Quantum corrections to DGKT and the Weak Gravity Conjecture

We study D4 brane domain walls in the scale-separated 4d $\mathcal{N}$=1 AdS$_4$ DGKT scenario. Classically, these are BPS and satisfy a no-force condition since their tension equals their charge. We show that this property is not stable against quantum corrections and that these increase the brane tension-to-charge ratio, rendering the branes self-attractive. As a result, DGKT seems to be in tension with the Weak Gravity Conjecture for membranes. The quantum effects we consider include non-perturbative gaugino condensation on the D4-brane worldvolume and Euclidean D2 brane instantons, which correct the tension-to-charge ratio because the DGKT construction breaks all parity symmetries. Similar results hold in other 4d $\mathcal{N}$=1 setups not protected by parity symmetries.