Symmetry Breaking for Bosonic Systems on Orbifolds

TL;DR

This paper explores how boundary conditions, including twists and jumps, affect the mass spectrum of bosonic fields in orbifold compactifications, revealing the equivalence of different descriptions through local field redefinitions.

Contribution

It introduces a comprehensive analysis of boundary conditions with discontinuities for bosons on S^1/Z_2 orbifolds, linking twists and jumps via field redefinitions.

Findings

Mass spectrum depends on twist and jumps

Different boundary conditions can describe the same physics

Localized lagrangian terms are needed for discontinuous fields

Abstract

We discuss a general class of boundary conditions for bosons living in an extra spatial dimension compactified on S^1/Z_2. Discontinuities for both fields and their first derivatives are allowed at the orbifold fixed points. We analyze examples with free scalar fields and interacting gauge vector bosons, deriving the mass spectrum, that depends on a combination of the twist and the jumps. We discuss how the same physical system can be characterized by different boundary conditions, related by local field redefinitions that turn a twist into a jump or vice-versa. When the description is in term of discontinuous fields, appropriate lagrangian terms should be localized at the orbifold fixed points.