A model of gravitation with global U(1)-symmetry

TL;DR

This paper proposes a gravitational model based on embedding 4-dimensional spacetime into a 12-dimensional flat space, incorporating global U(1) symmetry and relating it to SU(2) symmetry, with implications for unification theories.

Contribution

It introduces a novel embedding approach of general relativity into higher-dimensional space that exhibits a global U(1) symmetry linked to gauge unification.

Findings

Embedding of 4-space into 12-space yields a gravitation model with U(1) symmetry.

The model relates U(1) and SU(2) symmetries, estimating a Weinberg angle analog.

Transformation of discrete symmetry into SU(2) symmetry is demonstrated.

Abstract

It is shown that an embedding of the general relativity $4-$space into a flat $12-$space gives a model of gravitation with the global $U(1)-$symmetry and the discrete $D_{1}-$one. The last one may be transformed into the $SU(2)-$symmetry of the unified model, and the demand of independence of $U(1)-$ and $SU(2)-$transformations leads to the estimate $\sin^{2}\theta_{min}=0,20$ where $\theta_{min}$ is an analog of the Weinberg angle of the standard model.