Dimensional reduction via a novel Higgs mechanism

TL;DR

This paper introduces a new mechanism for dimensional reduction in quantum gravity theories by spontaneously breaking higher-dimensional Lorentz symmetry to lower dimensions within a gauge theory framework.

Contribution

It proposes a novel spontaneous symmetry breaking mechanism that reduces spacetime dimensions, offering an alternative to traditional compactification methods in quantum gravity.

Findings

Demonstrates spontaneous reduction of Lorentz symmetry to lower dimensions.

Shows scalar field coupling can induce dimensional reduction.

Provides a potential new approach for quantum gravity models.

Abstract

Many theories of quantum gravity live in higher dimensions, and their reduction to four dimensions via mechanisms such as Kaluza-Klein compactification or brane world models have associated problems. We propose a novel mechanism of dimensional reduction via spontaneous symmetry breaking of a higher dimensional local Lorentz group to one in lower dimensions. Working in the gauge theory formulation of gravity, we couple a scalar field to spin connections, include a potential for the field, and show that for a suitable choice of scalar vacuum, the local Lorentz symmetry of the action gets spontaneously reduced to one in a lower dimension. Thus effectively the dimension of spacetime gets reduced by one. This provides a viable mechanism for the dimensional reduction, and may have applications in theories of quantum gravity.