Non-Invertible Symmetries in 6d from Green-Schwarz Automorphisms
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| Format: | Preprint |
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2024
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| _version_ | 1866912119471996928 |
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| author | Apruzzi, Fabio Schafer-Nameki, Sakura Warman, Alison |
| author_facet | Apruzzi, Fabio Schafer-Nameki, Sakura Warman, Alison |
| contents | We construct non-invertible symmetries in 6d $\mathcal{N}=(2,0)$ superconformal field theories that arise from Green-Schwarz (GS) automorphisms, which form abelian or non-abelian groups. Applied to $\mathbb{Z}_2$, $\mathbb{Z}_3$ and $S_3$ GS automorphisms, gives rise to non-invertible duality, triality and $S_3$-ality defects, respectively, once combined with stacking symmetry protected topological phases (SPTs) and gauging 2-form symmetries. We derive the defects and their fusion rules from two distinct perspectives: from half-space gauging as well as from the Symmetry Topological Field Theory (SymTFT). This is the first concrete construction of symmetry defects in 6d forming a fusion 5-category whose fusions are intrinsically non-invertible and non-abelian. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_09674 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-Invertible Symmetries in 6d from Green-Schwarz Automorphisms Apruzzi, Fabio Schafer-Nameki, Sakura Warman, Alison High Energy Physics - Theory Strongly Correlated Electrons Category Theory We construct non-invertible symmetries in 6d $\mathcal{N}=(2,0)$ superconformal field theories that arise from Green-Schwarz (GS) automorphisms, which form abelian or non-abelian groups. Applied to $\mathbb{Z}_2$, $\mathbb{Z}_3$ and $S_3$ GS automorphisms, gives rise to non-invertible duality, triality and $S_3$-ality defects, respectively, once combined with stacking symmetry protected topological phases (SPTs) and gauging 2-form symmetries. We derive the defects and their fusion rules from two distinct perspectives: from half-space gauging as well as from the Symmetry Topological Field Theory (SymTFT). This is the first concrete construction of symmetry defects in 6d forming a fusion 5-category whose fusions are intrinsically non-invertible and non-abelian. |
| title | Non-Invertible Symmetries in 6d from Green-Schwarz Automorphisms |
| topic | High Energy Physics - Theory Strongly Correlated Electrons Category Theory |
| url | https://arxiv.org/abs/2411.09674 |