  Swampland criteria like the Weak Gravity Conjecture should not only apply to
particles, but also to other lower-codimension charged objects in 4d EFTs like
strings and membranes. However, the description of the latter is in general
subtle due to their large backreaction effects. In the context of 4d
$\mathcal{N}=1$ EFTs, we consider $\frac12$BPS strings and membranes which are
fundamental, in the sense that they cannot be resolved within the EFT regime.
We argue that, if interpreted from the EFT viewpoint, the 4d backreaction of
these objects translates into a classical RG flow of their couplings.
Constraints on the UV charges and tensions get then translated to constraints
on the axionic kinetic terms and scalar potential of the EFT. This uncovers new
relations among the Swampland Conjectures, which become interconnected by the
physical properties of low-codimension objects. In particular, using that
string RG flows describe infinite field distance limits, we show that the WGC
for strings implies the Swampland Distance Conjecture. Similarly,
WGC-saturating membranes generate a scalar potential satisfying the de Sitter
Conjecture.
