Homotopy Structure of 5d Vacua

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 ${\mathcal{M}}_5^{(n)}$, among which ${\mathcal{M}}_5^{(0)}$ and ${\mathcal{M}}_5^{(1)}$ 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).

8 pages

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