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Fermionic Non-Invertible Symmetries in (1+1)d: Gapped and Gapless Phases, Transitions, and Symmetry TFTs
by Lakshya Bhardwaj, Kansei Inamura, Apoorv Tiwari
Submission summary
| Authors (as registered SciPost users): | Lakshya Bhardwaj · Kansei Inamura · Apoorv Tiwari |
| Submission information | |
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| Preprint Link: | scipost_202503_00043v1 (pdf) |
| Date submitted: | 2025-03-24 13:07 |
| Submitted by: | Inamura, Kansei |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We study fermionic non-invertible symmetries in (1+1)d, which are generalized global symmetries that mix fermion parity symmetry with other invertible and non-invertible internal symmetries. Such symmetries are described by fermionic fusion supercategories, which are fusion $\pi$-supercategories with a choice of fermion parity. The aim of this paper is to flesh out the categorical Landau paradigm for fermionic symmetries. We use the formalism of Symmetry Topological Field Theory (SymTFT) to study possible gapped and gapless phases for such symmetries, along with possible deformations between these phases, which are organized into a Hasse phase diagram. The phases can be characterized in terms of sets of condensed, confined and deconfined generalized symmetry charges, reminiscent of notions familiar from superconductivity. Many of the gapless phases also serve as phase transitions between gapped phases. The associated fermionic conformal field theories (CFTs) can be obtained by performing generalized fermionic Kennedy-Tasaki (KT) transformations on bosonic CFTs describing simpler transitions. The fermionic non-invertible symmetries along with their charges and phases discussed here can be obtained from those of bosonic non-invertible symmetries via fermionization or Jordan-Wigner transformation, which is discussed in detail.
Author indications on fulfilling journal expectations
- 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
List of changes
Report #1
1. We added footnote 3. In addition, in the first paragraph of the Introduction, we mentioned that the anomaly is supposed to vanish mod 16.
2. We added footnote 11.
3. We added footnote 23.
Report #2
1. We added the last paragraph of Section III.B and footnote 15.
2. The quantum dimensions in fusion supercategories, including fermionic fusion supercategories, are briefly discussed around eq.(II.10).
3. One necessary condition is that all objects are m-type, although this is not a sufficient condition. We added a comment on this point in the first paragraph of Section II.E.6.
4. We are not sure about the fusion supercategory underlying the construction in Phys. Rev. B 94, 115115 (2016). Nevertheless, we added the second sentence of Section V.F. to mention the relation between the symmetry TFT and the gauged SPT phase.
5. We added the last paragraph of Section III.D.
6. We added the last sentence of the penultimate paragraph of Section III.B.
Current status:
Reports on this Submission
Report
The previous comments and questions are addressed in the new version of the manuscript. I recommend its publication in its current form.
Recommendation
Publish (surpasses expectations and criteria for this Journal; among top 10%)