Gauge invariance and radiative corrections in an extra dimensional theory

TL;DR

This paper examines the gauge structure and quantum corrections in a five-dimensional Yang-Mills theory compactified to four dimensions, highlighting the role of Kaluza-Klein modes and their impact on gauge invariance and loop calculations.

Contribution

It provides a detailed analysis of gauge invariance, gauge fixing, and one-loop radiative corrections in an extra-dimensional Yang-Mills framework, clarifying the nature of KK modes and their quantum effects.

Findings

KK modes are gauge fields only if gauge parameters propagate in the bulk.

One-loop KK contributions to WWV are finite and well-behaved at high energies.

The gauge structure involves two types of gauge transformations, affecting quantization and ghost sectors.

Abstract

The gauge structure of the four dimensional effective theory originated in a pure five dimensional Yang-Mills theory compactified on the orbifold $S^1/Z_2$, is discussed on the basis of the BRST symmetry. If gauge parameters propagate in the bulk, the excited Kaluza-Klein (KK) modes are gauge fields and the four dimensional theory is gauge invariant only if the compactification is carried out by using curvatures as fundamental objects. The four dimensional theory is governed by two types of gauge transformations, one determined by the KK zero modes of the gauge parameters and the other by the excited ones. Within this context, a gauge-fixing procedure to quantize the KK modes that is covariant under the first type of gauge transformations is shown and the ghost sector induced by the gauge-fixing functions is presented. If the gauge parameters are confined to the usual four dimensional space-time, the known result in the literature is reproduced with some minor variants, although it is emphasized that the excited KK modes are not gauge fields, but matter fields transforming under the adjoint representation of $SU_4(N)$. A calculation of the one-loop contributions of the excited KK modes of the electroweak gauge group on the off-shell WWV, with V a photon or a Z boson, is exhibited. Such contributions are free of ultraviolet divergences and well-behaved at high energies.