Asymptotic Weak Gravity Conjecture in M-theory on K3 × K3

The Asymptotic WGC has been proposed as a special case of the tower WGC that probes infinite distances in the moduli space corresponding to weakly coupled gauge regimes. The conjecture has been studied in M-theory on Calabi-Yau threefold (CY3) with finite volume inducing a 5D effective QFT. In this paper, we extend the scope of the previous study to encompass lower dimensions, particularly we generalise the obtained 5D asymptotic WGC to the effective field theory (EFT$_{3D}$) coupled to 3D gravity that descends from M-theory compactified on Calabi-Yau fourfold with an emphasis on $K3\times K3$. We find that the CY4 has three fibration structures labelled as line Type-$\mathbb {T}^{2}$, surface Type-$\mathbb {S}$ and bulk Type-$\mathbb {V}$. The emergent EFT$_{3D}$ is shown to have 2+2 towers of particles states termed as the BPS $\mathcal {T}_{M_{\mathrm{k}}\rightarrow 0}^{\rm{\small {BPS}}}$ and $\mathcal {T}_{M_{\mathrm{k}}\rightarrow \infty }^{\rm{\small {BPS}}}$ as well as the non-BPS $\mathcal {T}_{M_{\mathrm{k}}\rightarrow 0}^{\rm{\small {N-BPS}}}$ and $\mathcal {T}_{M_{\mathrm{k}}\rightarrow \infty }^{\rm{\small {N-BPS}}}$. To ensure the viability of the 3D Asymptotic WGC, we give explicit calculations to thoroughly test the swampland constraint for both the weakly and strongly gauge coupled regimes. Additional aspects, including the gauge symmetry breaking and duality symmetry are also investigated.