A Note on Membrane Interactions and the Scalar potential

TL;DR

This paper explores the interactions between BPS membranes in supergravity and their relation to scalar potentials, offering a new perspective that could impact the swampland conjectures.

Contribution

It provides a novel interpretation of the scalar potential in terms of membrane interactions, linking supergravity scalar potentials with membrane exchange processes.

Findings

Reinterpreted the F-term scalar potential via membrane exchange

Established a correspondence between scalar potentials and BPS membrane interactions

Suggested implications for the swampland program and charged object spectra

Abstract

We compute the tree-level potential between two parallel $p$-branes due to the exchange of scalars, gravitons and $(p+1)$-forms. In the case of BPS membranes in 4d $\mathcal{N}=1$ supergravity, this provides an interesting reinterpretation of the classical Cremmer et al. formula for the F-term scalar potential in terms of scalar, graviton and 3-form exchange. In this way, we present a correspondence between the scalar potential at every point in scalar field space and a system of two interacting BPS membranes. This could potentially lead to interesting implications for the swampland program by providing a concrete way to relate conjectures about the form of scalar potentials with conjectures regarding the spectrum of charged objects.