both situations are apparently very different. In particular the scalar has no charge which could create a blackhole stability problem as with charged fields under a $U(1)$, and the generalization is not obvious.

![ Pictorial representation of the the Strong Scalar Weak Gravity Conjecture[]{data-label="higgsfinal"}](Figura2.pdf)

A Strong scalar WGC
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As formulated by Palti, the above bound does not apply to any scalar, but only to WGC scalars which interact with a scalar $\phi$ and whose mass is a function of $\phi$. That is for example the case of some string particle (like a lightest KK mode) which depends on the moduli of a compactification. The conjecture does not apply as it stands to the fields $\phi$ themselves. With the above expression one finds that the marginal situation for the mass of the WGC scalar $H$ occurs for m\^2  =  m\_0\^2e\^[/M\_]{}  . This gives the expected behaviour which appears in the distance conjecture at large $\phi$ [@distance] (see also [@paltidistance]). So this scalar $H$ could be like the first member of a tower. However this exponential behaviour is at odds with the properties of axions, whose potential is periodic and hence inconsistent with eq.(\[palti\]). Also, the exponential must be $e^{-\phi/M_{\text{p}}}$ for 