the corresponding bound is [@swampland; @WGC; @WGC1; @review] S\_[inst]{} M\_  , where $S_{inst}$ is the instanton action. For the theory to be within control one asks for $S_{inst}\geq 1$, leading to the constraint $f\leq M_{\text{p}}$. This is relevant for models of natural inflation in which values for $f$ larger than $M_{\text{p}}$ are in general required in order to get appropriate inflation.

Palti formulated a first version of a Scalar Weak Gravity Conjecture (SWGC) in the following terms [@Palti] (see also [@timoscalar] and [@Lust; @review]). We consider a particle H with mass $m$ which is coupled to a light scalar $\phi$ with a trilinear coupling proportional to $\mu=\partial_\phi m$. Then the conjecture is that, as $m_\phi \rightarrow 0$, (\_m)\^2  . The statement is that the force mediated by $\phi$ must be stronger than the gravitational force and $m^2(\phi)$ is considered as a function of $\phi$ so that $m^2=V''$. So the above expression may be written as (V”’)\^2  . \[palti\] Here the particle $H$ acts as a WGC particle in the sense that it is there to guarantee that there is at least one particle with interactions stronger than gravity. The philosophy sounds similar to the WGC for gauge $U(1)$ interactions. However, 