Abstract
We embed a new three-form vector multiplet in mathcal{N} = 1 supergravity and we show that it can be used to generate dynamically the Hilbert-Einstein term. We then recast the theory into the standard Freedman model and we argue that a pure Fayet-Iliopoulos term is in tension with the Weak Gravity Conjecture. Finally, we couple the three-form to a super-membrane and study BPS domain walls within matter-coupled supergravity. In these models, the Planck mass takes different values on the domain wall sides.
Highlights
They can be used for instance to dynamically introduce the parameters which are present in effective theories coming from flux compactifications of string theory to four dimensions [38,39,40,41,42,43,44,45]
This multiplet can be viewed as an extension to local supersymmetry of an analogous three-form vector multiplet, which was studied in the global case in [24, 46, 47]
In order to obtain a theory of gravity, superconformal or super-Weyl invariance have to be broken to local supersymmetry and the Planck scale has to be introduced into the theory
Summary
We review the embedding of a gauge three-form into an abelian vector superfield in global supersymmetry This discussion is meant to be a warm-up for the section, where we are going to generalize and extend the results to supergravity. Given the properties of Σ, one can check that U is a well-defined vector superfield Without the proper boundary term, we would obtain a wrong sign in the scalar potential, once the solution of the equations of motion is inserted back into the Lagrangian More details about this can be found in [24], together with a systematic procedure to compute explicitly Lbd for the three-form vector multiplet. We are going to describe the generalization of such a dualization procedure in supergravity
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