SymTh for non-finite symmetries
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912977976819712 |
|---|---|
| author | Apruzzi, Fabio Bedogna, Francesco Dondi, Nicola |
| author_facet | Apruzzi, Fabio Bedogna, Francesco Dondi, Nicola |
| contents | Symmetry topological field theory (SymTFT) is a convenient tool for studying finite generalized symmetries of a given quantum field theory (QFT). In particular, SymTFTs encode all the symmetry structures and properties, including anomalies. Recently, this tool has been applied for non-finite symmetries as well. In this paper, we take a different route, which consists of considering a free theory rather than a topological field theory in the bulk. We call it Symmetry Theory (SymTh). We study its topological operators together with the free boundary conditions. We also propose a procedure that is analogous to the sandwich construction of SymTFTs and allows us to obtain the physical QFT. We apply this to many examples, ranging from abelian $p$-form symmetries to 2-groups, and the (solvable) case of group-like symmetries in quantum mechanics. Finally, we provide a derivation of the SymTh of $\mathbb Q/ \mathbb Z$ non-invertible symmetries from the dimensional reduction of IIB supergravity on the conifold. In addition, we give an ultraviolet interpretation of the quantum Hall states dressing the non-invertible $\mathbb Q/ \mathbb Z$ topological defects, in terms of branes in the IIB supergravity background. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_14813 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | SymTh for non-finite symmetries Apruzzi, Fabio Bedogna, Francesco Dondi, Nicola High Energy Physics - Theory Symmetry topological field theory (SymTFT) is a convenient tool for studying finite generalized symmetries of a given quantum field theory (QFT). In particular, SymTFTs encode all the symmetry structures and properties, including anomalies. Recently, this tool has been applied for non-finite symmetries as well. In this paper, we take a different route, which consists of considering a free theory rather than a topological field theory in the bulk. We call it Symmetry Theory (SymTh). We study its topological operators together with the free boundary conditions. We also propose a procedure that is analogous to the sandwich construction of SymTFTs and allows us to obtain the physical QFT. We apply this to many examples, ranging from abelian $p$-form symmetries to 2-groups, and the (solvable) case of group-like symmetries in quantum mechanics. Finally, we provide a derivation of the SymTh of $\mathbb Q/ \mathbb Z$ non-invertible symmetries from the dimensional reduction of IIB supergravity on the conifold. In addition, we give an ultraviolet interpretation of the quantum Hall states dressing the non-invertible $\mathbb Q/ \mathbb Z$ topological defects, in terms of branes in the IIB supergravity background. |
| title | SymTh for non-finite symmetries |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2402.14813 |