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arXiv · 2509.10343

SymTFT for Continuous Symmetries: Non-linear Realizations and Spontaneous Breaking

Federico Bonetti·Michele Del Zotto·Ruben Minasian
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Abstract

It is well known that continuous symmetries of quantum fields can be realized non-linearly, e.g. in the context of sigma models, and can also be spontaneously broken on non-compact spacetimes. In this note we study how these effects are realized in the context of the topological symmetry theory for continuous symmetries. In particular, we explain coset realizations and their higher $p$-form symmetry versions from this perspective, as well as uplifts to higher groups and non-invertible symmetries. Moreover, using a setup with boundaries and corners, we explore spontaneous symmetry breaking scenarios for higher $p$-form symmetries as well as non-Abelian $0$-form symmetries.

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Federico Bonetti, Michele Del Zotto, Ruben Minasian. 2025-09-12. SymTFT for Continuous Symmetries: Non-linear Realizations and Spontaneous Breaking. https://arxiv.org/abs/2509.10343

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