On the relationship of gravitational constants in KK reduction

Abstract

In this short note, we try to clarify a seemly trivial but often confusing question in relating a higher-dimensional physical gravitational constant to its lower-dimensional correspondence in Kaluza-Klein reduction. In particular, we re-derive the low-energy M-theory gravitational constant in terms of type-IIA string coupling gs and constant α′ through the metric relation between the two theories.