Selecting Gauge Theories on an Interval by 5D Gauge Transformations

TL;DR

This paper investigates gauge symmetry breaking via boundary conditions in 5D warped geometries, revealing new boundary conditions that violate unitarity and are inconsistent with gauge transformations.

Contribution

It identifies a broader class of boundary conditions in 5D gauge theories allowed by the variational principle, and shows their incompatibility with gauge transformation definitions.

Findings

Certain boundary conditions violate Ward-Takahashi identities.

Some boundary conditions lead to amplitudes increasing with energy.

These boundary conditions are inconsistent with 5D gauge transformations.

Abstract

Gauge symmetry breaking by boundary conditions is studied in a general warped geometry in five dimensions. It has been suggested that a wider class of boundary conditions is allowed by requiring only vanishing surface terms when deriving the field equations for gauge theories on an interval (i.e., employing a variational principle), in comparison to the twist in orbifolding with automorphisms of the Lie algebra. We find that there are classes of boundary conditions allowed by the variational principle which violate the Ward-Takahashi identity and give four-point tree amplitudes that increase with energy in channels that have not yet been explored, leading to cross sections that increase as powers of the energy (which violates the tree level unitarity). We also find that such boundary conditions are forbidden by the requirement that the definitions of the restricted class of five-dimensional (5D) gauge transformations be consistent.