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

John Huerta, Hisham Sati, Urs Schreiber

Research output: Contribution to journalArticlepeer-review


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 S4-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.

Original languageEnglish (US)
Pages (from-to)425-524
Number of pages100
JournalCommunications In Mathematical Physics
Issue number2
StatePublished - Oct 1 2019

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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