### Abstract

We review how core structures of string/M-theory emerge as higher structures in super homotopy theory; namely from systematic analysis of the brane bouquet of universal invariant higher central extensions growing out of the superpoint. Since super homotopy theory is immensely rich, to start with we consider this in the rational/infinitesimal approximation which ignores torsion-subgroups in brane charges and focuses on tangent spaces of super space-time. Already at this level, super homotopy theory discovers all super p-brane species, their intersection laws, their M/IIA-, T- and S-duality relations, their black brane avatars at ADE-singularities, including their instanton contributions, and, last not least, Dirac charge quantization: for the D-branes it recovers twisted K-theory, rationally, but for the M-branes it gives cohomotopy cohomology theory. We close with an outlook on the lift of these results beyond the rational/infinitesimal approximation to a candidate formalization of microscopic M-theory in super homotopy theory.

Original language | English (US) |
---|---|

Article number | 1910017 |

Journal | Fortschritte der Physik |

DOIs | |

State | Published - Jan 1 2019 |

### Fingerprint

### Keywords

- cohomotopy
- equivariant homotopy theory
- gauge enhancement
- higher structures
- M-theory
- p-branes
- rational homotopy theory
- supersymmetry
- T-duality

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Fortschritte der Physik*, [1910017]. https://doi.org/10.1002/prop.201910017

**The Rational Higher Structure of M-theory : LMS/EPSRC Durham Symposium on Higher Structures in M-Theory.** / Fiorenza, Domenico; Sati, Hisham; Schreiber, Urs.

Research output: Contribution to journal › Review article

}

TY - JOUR

T1 - The Rational Higher Structure of M-theory

T2 - LMS/EPSRC Durham Symposium on Higher Structures in M-Theory

AU - Fiorenza, Domenico

AU - Sati, Hisham

AU - Schreiber, Urs

PY - 2019/1/1

Y1 - 2019/1/1

N2 - We review how core structures of string/M-theory emerge as higher structures in super homotopy theory; namely from systematic analysis of the brane bouquet of universal invariant higher central extensions growing out of the superpoint. Since super homotopy theory is immensely rich, to start with we consider this in the rational/infinitesimal approximation which ignores torsion-subgroups in brane charges and focuses on tangent spaces of super space-time. Already at this level, super homotopy theory discovers all super p-brane species, their intersection laws, their M/IIA-, T- and S-duality relations, their black brane avatars at ADE-singularities, including their instanton contributions, and, last not least, Dirac charge quantization: for the D-branes it recovers twisted K-theory, rationally, but for the M-branes it gives cohomotopy cohomology theory. We close with an outlook on the lift of these results beyond the rational/infinitesimal approximation to a candidate formalization of microscopic M-theory in super homotopy theory.

AB - We review how core structures of string/M-theory emerge as higher structures in super homotopy theory; namely from systematic analysis of the brane bouquet of universal invariant higher central extensions growing out of the superpoint. Since super homotopy theory is immensely rich, to start with we consider this in the rational/infinitesimal approximation which ignores torsion-subgroups in brane charges and focuses on tangent spaces of super space-time. Already at this level, super homotopy theory discovers all super p-brane species, their intersection laws, their M/IIA-, T- and S-duality relations, their black brane avatars at ADE-singularities, including their instanton contributions, and, last not least, Dirac charge quantization: for the D-branes it recovers twisted K-theory, rationally, but for the M-branes it gives cohomotopy cohomology theory. We close with an outlook on the lift of these results beyond the rational/infinitesimal approximation to a candidate formalization of microscopic M-theory in super homotopy theory.

KW - cohomotopy

KW - equivariant homotopy theory

KW - gauge enhancement

KW - higher structures

KW - M-theory

KW - p-branes

KW - rational homotopy theory

KW - supersymmetry

KW - T-duality

UR - http://www.scopus.com/inward/record.url?scp=85065401291&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85065401291&partnerID=8YFLogxK

U2 - 10.1002/prop.201910017

DO - 10.1002/prop.201910017

M3 - Review article

AN - SCOPUS:85065401291

JO - Fortschritte der Physik

JF - Fortschritte der Physik

SN - 0015-8208

M1 - 1910017

ER -