4D equivalence theorem and gauge symmetry on orbifold

TL;DR

This paper explores the high-energy scattering amplitudes in 5D orbifold gauge theories, establishing a 4D equivalence theorem that relates massive gauge boson amplitudes to NG-like fields, with implications for gauge symmetry and unification.

Contribution

It derives a 4D equivalence theorem for orbifold gauge theories, confirming the relation between gauge boson and NG-like field amplitudes in a 5D SU(5) GUT model.

Findings

Confirmed the equivalence theorem explicitly through amplitude calculations.

Established the BRST formalism for the 4D effective theory on the orbifold.

Demonstrated gauge symmetry compatibility with boundary conditions.

Abstract

We investigate the high-energy behavior of the scattering amplitudes in the extra dimensional gauge theory where the gauge symmetry is broken by the boundary condition. We study, in particular, the 5-dimensional SU(5) grand unified theory whose 5th-dimensional coordinate is compactified on S^1/Z_2. We pay attention to the gauge symmetry compatible with the boundary condition on the orbifold and give the BRST formalism of the 4D theory which is obtained through integration of the 5D theory along the extra dimension. We derive the 4D equivalence theorem on the basis of the Slavnov-Taylor identities. We calculate the amplitudes of the process including four massive gauge bosons in the external lines and compare them with the ones for the connected reactions where the gauge fields are replaced by the corresponding would-be NG-like fields. We explicitly confirm the equivalence theorem to hold.