Real ADE-Equivariant (co)Homotopy and Super M-Branes

  • John Huerta
  • Hisham Sati
  • Urs SchreiberEmail author


A key open problem in M-theory is the identification of the degrees of freedom that are expected to be hidden at ADE-singularities in spacetime. Comparison with the classification of D-branes by K-theory suggests that the answer must come from the right choice of generalized cohomology theory for M-branes. Here we show that real equivariant Cohomotopy on superspaces is a consistent such choice, at least rationally. After explaining this new approach, we demonstrate how to use Elmendorf’s Theorem in equivariant homotopy theory to reveal ADE-singularities as part of the data of equivariant \(S^{4}\)-valued super-cocycles on 11d super-spacetime. We classify these super-cocycles and find a detailed black brane scan that enhances the entries of the old brane scan to cascades of fundamental brane super-cocycles on strata of intersecting black M-brane species. We find that on each singular stratum the black brane’s instanton contribution, namely its super Nambu–Goto/Green–Schwarz action, appears as the homotopy datum associated to the morphisms in the orbit category.



We thank Vincent Braunack-Mayer, David Corfield, Mike Duff, David Roberts, and Christian Saemann for useful comments. We thank the anonymous referee for careful reading and useful suggestions.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.CAMGSDInstituto Superior TécnicoLisboaPortugal
  2. 2.Division of Science and MathematicsNew York UniversityAbu DhabiUAE

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