Abstract
The Weak Gravity Conjecture (WGC) is usually formulated in terms of the stability of extremal black-holes or in terms of long distance Coulomb/Newton potentials. However one can think of other physical processes to compare the relative strength of gravity versus other forces. We argue for an alternative formulation in terms of particle pair production at threshold or, equivalently, pair annihilation at rest. Imposing that the production rate by any force mediator (photon or scalar) of pairs of charged particles be larger or equal to graviton production, we recover known conditions for the U(1) WGC and its extensions. Unlike other formulations though, threshold pair production is sensitive to short range couplings present in scalar interactions and gives rise to a Scalar WGC. Application to moduli scalars gives rise to specific conditions on the trilinear and quartic couplings which involve first and second derivatives of the WGC particle mass with respect to the moduli. Some solutions saturating equations correspond to massive states behaving like BPS, KK and winding states which feature duality invariance and are in agreement with the Swampland distance conjecture. Conditions for N = 2 BPS states saturate our bounds and we discuss specific examples of BPS states which become massless at large Kahler moduli in Type IIA N=2, D=4 CY and orbifold compactifications. We study possible implications for potentials depending on moduli only through WGC massive states. For some simple classes of potentials one recovers constraints somewhat similar but not equivalent to a Swampland dS conjecture.
Highlights
The situation becomes more complicated in the presence of scalar couplings
Other previous discussion of a scalar WGC (SWGC) do not follow in such a direct way since in particular both scalars and gravitons lead to attractive interactions at large distances and no-bound-state arguments fail in this case
In this paper we have proposed pair production of massive particles at threshold as a means to compare the gravitational to the gauge and scalar interactions
Summary
Once we have seen how the PPWGC criterium encompasses the WGC conjecture and its extensions, we will show how its application to production from scalars leads to interesting novel results. N parameterising a hermitian manifold with a metric gij this is generalised to gij n (∂im2)(∂ ̄jm2) − m2(∂i∂ ̄jm2) This is the general form of the scalar WGC for n complex moduli. The contribution of all moduli should be compared with n-times the production rate from gravitons in order to have a fair comparison Such an averaging was not needed in the case of production from photons in an U(1)n theory with canonical kinetic basis because for any given charged particle one can always find a basis in which it couples to a single U(1). Given any set of moduli scalars, there must be a massive particle H with mass m coupled to them such that their average production rate at threshold from moduli is larger than the corresponding rate from gravitons
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