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 AdS₇ × RP⁴ 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 ℤ₂ 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 ≥ 1. We highlight several subtle points related to the non-orientability of RP⁴, the half-integral G₄-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.