Effective actions for dual massive (super) p-forms

In d dimensions, the model for a massless p-form in curved space is known to be a reducible gauge theory for p > 1, and therefore its covariant quantisation cannot be carried out using the standard Faddeev-Popov scheme. However, adding a mass term and also introducing a Stueckelberg reformulation of the resulting p-form model, one ends up with an irreducible gauge theory which can be quantised a la Faddeev and Popov. We derive a compact expression for the massive p-form effective action, Gamma((m))(p) in terms of the functional determinants of Hodge-de Rham operators. We then show that the effective actions Gamma((m))(p) and Gamma((m))(d-p-1) differ by a topological invariant. This is a generalisation of the known result in the massless case that the effective actions Gamma(p) and Gamma(d-p-2) coincide modulo a topological term. Finally, our analysis is extended to the case of massive super p-forms coupled to background N = 1 supergravity in four dimensions. Specifically, we study the quantum dynamics of the following massive super p-forms: (i) vector multiplet; (ii) tensor multiplet; and (iii) three-form multiplet. It is demonstrated that the effective actions of the massive vector and tensor multiplets coincide. The effective action of the massive three-form is shown to be a sum of those corresponding to two massive scalar multiplets, modulo a topological term.

Automated summary

The study investigates the massless and massive p-form models in curved space, revealing differences in their quantisation methods but demonstrating that an achievable quantisation can be obtained by introducing a mass term and Stueckelberg reformulation. Additionally, the analysis extends to the case of massive super p-forms coupled to background N=1 supergravity, showing interesting relationships between the effective actions of different multiplets.