SymTFTs and Non-Invertible Symmetries of 6d (2,0) SCFTs of Type $D$ from M-theory

Abstract

We revisit 6d (2,0) SCFTs of type $D_N$ and their realization in M-theory, focusing on absolute variants of these theories and on their global finite 0- and 2-form symmetries. We derive the 7d SymTFT capturing these global symmetries from M-theory, both from the point of view of the low-energy supergravity action on $Ad{S}_7\times {\mathbb{RP}}^4$ and from M2- and M5-branes giving rise to its topological operators. Along the way, results by Gukov, Hsin, and Pei are extended by keeping track of an additional 7d ${\mathbb{Z}}_2$ gauge field, associated to the outer automorphism of the $D_N$ algebra. In particular, we find an interplay of non-invertible symmetries and mixed anomalies for absolute 6d (2,0) $D_{4k}$ SCFTs with $k\ge 1$. We highlight several subtle points related to the non-orientability of ${\mathbb{RP}}^4$, the half-integral $G_4$-flux that threads it, and the non-commutativity of fluxes. All these also play an essential role in a holographic derivation of the anomaly polynomial of 6d (2,0) $D_N$ SCFTs.

51 pages plus appendices

Cited by in corpus (1)

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