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.
Highlights
We present a correspondence between the scalar potential at every point in scalar field space and a system of two interacting BPS membranes
This form of the potential has been argued to be valid fore more general N = 1 setups in [55,56,57,58,59] and this is expected to be quite general at least at the level of any 4d EFT, since a cosmological constant term can be always rewritten in terms of 4-forms, so allowing for field dependent kinetic terms seems to be enough to encode this kind of scalar potentials
We have studied the tree-level interaction between p-branes due to exchange of scalars, gravitons and (p + 1)-forms
Summary
We begin by reviewing the field theory calculation of the tree-level potential between two parallel, infinite p-branes in D-dimensional Minkowski space [41, 42].2 The goal of this section is to review this calculation in detail to fix the conventions and explicitly keep track of the units, which is crucial for comparison with Swampland Conjectures. We begin by reviewing the field theory calculation of the tree-level potential between two parallel, infinite p-branes in D-dimensional Minkowski space [41, 42].2. Let us consider a D-dimensional generalization of the low energy effective action of type II supergravity and include source terms corresponding to Dp-branes with charge Qp and tension Tp (in string units) [41, 42, 44]. This action is expressed in the string frame and the quantities are measured in string units.. The propagators associated to the graviton, scalar and (p + 1)-form can be obtained from Sbulk and the interaction vertices between the brane and the fields from SDBI (for the scalar and graviton) and SCS (for the (p + 1)-form)
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