Schreiber Nesselwang 2026

A lecture series that we have given:

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• Urs Schreiber$\;\;$ with $\;\;$ Grigorios Giotopoulos:

  
  

  Higher Superspace Supergravity and its IR Completions

  lecture notes: pdf

  
  

  lectures held at:

  
  

• Fundamental Challenges in Theoretical Physics Workshop —

  Symmetries, Protected Quantities, and Exact Computations in Supergravity,

  Johannishof, Nesselwang near Munich

  29 Jun – 3 Jul 2026

Abstract. 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 (i.e., “duality-symmetric”) flux quantization laws $\mathcal{A}$ lifting the coefficient $L_\infty$-algebra $\mathfrak{l}\mathcal{A}$ of the super-Bianchi identities. After surveying necessary background, we highlight:

• our recent proof that solutions of 11D SuGra are equivalent to the $\mathfrak{l}S^4$-Bianchi identities on super C-field flux over super-torsion-free 11D super-spacetimes,

• how from this the nonlinearly self-dual gauge sector on 6D M5-brane worldvolumes is equivalent to the $\mathfrak{l}_{S^4}S^7$-Bianchi identity on super $B$-field flux,

• and the recent complete discussion of superspace dimensional reduction of this situation to 10D IIA SuGra via $\mathfrak{l}\mathrm{Cyc}(S^4)$-Bianchi identities on super NS/RR-flux.

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 relative 7-Cohomotopy. The latter admits geometric engineering of experimentally relevant topological quantum orders.

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Based on (with G. Giotopoulos and H. Sati):

• Flux Quantization on 11D Superspace [doi:10.1007/JHEP07(2024)082]

• Flux Quantization on M5-Branes [doi:10.1007/JHEP10(2024)140]

• Holographic M-Brane Super-Embeddings [doi:10.1142/S0129055X25500230]

• Engineering of Anyons on M5-Probes [doi:10.21468/SciPostPhysLectNotes.107]

and (by G. Giotopoulos and H. Sati):

• Flux Quantization on 10D Type IIA Superspace via Cyclification from 11D

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Some photos: