Higher-Dimensional Geometric Sigma Models

TL;DR

This paper introduces a modified higher-dimensional geometric sigma model that overcomes previous limitations by enabling massless gauge fields after dimensional reduction, with potential implications for theories unifying gravity and gauge interactions.

Contribution

It proposes a new version of geometric sigma models that successfully produce massless gauge fields in Kaluza-Klein frameworks, addressing a key challenge in higher-dimensional theories.

Findings

Successfully constructs a modified geometric sigma model with desired properties.

Achieves vanishing cosmological constant in the higher-dimensional setup.

Provides a framework for realistic unification models in higher dimensions.

Abstract

Geometric $\sigma$-models have been defined as purely geometric theories of scalar fields coupled to gravity. By construction, these theories possess arbitrarily chosen vacuum solutions. Using this fact, one can build a Kaluza--Klein geometric $\sigma$-model by specifying the vacuum metric of the form $M^4\times B^d$. The obtained higher dimensional theory has vanishing cosmological constant but fails to give massless gauge fields after the dimensional reduction. In this paper, a modified geometric $\sigma$-model is suggested, which solves the above problem.