In Kaluza–Klein theories, after dimensional reduction, the effective Planck mass varies as some power of the volume of compactified space.
The exponential of its vacuum expectation value determines the coupling constant g and the Euler characteristic χ = 2 − 2g as
In supersymmetry the superpartner of the dilaton or here the dilatino, combines with the axion to form a complex scalar field.
However, it has become central to the lower-dimensional many-bodied gravity problem[2] based on the field theoretic approach of Roman Jackiw.
The impetus arose from the fact that complete analytical solutions for the metric of a covariant N-body system have proven elusive in general relativity.
This outcome revealed a previously unknown and already existing natural link between general relativity and quantum mechanics.
However, a recent derivation in 3 + 1 dimensions under the right coordinate conditions yields a formulation similar to the earlier 1 + 1, a dilaton field governed by the logarithmic Schrödinger equation[5] that is seen in condensed matter physics and superfluids.
The field equations are amenable to such a generalization, as shown with the inclusion of a one-graviton process,[6] and yield the correct Newtonian limit in d dimensions, but only with a dilaton.