Abstract
We investigate theories of Nambu-Goldstone bosons where the spontaneously broken continuous symmetry is non-invertible. In such theories, the vacua generically parameterize an orbifold. We study in detail the simplest example of a single free scalar with shift symmetry, modded by reflection symmetry. At singular points of the vacuum manifold, we show that the spectrum of NG excitations is reduced, in particular there are no single-particle states. At the smooth points, on the other hand, single NG modes are present. We show that this is a consequence of the fact that at those points one can construct invertible operators implementing the continuous symmetry on the Hilbert space.
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Acknowledgments
We thank Andrea Antinucci, Giovanni Galati, Iñaki Garcia-Etxebarria, Diego Hofman, Zohar Komargodski, Ho Tat Lam, Giovanni Rizi, Luigi Tizzano, Stathis Vitouladitis and Sasha Zhiboedov for helpful discussions. J.A.D. and R.A. are respectively a Postdoctoral Researcher and a Research Director of the F.R.S.-FNRS (Belgium). S.C. is partially supported by funds from the Solvay Family. The research of J.A.D., R.A. and S.C. is supported by IISN-Belgium (convention 4.4503.15) and through an ARC advanced project.
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Damia, J.A., Argurio, R. & Chaudhuri, S. When the moduli space is an orbifold: spontaneous breaking of continuous non-invertible symmetries. J. High Energ. Phys. 2024, 42 (2024). https://doi.org/10.1007/JHEP03(2024)042
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DOI: https://doi.org/10.1007/JHEP03(2024)042