Radiative Effects on the Chiral Square

Abstract

We consider general field theories in six dimensions, with two of the dimensions compactified on a T_{2}/Z_{4} orbifold. Six-dimensional Weyl fermions propagating on this background give rise to a chiral zero-mode, which makes them interesting for phenomenological applications. The compact two-dimensional space is flat and has three conical singularities. We consider the one-loop structure of these theories, and show that the presence of logarithmic divergences requires the introduction of counterterms precisely at these three singular points. We also show that the corresponding localized operators are rotationally symmetric in the plane of the two extra dimensions, as expected from the geometry about the singularities. We derive the propagators for spin-0, spin-1/2 and spin-1 fields in momentum space, in such a way that the appropriate boundary conditions are satisfied. This allows us to efficiently calculate loop diagrams in any given model. We give general expressions for the mass splittings among Kaluza-Klein modes within a given level. Our results can also be used to obtain interesting KK-parity preserving interactions among Kaluza-Klein modes. We pay special attention to the components of six-dimensional gauge fields that transform as scalars under the four-dimensional Lorentz group. These states provide a characteristic signature for these scenarios. In particular, we find that they can easily be the lightest particles in the Kaluza-Klein spectrum.