A covariantly foliated higher dimensional space-time: Implications for short distance gravity and BSM physics

TL;DR

This paper explores a covariantly foliated higher-dimensional space-time model with a principal bundle structure, analyzing its implications for short-distance gravity, Standard Model problems, neutrino masses, and dark matter.

Contribution

It introduces a novel covariant foliation of higher-dimensional space-time with gauge fields and moduli stabilization, offering new insights into gravity and beyond Standard Model physics.

Findings

Bulk gauge fields determine local external space directions.

Moduli stabilization fixes the size of internal spaces dynamically.

Potential solutions to neutrino mass and dark matter issues are proposed.

Abstract

We consider the space-time at short distances in which it is described by a $D$-dimensional manifold (bulk) carrying out the principal bundle structure. As a result, this space-time manifold is foliated in the covariant way by the $(D-4)$-dimensional submanifolds, realized as the space-like internal spaces, that are smooth copies of the Lie group $G$ considered in this paper as the special unitary group. The submanifolds being transversal to the internal spaces are realized as the external spaces and in fact identified as the usual $4$-dimensional world. The fundamental degrees of freedom determining the geometrical dynamics of the bulk corresponding with short distance gravity are given by the gauge fields, the external metric field and the modulus fields setting dynamically the volume of the internal spaces. These gauge fields laying the bulk is to point precisely out the local directions of the external spaces which depend on the topological non-triviality of the space-time principal bundle. The physical size of the internal spaces is fixed dynamically by the moduli stabilization potential which completely arise from the intrinsic geometry of the bulk. A detail description of the low energy bulk gravity in the weak field limit is given around the classical ground state of the bulk. Additionally, we investigate the dynamics of the fundamentally $4$-dimensional Weyl spinor fields and the fields of carrying out the non-trivial representations of the Lie group $G$ propagating in the bulk in a detail study. These results suggest naturally the possible solutions to some the experimental problems of Standard Model, the smallness of the observed neutrino masses and a dark matter candidate.