Invariant Connections with Torsion on Group Manifolds and Their Application in Kaluza-Klein Theories

TL;DR

This paper studies invariant connections with torsion on simple group manifolds, deriving explicit formulas and applying them to multidimensional gravity theories to analyze scalar field potentials and stability of compactification.

Contribution

It provides explicit formulas for invariant connections with torsion on simple group manifolds and applies these results to Kaluza-Klein theories for dimensional reduction.

Findings

Derived explicit formulas for invariant connections with torsion.

Calculated scalar field potentials from extra metric components.

Analyzed torsion's role in the stability of spontaneous compactification.

Abstract

Invariant connections with torsion on simple group manifolds $S$ are studied and an explicit formula describing them is presented. This result is used for the dimensional reduction in a theory of multidimensional gravity with curvature squared terms on $M^{4} \times S$. We calculate the potential of scalar fields, emerging from extra components of the metric and torsion, and analyze the role of the torsion for the stability of spontaneous compactification.