Swampland cobordism conjecture and non-Abelian duality groups

We study the cobordism conjecture of McNamara and Vafa which asserts that bordism group quantum gravity is trivial. In context type IIB string theory compactified on a circle, this predicts presence D7-branes. On other hand, non-Abelian structure duality $SL(2,\mathbb{Z})$ implies existence additional $[p,q]$ 7-branes. find information instead captured by space closed paths moduli elliptic curves parameterizing distinct values axio-dilaton. This description allows to recover full braid statistics for Combining with an earlier Swampland Ooguri Vafa, we argue only certain congruence subgroups $\mathrm{\ensuremath{\Gamma}}\ensuremath{\subset}SL(2,\mathbb{Z})$ specifying genus zero modular can appear in 8D F-theory vacua. leads successful prediction allowed Mordell--Weil torsion groups