Fermionic non-invertible symmetries in (1+1)d: Gapped and gapless phases, transitions, and symmetry TFTs
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 wit...
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2025-06-01
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| author | Lakshya Bhardwaj, Kansei Inamura, Apoorv Tiwari |
| author_facet | Lakshya Bhardwaj, Kansei Inamura, Apoorv Tiwari |
| author_sort | Lakshya Bhardwaj, Kansei Inamura, Apoorv Tiwari |
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| description | 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. |
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| institution | DOAJ |
| issn | 2542-4653 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | SciPost |
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| spelling | doaj-art-b39d8f83d4d543368512c776ec0d7cd62025-08-20T03:22:08ZengSciPostSciPost Physics2542-46532025-06-0118619410.21468/SciPostPhys.18.6.194Fermionic non-invertible symmetries in (1+1)d: Gapped and gapless phases, transitions, and symmetry TFTsLakshya Bhardwaj, Kansei Inamura, Apoorv TiwariWe 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.https://scipost.org/SciPostPhys.18.6.194 |
| spellingShingle | Lakshya Bhardwaj, Kansei Inamura, Apoorv Tiwari Fermionic non-invertible symmetries in (1+1)d: Gapped and gapless phases, transitions, and symmetry TFTs SciPost Physics |
| title | Fermionic non-invertible symmetries in (1+1)d: Gapped and gapless phases, transitions, and symmetry TFTs |
| title_full | Fermionic non-invertible symmetries in (1+1)d: Gapped and gapless phases, transitions, and symmetry TFTs |
| title_fullStr | Fermionic non-invertible symmetries in (1+1)d: Gapped and gapless phases, transitions, and symmetry TFTs |
| title_full_unstemmed | Fermionic non-invertible symmetries in (1+1)d: Gapped and gapless phases, transitions, and symmetry TFTs |
| title_short | Fermionic non-invertible symmetries in (1+1)d: Gapped and gapless phases, transitions, and symmetry TFTs |
| title_sort | fermionic non invertible symmetries in 1 1 d gapped and gapless phases transitions and symmetry tfts |
| url | https://scipost.org/SciPostPhys.18.6.194 |
| work_keys_str_mv | AT lakshyabhardwajkanseiinamuraapoorvtiwari fermionicnoninvertiblesymmetriesin11dgappedandgaplessphasestransitionsandsymmetrytfts |