect CFT data. We discuss low-spin ambiguities that affect every result computed through the dispersion relation and we use a combination of consistency conditions and explicit diagrammatic calculations to fix this ambiguity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_05221 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Analytic bootstrap for magnetic impurities Bianchi, Lorenzo Bonomi, Davide de Sabbata, Elia Gimenez-Grau, Aleix High Energy Physics - Theory We study the $O(3)$ critical model and the free theory of a scalar triplet in the presence of a magnetic impurity. We use analytic bootstrap techniques to extract results in the $\varepsilon$-expansion. First, we extend by one order in perturbation theory the computation of the beta function for the defect coupling in the free theory. Then, we analyze in detail the low-lying spectrum of defect operators, focusing on their perturbative realization when the defect is constructed as a path-ordered exponential. After this, we consider two different bulk two-point functions and we compute them using the defect dispersion relation. For a free bulk theory, we are able to fix the form of the correlator at all orders in $\varepsilon$. In particular, taking $\varepsilon\to1$, we can show that in $d=3$ one does not have a consistent and non-trivial defect CFT. For an interacting bulk, we compute the correlator up to second order in $\varepsilon$. Expanding these results in the bulk and defect block expansions, we are able to extract an infinite set of defect CFT data. We discuss low-spin ambiguities that affect every result computed through the dispersion relation and we use a combination of consistency conditions and explicit diagrammatic calculations to fix this ambiguity. |
| title | Analytic bootstrap for magnetic impurities |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2312.05221 |