A note on membrane interactions and the scalar potential

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 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.