Homotopy Structure of 5d Vacua

TL;DR

This paper reveals that the vacua of 5d Kaluza-Klein theory have a rich homotopy structure, with an infinite set of distinct spacetimes generated by Kaluza-Klein excitations, connecting ground states of 5d theories.

Contribution

It demonstrates the non-trivial homotopy structure of 5d vacua and classifies an infinite set of homotopically different spacetimes in Kaluza-Klein theory.

Findings

Identification of an infinite set of homotopically different vacua.

Ground states correspond to $M_4 \times S^1$ and $M_5$.

Homotopy structure generated by Kaluza-Klein excitations.

Abstract

It is shown that flat zero-energy solutions (vacua) of the 5d Kaluza-Klein theory admit a non-trivial homotopy structure generated by certain Kaluza-Klein excitations. These vacua consist of an infinite set of homotopically different spacetimes denoted by $\mathcal{M}^{(n)}_5$, among which $\mathcal{M}^{(0)}_5$ and $\mathcal{M}^{(1)}_5$ are especially identified as $M_{4} \times S^{1}$ and $M_5$, the ground states of the 5d Kaluza-Klein theory and the 5d general relativity, respectively (where $M_k$ represents the $k$-dimensional Minkowski space).