Antisymmetric Tensor Gauge Fields on S_4

TL;DR

This paper formulates antisymmetric tensor gauge fields on a four-dimensional sphere, exploring their equivalence to scalar models and their interactions with gauge and spinor fields, including novel gauge-invariant interactions.

Contribution

It introduces models for antisymmetric tensor gauge fields on S_4 with interactions similar to flat space and novel gauge-invariant couplings with spinor fields.

Findings

Free field model equivalent to scalar model on S_4

Feasibility of gauge interactions similar to flat space models

Existence of new gauge-invariant interactions with spinor fields

Abstract

Antisymmetric tensor gauge fields phi_{ab}(eta) are formulated on the surface of a sphere S_4t(eta^2 = a^2) embedded in five dimensions. The free field model is equivalent to a scalar model on this sphere. Interactions with gauge fields are discussed. It is feasable to formulate models for interactions with U(1) gauge fields A_a(eta) that are akin to those of Freedman and Townsend in flat space. In addition, it proves possible to have a novel interaction of phi_{ab}with A_a and a spinor field Psi(eta) on S_4 with both Abelian and non-Abelian gauge invariance. In these models, A_a plays the role of a Stueckelberg field.