Abstract
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 à la Faddeev and Popov. We derive a compact expression for the massive p-form effective action, \( {\Gamma}_p^{(m)} \), in terms of the functional determinants of Hodge-de Rham operators. We then show that the effective actions \( {\Gamma}_p^{(m)} \) and \( {\Gamma}_{d-p-1}^{(m)} \) differ by a topological invariant. This is a generalisation of the known result in the massless case that the effective actions Γp and Γd−p−2 coincide modulo a topological term. Finally, our analysis is extended to the case of massive super p-forms coupled to background \( \mathcal{N} \) = 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.
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Dedicated to the memory of Professor Omar Foda
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Kuzenko, S.M., Turner, K. Effective actions for dual massive (super) p-forms. J. High Energ. Phys. 2021, 40 (2021). https://doi.org/10.1007/JHEP01(2021)040
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DOI: https://doi.org/10.1007/JHEP01(2021)040