Broken sigma-model isometries in very special geometry

TL;DR

This paper investigates how supergravity interactions affect the symmetries of scalar manifolds in different dimensions, revealing that isometries can be broken in five dimensions but are preserved in four dimensions, with implications for string compactifications.

Contribution

It demonstrates the breaking of sigma-model isometries in five-dimensional supergravity and their preservation upon dimensional reduction to four dimensions.

Findings

Isometries are broken in 5D supergravity due to interactions.

Isometries remain intact in 4D after dimensional reduction.

Relevance to superstring compactifications.

Abstract

We show that the isometries of the manifold of scalars in $N=2$ supergravity in $d=5$ space-time dimensions can be broken by the supergravity interactions. The opposite conclusion holds for the dimensionally reduced $d=4$ theories, where the isometries of the scalar manifold are always symmetries of the full theory. These spaces, which form a subclass of the {\em special} K\"ahler manifolds, are relevant for superstring compactifications.