On the Swampland Cobordism Conjecture and Non-Abelian Duality Groups

Understand

We study the cobordism conjecture of McNamara and Vafa which asserts that the bordism group of quantum gravity is trivial.

• In the context of type IIB string theory compactified on a circle, this predicts the presence of D7-branes.
• On the other hand, the non-Abelian structure of the IIB duality group $SL(2,\mathbb{Z})$ implies the existence of additional $[p,q]$ 7-branes.
• We find that this additional information is instead captured by the space of closed paths on the moduli space of elliptic curves parameterizing distinct values of the type IIB axio-dilaton.