Double fibration in G-theory and the cobordism conjecture

TL;DR

This paper explores Type IIB flux compactifications with varying dilaton and fluxes, analyzing cobordism and bordism groups to understand the emergence of non-perturbative objects and their mathematical structure.

Contribution

It introduces a G-theory motivated compactification with coordinate-dependent fluxes and dilaton, revealing the role of End of the World branes and bordism groups in cobordism conjecture.

Findings

Existence of End of the World branes to trivialize cohomology classes

Computation of the associated bordism group revealing additional non-perturbative objects

Identification of a mathematical structure linking energy scales with physics emergence

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.