Higher-form entanglement asymmetry. Part I. The limits of symmetry breaking

• URL: http://arxiv.org/abs/2512.15898v1
• Date: Wed, 17 Dec 2025 19:11:15 GMT
• Title: Higher-form entanglement asymmetry. Part I. The limits of symmetry breaking
• Authors: Francesco Benini, Eduardo García-Valdecasas, Stathis Vitouladitis,
• Abstract summary: Entanglement asymmetry is a relative entropy that faithfully diagnoses symmetry breaking in quantum states.<n>We extend such framework to higher-form symmetries and compute entanglement asymmetry in theories with spontaneously-broken continuous zero- and higher-form symmetries.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Entanglement asymmetry is a relative entropy that faithfully diagnoses symmetry breaking in quantum states, possibly within a spatial subregion. In this work, we extend such framework to higher-form symmetries and compute entanglement asymmetry in theories with spontaneously-broken continuous zero- and higher-form symmetries. One of our central results is an entropic Coleman--Mermin--Wagner theorem, for $0$- and $p$-form symmetries, valid also on subregions, which forbids spontaneous breaking of continuous $p$-form symmetries in spacetime dimensions $d\leq p+2$. Our theorem not only qualifies symmetry breaking, it also quantifies it: spontaneous breaking triggers a nonvanishing entanglement asymmetry that grows monotonically towards the infrared, and counts the number of Goldstone fields. Along the way, we derive standalone results concerning the entanglement entropy of Goldstone bosons and gauge fields.

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