Dynamical Gauge Field induced by the Berry Phase Mechanism

TL;DR

This paper demonstrates that in a specific compactification scenario, gauge fields in four dimensions can be dynamically generated via a Berry phase mechanism from topological holonomies, rather than traditional Kaluza-Klein modes.

Contribution

It introduces a novel mechanism for inducing gauge fields in four dimensions through Berry phases associated with compactified extra dimensions, expanding understanding beyond Kaluza-Klein theory.

Findings

Induced gauge fields form a product of U(1) groups in four dimensions.

Holonomies of the compactified space generate the dynamical gauge degrees of freedom.

Kinetic terms for the induced fields are produced via the Berry phase mechanism.

Abstract

Some part of the local gauge symmetries in the low energy region, say, lower than GUT or the Planck energy can be an induced symmetry describable with the holonomy fields associated with a topologically non-trivial structure of partially compactified space. In the case where a six dimensional space is compactified by the Kaluza-Klein mechanism into a product of the four dimensional Minkowski space $M_{4}$ and a two dimensional Riemann surface with the genus $g$, $\Sigma_{g}$, we show that, in a limit where the compactification mass scale is sent to infinity, a model lagrangian with a U(1) gauge symmetry produces the dynamical gauge fields in $M_{4}$ with a product of $g$ U(1)'s symmetry, i.e., U(1)$\times \cdots\times$U(1). These fields are induced by a Berry phase mechanism, not by the Kaluza-Klein. The dynamical degrees of freedom of the induced fields are shown to come from the holonomies, or the solenoid potentials, associated with the cycles of $\Sigma_{g}$. The production mechanism of kinetic energy terms for the induced fields are discussed in detail.