GRADED GEOMETRIC STRUCTURES UNDERLYING F-THEORY RELATED DEFECT THEORIES

Abstract

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 fiber bundles, which include the graded affine vector space and demonstrate that the composite sections of this fiber 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.