10D to 4D Euclidean Supergravity over a Calabi-Yau three-fold

TL;DR

This paper performs a dimensional reduction of 10D Euclidean type IIA supergravity over a Calabi-Yau three-fold, resulting in a 4D Euclidean supergravity theory with specific geometric structures.

Contribution

It explicitly derives the 4D Euclidean supergravity coupled to matter multiplets and characterizes the scalar target manifolds as projective special para-Kahler and quaternionic Kahler.

Findings

Scalar target manifold of vector-multiplets is projective special para-Kahler.

Target manifold of hyper-multiplets is quaternionic Kahler.

The reduced theory describes 4D, N=2 Euclidean supergravity with matter.

Abstract

We dimensionally reduce the bosonic sector of 10D Euclidean type IIA supergravity over a Calabi-Yau three-fold. The resulting theory describes the bosonic sector of 4D, N = 2 Euclidean supergravity coupled to vector- and hyper-multiplets. We show that the scalar target manifold of the vector-multiplets is projective special para-Kahler, and is therefore of split signature, whereas the target manifold of the hyper-multiplets is (positive-definite) quaternionic Kahler.