English

Geometric flow equations for the number of space-time dimensions

High Energy Physics - Theory 2022-02-09 v2 Differential Geometry

Abstract

In this paper we consider new geometric flow equations, called D-flow, which describe the variation of space-time geometries under the change of the number of dimensions. The D-flow is originating from the non-trivial dependence of the volume of space-time manifolds on the number of space-time dimensions and it is driven by certain curvature invariants. We will work out specific examples of D-flow equations and their solutions for the case of D-dimensional spheres and Freund-Rubin Compactification. The discussion of the paper is motivated from recent swampland considerations, where the number DD of space-time dimensions is treated as a new swampland parameter.

Keywords

Cite

@article{arxiv.2104.05621,
  title  = {Geometric flow equations for the number of space-time dimensions},
  author = {Davide De Biasio and Julian Freigang and Dieter Lust},
  journal= {arXiv preprint arXiv:2104.05621},
  year   = {2022}
}

Comments

30 pages, 6 figures