Abstract
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 ε-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 ε. In particular, taking ε → 1, 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 ε. 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.
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Acknowledgments
We are grateful to M. Billò, M. Meineri, M. Lemos for useful discussions. The research of LB is funded through the MIUR program for young researchers “Rita Levi Montalcini”. The research of DB received partial support through the STFC grant ST/S005803/1 and through the Grant for Internationalization of the University of Torino. DB would also like to thank IHES for hospitality during completion of this work. AGG is supported by the Simons Foundation by grants 915279 (IHES) and 733758 (Bootstrap Collaboration).
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Bianchi, L., Bonomi, D., de Sabbata, E. et al. Analytic bootstrap for magnetic impurities. J. High Energ. Phys. 2024, 80 (2024). https://doi.org/10.1007/JHEP05(2024)080
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DOI: https://doi.org/10.1007/JHEP05(2024)080