Dimensionality in the Freund-Rubin Cosmology

TL;DR

This paper generalizes the relationship between spacetime dimension and antisymmetric tensor field rank in Freund-Rubin cosmology, extending previous supergravity results to arbitrary dimensions and tensor ranks.

Contribution

It provides a generalized formula linking the dimension of external spacetime to the rank of the antisymmetric tensor field in n-dimensional Freund-Rubin models.

Findings

External spacetime dimension equals the minimum of s and n-s.

Generalizes previous 11-dimensional supergravity results.

Clarifies the role of tensor rank in cosmological models.

Abstract

In the $n-$dimensional Freund-Rubin model with an antisymmetric tensor field of rank $s-1$, the dimension of the external spacetime we live in must be $min(s, n-s)$. This result is a generalization of the previous result in the $d=11$ supergravity case, where $s = 4$.