Double fibration in G-theory and the cobordism conjecture

Abstract

We investigate Type IIB compactifications with spatially varying fluxes and dilaton profiles in the setting of dynamical cobordism. In particular, we analyze a G-theory motivated compactification in which the fluxes and the dilaton depend on coordinates of a complex two-dimensional plane. From the equations of motion, we deduce the existence of End of the World branes. In a cohomological interpretation, these branes appear precisely in order to trivialize the relevant cohomology class. Furthermore, we compute the associated bordism group and show that additional non-perturbative objects are needed to cancel the class, while retaining the cohomological contribution as a subgroup. This suggests a mathematical structure that connects energy scales with the emergence of perturbative and non-perturbative physics.

26+1 pages. v2: Some typos corrected. Recalculation corrected the homology groups and the final order of the bordism group, without affecting our conclusions. Comments about the fermionic component of the group were added