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SymTFT construction of gapless exotic-foliated dual models
by Fabio Apruzzi, Francesco Bedogna, Salvo Mancani
Submission summary
| Authors (as registered SciPost users): | Salvatore Mancani |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2504.11449v2 (pdf) |
| Date submitted: | Aug. 5, 2025, 10:38 a.m. |
| Submitted by: | Salvatore Mancani |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We construct Symmetry Topological Field Theories (SymTFTs) for continuous subsystem symmetries, which are inherently non-Lorentz-invariant. Our framework produces dual bulk descriptions -- gapped foliated and exotic SymTFTs -- that generate gapless boundary theories with spontaneous subsystem symmetry breaking via interval compactification. In analogy with the sandwich construction of SymTFT, we call this Mille-feuille. This is done by specifying gapped and symmetry-breaking boundary conditions. In this way we obtain the foliated dual realizations of various models, including the XY plaquette, XYZ cube, and $\phi$, $\hat{\phi}$ theories. This also captures self-duality symmetries as condensation defects and provides a systematic method for generating free theories that non-linearly realize subsystem symmetries.
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- Present a breakthrough on a previously-identified and long-standing research stumbling block
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This work is a natural generalization in this field and will help the further study of gapless models, or spontaneous symmetry breaking phases, with subsystem symmetries. However, I hope the authors can clarify the following points in the requested changes.
Requested changes
The SymTFT gains its power at separating the symmetrical and dynamical data at different boundaries, and is universal for different models if the symmetry is given. In this paper the authors only studied one specific choice of boundary condition that is used to reproduce the models reviewed in section 3. This may diminish this article's significance and impact. Therefore, I hope the authors can address the following questions:
- Is it easy to study or classify different topological boundary conditions (e.g. Dirichlet or Neumann) using Mille-feuille method?
- What is the bulk operator that implement the change of boundary conditions? (Is it the condensation operator?)
- What is the dual models after changing a different boundary conditions?
- Usually the condensation operators obeys noninvertible fusion rules. What is the fusion rules in this case?
- Does the Mille-feuille method help us understand the UV-IR mixing related to subsystem symmetry? For example, after Eq (4.20), the authors claimed "For instance, we required scale invariance when constructing the physical boundary, not allowing for some terms that, due to UV/IR mixing, will contribute to the energy at leading order. As a consequence, the energy of our ground state is shifted. " Can you give the details of this?
At least, I hope the authors can clarify the questions in the example related to XY-plaquette models.
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