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arXiv · 1805.05987

Real ADE-equivariant (co)homotopy and Super M-branes

John Huerta·Hisham Sati·Urs Schreiber
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Abstract

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 4-sphere-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.

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John Huerta, Hisham Sati, Urs Schreiber. 2019-03-04. Real ADE-equivariant (co)homotopy and Super M-branes. https://doi.org/10.1007/s00220-019-03442-3

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