### Abstract

We interpret heterotic M-theory in terms of h-cobordism, that is the eleven-manifold is a product of the ten-manifold times an interval is translated into a statement that the former is a cobordism of the latter which is a homotopy equivalence. In the non-simply connected case, which is important for model building, the interpretation is then in terms of s-cobordism, so that the cobordism is a simple-homotopy equivalence. This gives constraints on the possible cobordisms depending on the fundamental groups and hence provides a characterization of possible compactification manifolds using the Whitehead group - a quotient of algebraic K-theory of the integral group ring of the fundamental group - and a distinguished element, the Whitehead torsion. We also consider the effect on the dynamics via diffeomorphisms and general dimensional reduction, and comment on the effect on F-theory compactifications.

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

Pages (from-to) | 739-759 |

Number of pages | 21 |

Journal | Nuclear Physics B |

Volume | 853 |

Issue number | 3 |

DOIs | |

State | Published - Dec 21 2011 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

**Constraints on heterotic M-theory from s-cobordism.** / Sati, Hisham.

Research output: Contribution to journal › Article

*Nuclear Physics B*, vol. 853, no. 3, pp. 739-759. https://doi.org/10.1016/j.nuclphysb.2011.08.006

}

TY - JOUR

T1 - Constraints on heterotic M-theory from s-cobordism

AU - Sati, Hisham

PY - 2011/12/21

Y1 - 2011/12/21

N2 - We interpret heterotic M-theory in terms of h-cobordism, that is the eleven-manifold is a product of the ten-manifold times an interval is translated into a statement that the former is a cobordism of the latter which is a homotopy equivalence. In the non-simply connected case, which is important for model building, the interpretation is then in terms of s-cobordism, so that the cobordism is a simple-homotopy equivalence. This gives constraints on the possible cobordisms depending on the fundamental groups and hence provides a characterization of possible compactification manifolds using the Whitehead group - a quotient of algebraic K-theory of the integral group ring of the fundamental group - and a distinguished element, the Whitehead torsion. We also consider the effect on the dynamics via diffeomorphisms and general dimensional reduction, and comment on the effect on F-theory compactifications.

AB - We interpret heterotic M-theory in terms of h-cobordism, that is the eleven-manifold is a product of the ten-manifold times an interval is translated into a statement that the former is a cobordism of the latter which is a homotopy equivalence. In the non-simply connected case, which is important for model building, the interpretation is then in terms of s-cobordism, so that the cobordism is a simple-homotopy equivalence. This gives constraints on the possible cobordisms depending on the fundamental groups and hence provides a characterization of possible compactification manifolds using the Whitehead group - a quotient of algebraic K-theory of the integral group ring of the fundamental group - and a distinguished element, the Whitehead torsion. We also consider the effect on the dynamics via diffeomorphisms and general dimensional reduction, and comment on the effect on F-theory compactifications.

UR - http://www.scopus.com/inward/record.url?scp=80052964966&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80052964966&partnerID=8YFLogxK

U2 - 10.1016/j.nuclphysb.2011.08.006

DO - 10.1016/j.nuclphysb.2011.08.006

M3 - Article

AN - SCOPUS:80052964966

VL - 853

SP - 739

EP - 759

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 3

ER -