Abstract
Coleman’s theorem states that continuous internal symmetries cannot be spontaneously broken in two-dimensional quantum field theories (QFTs). In this work we consider surface (i.e. two-dimensional) defects in d-dimensional conformal field theories (CFTs) invariant under a continuous internal symmetry group G. We study under which conditions it is possible for a surface defect to break spontaneously a continuous internal symmetry. We find that spontaneous symmetry breaking (SSB) is impossible under reasonable assumptions on the defect Renormalization Group (RG) flow. Counterexamples are possible only for exotic RG flows, that do not terminate at a fixed-point. We discuss an example of this kind. We also illustrate our no-go result with an effective field theory analysis of generic defect RG flows. We find a generic weakly coupled defect universality class (with no SSB), where correlation functions decay logarithmically. Our analysis generalizes the recent discovery by Metlitski of the extraordinary-log boundary universality class in the O(N) model.
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Acknowledgments
We thank P. Ferrero, A.Gimenez-Grau, P.Kravchuk, A. Podo and S.Zhong for useful discussions. We are particularly grateful to M. Mezei for collaboration at the early stages of this project and to Z. Komargodski, M. Metlitski, and A. Raviv-Moshe for valuable comments on a preliminary version of this manuscript. We also thank M. Meineri for carefully reviewing this manuscript, providing several useful comments. GC is supported by the Simons Foundation (Simons Collaboration on the Non-perturbative Bootstrap) grants 488647 and 397411.
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Cuomo, G., Zhang, S. Spontaneous symmetry breaking on surface defects. J. High Energ. Phys. 2024, 22 (2024). https://doi.org/10.1007/JHEP03(2024)022
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DOI: https://doi.org/10.1007/JHEP03(2024)022