Abstract
We extend the recent construction of 4d mathcal{N}=1 three-form Lagrangians by including the most general three-form multiplets necessary to reproduce any F-term potential in string flux compactifications. In this context we find an obstruction to dualize all fluxes to three-forms in the effective field theory. This implies that, generically, a single EFT cannot capture all the membrane-mediated flux transitions expected from a string theory construction, but only a sublattice of them. The obstruction can be detected from the maximal number of three-forms per scalar in any supermultiplet, and from the gaugings involving three-forms that appear in the EFT. Some gaugings are related to the appearance of fluxes in the tadpole conditions, and give a general obstruction. Others are related to the anomalous axionic strings present in a specific compactification regime. We illustrate the structure of the three-form Lagrangian in type II and F/M-theory setups, where we argue that the above obstructions correlate with the different 4d membrane tensions with respect to the EFT energy scales.
Highlights
In the past few years, there has been a renewed interest in the conditions that quantum field theories need to satisfy in order to be embedded into a fully-fledged theory of quantum gravity, a line of research known as the Swampland Program [1]
We extend the recent construction of 4d N = 1 three-form Lagrangians by including the most general three-form multiplets necessary to reproduce any F-term potential in string flux compactifications
Progress on this front is oftentimes achieved by testing different conjectures on Effective Field Theories (EFTs) obtained from string theory compactifications, or by proposing new conjectures based on their general features
Summary
In the past few years, there has been a renewed interest in the conditions that quantum field theories need to satisfy in order to be embedded into a fully-fledged theory of quantum gravity, a line of research known as the Swampland Program [1] (see [2, 3] for reviews). The more general class of multiplets, which we dub master three-form multiplets, are essentially defined in terms of the periods corresponding to each of the fluxes of the EFT, and provide a formalism overarching previous examples of supersymmetric three-form Lagrangians As it turns out, within this more general scheme certain limitations of supersymmetric three-form EFTs are exposed, more precisely the inability to treat as dynamical the whole set of fluxes that we typically associate to a given string theory compactification. One may extend this analysis to understand why even different choices of Γ are considered in opposite regimes of the same class of constructions, like it is illustrated by the weak and strong coupling regimes of type IIA compactifications Needless to say, this limitation of a single 4d EFT to capture the full spectrum of flux vacua and the possible transition between them could be understood as a swampland criterium. Appendix C describes the structure of the boundary terms that appear in the manifestly supersymmetric actions of the main text
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