Dilaton invading from infinitesimal extra dimension

TL;DR

This paper derives the dilaton effective action in even dimensions by dimensional reduction of Lovelock gravity in a higher-dimensional setting, providing explicit formulas and insights into conformal symmetry breaking.

Contribution

It introduces a novel method to obtain the dilaton effective action through Kaluza-Klein reduction of Lovelock gravity in infinitesimal extra dimensions.

Findings

Explicit form of dilaton effective action in even dimensions

Connection between Lovelock gravity and conformal symmetry breaking

Method applicable to any even dimension

Abstract

We show that the Wess-Zumino action for the spontaneously broken Weyl (or conformal) symmetry, a.k.a dilaton effective action, in even $D$ dimensions can be obtained from the Kaluza-Klein dimensional reduction of the Lovelock action in $D+\epsilon$ dimensions by taking the $\epsilon \to 0$ limit, where the dilaton is identified with the metric in the extra dimension. The construction gives an explicit form of the dilaton effective action in any even dimensions.