Gauge Theory on Fiber Bundle of Hypercomplex Algebras

TL;DR

This paper constructs a novel gauge theory on hypercomplex algebra fiber bundles, demonstrating a mechanism for natural vacuum selection via domain walls and parity considerations, potentially explaining the origin of the physical vacuum.

Contribution

It introduces a new gauge theory framework on hypercomplex fiber bundles and shows how vacuum selection can occur through intrinsic parity and domain walls.

Findings

Presence of an impenetrable domain wall prevents phase transitions.

A specific vacuum can be dynamically selected due to parity symmetry.

The theory offers a potential solution to the vacuum selection problem.

Abstract

I introduce a way of constructing a fiber bundle whose fibers are given by hypercomplex algebras and woven by appropriate structure group, and present that a novel gauge theory can be built on the hypercomplex fiber bundle. In this work, I aim to answer a question about how nature selects one preferred vacuum among degenerate physical vacua, called {\it vacuum selection problem}. In the end, I found presence of the impenetrable domain wall that prohibits phase transition between the two vacua. To be specific, I found that in this theory, one particular vacuum between two degenerate physical vacua for Higgs-like scalar potential can be dynamically chosen with priority due to intrinsic even parity of both a scalar field and its vacuum under a $\mathbb{Z}_2$ symmetry, even though its scalar potential is given to be $\mathbb{Z}_2$-symmetric under both odd- and even-parity transformations of the scalar field. This means that the vacuum selection problem can be resolved in this gauge theory. I suggest that this work may be a gateway to addressing the theoretical origin of the true physical vacuum that nature takes.