2026/07/22 by Grigorios Giotopoulos, Hisham Sati, Urs Schreiber
#hep-th #gr-qc #math-ph #math.AT #math.DG #math.MP
It is an old idea that higher-dimensional super-gravity (SuGra) is put on-shell just by imposing Bianchi identities on super-field strengths over super-spacetimes subject to super-torsion constraints. We give a modernized, rigorous account and review recent developments, pointing out how this perspective lends itself to the construction of infrared completions of SuGra by electromagnetic flux quantization in differential nonabelian cohomology theories Adff lifting the coefficient L_∞-algebra \mathfraklA of the super-Bianchi identities. After surveying necessary background, we highlight: (1.) our recent proof that solutions of 11D SuGra are equivalent to the \mathfraklS4-Bianchi identities on super C-field flux over super-torsion-free 11D super-spacetimes, (2.) how from this the nonlinearly self-dual gauge sector on 6D M5-brane worldvolumes is equivalent to the \mathfraklS4S7-Bianchi identity on super B-field flux, (3.) and the recent complete discussion of superspace dimensional reduction of this situation to 10D IIA SuGra via \mathfraklCyc(S4)-Bianchi identities on super NS/RR-flux, together with its extension to further reduction to 9 SuGra via \mathfraklTor(S4)-Bianchis on the corresponding super-fluxes. We close by indicating how this implies consistent infrared completions of 11D SuGra by C-field flux quantization in 4-Cohomotopy, of 10D IIA SuGra by NS/RR-field flux-quantization in a form of twisted unstable K-theory, and of M5-brane worldvolumes by B-field flux-quantization in twisted (twistorial) relative Cohomotopy. The latter admits geometric engineering of experimentally relevant topological quantum orders.