## Abstract

The macroscopic dimensions of space-time should not be input but rather output of a general model for physics. Here, dimensionality arises from a recently discovered mathematical bifurcation: positive versus indefinite manifold pairings. It is used to build actions on a formal chain of combinatorial space-times of arbitrary dimension. The context for such actions is 2-field theory where Feynman integrals are not over classical, but previously quantized configurations. A topologically enforced singularity of the action can terminate the dimension at four and, in fact, the final fourth dimension is Lorentzian due to light-like vectors in the four dimensional manifold pairing. Our starting point is the action of causal dynamical triangulations but in a dimension-agnostic setting. Curiously, some hint of extra compact dimensions emerges from our action.

Original language | English |
---|---|

Title of host publication | Essays in Mathematics and its Applications |

Subtitle of host publication | In Honor of Stephen Smale's 80th Birthday |

Publisher | Springer-Verlag Berlin Heidelberg |

Pages | 111-140 |

Number of pages | 30 |

Volume | 9783642288210 |

ISBN (Electronic) | 9783642288210 |

ISBN (Print) | 3642288200, 9783642288203 |

DOIs | |

State | Published - 1 Jun 2012 |

Externally published | Yes |

### Bibliographical note

Publisher Copyright:© 2012 Springer-Verlag Berlin Heidelberg. All rights are reserved.

## ASJC Scopus subject areas

- General Mathematics