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SymTFT for (3+1)d Gapless SPTs and Obstructions to Confinement
by Andrea Antinucci, Christian Copetti, Sakura Schafer-Nameki
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Submission summary
| Authors (as registered SciPost users): | Andrea Antinucci · Sakura Schäfer-Nameki |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2408.05585v3 (pdf) |
| Date accepted: | 2025-03-18 |
| Date submitted: | 2025-02-27 11:27 |
| Submitted by: | Antinucci, Andrea |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We study gapless phases in (3+1)d in the presence of 1-form and non-invertible duality symmetries. Using the Symmetry Topological Field Theory (SymTFT) approach, we classify the gapless symmetry-protected (gSPT) phases in these setups, with particular focus on intrinsically gSPTs (igSPTs). These are symmetry protected critical points which cannot be deformed to a trivially gapped phase without spontaneously breaking the symmetry. Although these are by now well-known in (1+1)d, we demonstrate their existence in (3+1)d gauge theories. Here, they have a clear physical interpretation in terms of an obstruction to confinement, even though the full 1-form symmetry does not suffer from 't Hooft anomalies. These igSPT phases provide a new way to realize 1-form symmetries in CFTs, that has no analog for gapped phases. The SymTFT approach allows for a direct generalization from invertible symmetries to non-invertible duality symmetries, for which we study gSPT and igSPT phases as well. We accompany these theoretical results with concrete physical examples realizing such phases and explain how obstruction to confinement is detected at the level of symmetric deformations.
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- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
In particular the point raised by referee 2 is very interesting as it open the possibility of realizing new igSPTs in dimension (3+1)d, that can only be detected on non-spin manifolds. We commented about this at the end of Section 3.3.2. However we couldn't find a clear physical application, and we leave this interesting problem for the future.
We also agree with all the comments of referee 1.
List of changes
More in detail:
1. We added footnote 8 to clarify this point. The referee is indeed absolutely right, but in the specific examples discussed in our paper this issue never arises, so we use the expression "Lagrangian algebra" to mean "Lagrangian algebra object".
2. The referee is absolutely right, and we made substantial changes in the paragraph "Structure of $ Aut(A x \mathbb{A}^\vee)$". As this was never really used, the previous mistake does not propagate in the rest of the paper.
3. Corrected.
We also corrected all the typos and suggestions.
Published as SciPost Phys. 18, 114 (2025)
Reports on this Submission
Report
This paper generalizes the notion of igSPT in 2-dim to igSPT in 4-dim and discuss the three types of igSPT of G-extension of Abelian symmetries in both 2-dim and 4-dim. It is a solid progress in the study of categorical symmetries and reveals some interesting future research directions. The paper is well-written with a nice combination of generic result and concrete examples. I recommend the paper to be published.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)