A note on membrane interactions and the scalar potential

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 $$ \mathcal{N} $$ 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.

Swampland Conjectures for strings and membranes

“…Note added. While this paper was being prepared for submission we received [23] which also points out the interpretation of the N = 1 F-term potential as a no-force condition for membranes. It therefore has partial overlap with section 2.2 and appendix A.2.…”

“…Performing a field theory computation as in appendix A.2 (see also [23]), we find out that the net force between two membranes is constant and given by…”

“…This means that the above geometrical description breaks down. 23 Hence, only EFT strings will lie over the polytope ∆ ∩ H (Λ) along the entire RG flow and reach the UV attractor point (5.27), which suggests that only such EFT weakly coupled strings saturate the WGC bound.…”

“…Along the lines of the previous section, the forces between two identical membranes may be computed starting from the potential of a configuration with two parallel membranes, in the non-relativistic approximation (see [23] for a more general computation). We therefore couple the bulk action to two identical membranes with actions (A.…”

Dynamical tadpoles and Weak Gravity Constraints

“…We start with a review of supergravity backgrounds sourced by D-branes (D3-branes, D7branes, and bound states thereof), and the backreaction effects on ED3-branes preserving 1 This view aligns with the recent progress in relating swampland constraints on spacetime configurations and on properties of states defined on them, see for instance [30,31].…”