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<p>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 <i>p</i>-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 <i>p</i>-form symmetries as well as non-Abelian 0-form symmetries.</p>

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SymTFT for continuous symmetries: non-linear realizations and spontaneous breaking

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月6日

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  • Federico Bonetti,
  • Michele Del Zotto,
  • Ruben Minasian

摘要

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.