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arXiv · 2503.03776

A gap between two approaches of dimensional reduction for a six-dimensional Kaluza-Klein theory

Tuan Q. Do·W. F. Kao
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Abstract

Inspired by the five-dimensional Kaluza-Klein theory, we would like to study the dimensional reduction issue of six-dimensional Kaluza-Klein extension in this paper. In particular, we will examine two possible approaches of dimensional reduction from six-dimensional spacetimes to four-dimensional ones. The first one is a direct dimensional reduction, i.e., from six-dimensional spacetimes directly to four-dimensional ones, via a $T^2\equiv S^1 \times S^1$ compactification, while the second one is an indirect dimensional reduction, i.e., from six-dimensional spacetimes to five-dimensional ones then four-dimensional ones, via two separated $S^1$ compactifications. Interestingly, we show that these two approaches lead to different four-dimensional effective actions although using the same six-dimensional metric. It could therefore address an important question of which approach is more reliable than the other.

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Tuan Q. Do, W. F. Kao. 2025-03-04. A gap between two approaches of dimensional reduction for a six-dimensional Kaluza-Klein theory. https://doi.org/10.1140/epjp%2Fs13360-025-06080-y

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