Consistency analysis of Kaluza-Klein geometric sigma models

TL;DR

This paper examines the consistency and stability of Kaluza-Klein geometric sigma models during dimensional reduction, revealing that internal excitations can have negative modes, affecting vacuum stability.

Contribution

It provides a detailed analysis of the consistency and stability of dimensional reduction in Kaluza-Klein geometric sigma models with group and coset spaces.

Findings

Internal excitations in SO(n) groups have negative mass modes.

Coset spaces allow only stable modes, but vacuum stability is unresolved.

Dimensional reduction is consistent for group manifolds.

Abstract

Geometric sigma models are purely geometric theories of scalar fields coupled to gravity. Geometrically, these scalars represent the very coordinates of space-time, and, as such, can be gauged away. A particular theory is built over a given metric field configuration which becomes the vacuum of the theory. Kaluza-Klein theories of the kind have been shown to be free of the classical cosmological constant problem, and to give massless gauge fields after dimensional reduction. In this paper, the consistency of dimensional reduction, as well as the stability of the internal excitations, are analyzed. Choosing the internal space in the form of a group manifold, one meets no inconsistencies in the dimensional reduction procedure. As an example, the SO(n) groups are analyzed, with the result that the mass matrix of the internal excitations necessarily possesses negative modes. In the case of coset spaces, the consistency of dimensional reduction rules out all but the stable mode, although the full vacuum stability remains an open problem.