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arXiv · 2411.09674

Non-Invertible Symmetries in 6d from Green-Schwarz Automorphisms

Fabio Apruzzi·Sakura Schafer-Nameki·Alison Warman
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Abstract

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.

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Fabio Apruzzi, Sakura Schafer-Nameki, Alison Warman. 2024-11-14. Non-Invertible Symmetries in 6d from Green-Schwarz Automorphisms. https://arxiv.org/abs/2411.09674

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