# How many fluxes fit in an EFT?

## TL;DR

This paper explores the limitations of effective field theories in capturing all string fluxes via three-form multiplets, revealing an obstruction to dualizing all fluxes and implications for membrane transitions in string compactifications.

## Contribution

It extends 4d $
abla=1$ three-form Lagrangians to include general multiplets, identifying obstructions to flux dualization and their relation to fluxes, gaugings, and membrane tensions.

## Key findings

- Not all fluxes can be dualized to three-forms in EFTs.
- Obstructions relate to fluxes in tadpole conditions and anomalous axionic strings.
- Different membrane tensions correlate with EFT energy scales.

## 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.