  We explore BPS strings in supergravity theories in six-dimensions and related
Swampland Conjectures. We first propose a general modular ansatz for
bootstrapping elliptic genera of 2d worldvolume theories on strings in the 6d
theories. By employing mirror symmetry on F-theory examples, we explicitly
compute the elliptic genera and validate our ansatz. We extend this approach to
investigate BPS strings and their spectrum in non-geometric 6d theories which
have no known F-theory constructions, and confirm the Swampland conjectures,
including the Weak Gravity Conjecture, Distance Conjecture, and Emergent String
Conjecture. We also discuss tensionless little strings that emerge near
infinite-distance limits of strong gauge coupling in the moduli space of
certain special theories.
