The web of swampland conjectures and the TCC bound
  We consider the swampland distance and de Sitter conjectures, of respective
order one parameters $\lambda$ and $c$. Inspired by the recent Trans-Planckian
Censorship conjecture (TCC), we propose a generalization of the distance
conjecture, which bounds $\lambda$ to be a half of the TCC bound for $c$, i.e.
$\lambda \geq \frac{1}{2}\sqrt{\frac{2}{3}}$ in 4d. In addition, we propose a
correspondence between the two conjectures, relating the tower mass $m$ on the
one side to the scalar potential $V$ on the other side schematically as $m\sim
|V|^{\frac{1}{2}}$, in the large distance limit. These proposals suggest a
generalization of the scalar weak gravity conjecture, and are supported by a
variety of examples. The lower bound on $\lambda$ is verified explicitly in
many cases in the literature. The TCC bound on $c$ is checked as well on ten
different no-go theorems, which are worked-out in detail, and $V$ is analysed
in the asymptotic limit. In particular, new results on 4d scalar potentials
from type II compactifications are obtained.
