### 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 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.

Original language | English (US) |
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Journal | Communications in Mathematical Physics |

DOIs | |

State | Published - Jan 1 2019 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Communications in Mathematical Physics*. https://doi.org/10.1007/s00220-019-03442-3

**Real ADE-Equivariant (co)Homotopy and Super M-Branes.** / Huerta, John; Sati, Hisham; Schreiber, Urs.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*. https://doi.org/10.1007/s00220-019-03442-3

}

TY - JOUR

T1 - Real ADE-Equivariant (co)Homotopy and Super M-Branes

AU - Huerta, John

AU - Sati, Hisham

AU - Schreiber, Urs

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85066011771&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85066011771&partnerID=8YFLogxK

U2 - 10.1007/s00220-019-03442-3

DO - 10.1007/s00220-019-03442-3

M3 - Article

AN - SCOPUS:85066011771

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

ER -