Graded Geometric Structures Underlying F-Theory Related Defect Theories

In the context of F-theory, we study the related eight dimensional super-Yang-Mills theory and reveal the underlying supersymmetric quantum mechanics algebra that the fermionic fields localized on the corresponding defect theory are related to. Particularly, the localized fermionic fields constitute a graded vector space, and in turn this graded space enriches the geometric structures that can be built on the initial eight-dimensional space. We construct the implied composite fibre bundles, which include the graded affine vector space and demonstrate that the composite sections of this fibre bundle are in one-to-one correspondence to the sections of the square root of the canonical bundle corresponding to the submanifold on which the zero modes are localized.