Few exact results on gauge symmetry factorizability on intervals

TL;DR

This paper investigates how gauge symmetries can be factorized via boundary conditions on intervals across various dimensions, revealing a solvable structure in five dimensions and complex mixing in higher dimensions.

Contribution

It establishes a limit theorem for gauge symmetry factorization in five dimensions and constructs explicit symmetry mixing mechanisms in higher dimensions.

Findings

KK decomposition in 5D can be factorized into subsets of gauge symmetries

A limit theorem for gauge symmetry factorizability is formulated

Explicit construction of gauge symmetry mixing in higher dimensions

Abstract

We study the gauge symmetry factorizability by boundary conditions on intervals of any dimensions. With Dirichlet-Neumann BCs, the Kaluza-Klein decomposition in five-dimension for arbitrary gauge group can always be factorized into that for separate subsets of at most two gauge symmetries, and so is completely solvable. Accordingly, we formulate a limit theorem on gauge symmetry factorizability on intervals to recapitulate this remarkable feature of five-dimension case. In higher-dimensional space-time, an interesting chained mixing of gauge symmetries by Dirichlet-Neumann BCs is explicitly constructed. The systematic decomposition picture obtained in this work constitutes the initial step towards determining the general symmetry breaking scheme by boundary conditions.