Holonomy Groups Coming From F-Theory Compactification

TL;DR

This paper investigates the holonomy groups arising from F-theory compactifications, emphasizing their mathematical structure, relation to octonions, and implications for higher-dimensional theories and dualities.

Contribution

It provides a detailed analysis of specific holonomy groups from F-theory, exploring their mathematical properties and connections to octonions and dualities in string theory.

Findings

Holonomy groups like SO(8), SU(4), Spin(7), G2, and SU(3) are relevant in F-theory compactifications.

The relation between these groups and octonions is significant for understanding higher-dimensional theories.

Various mathematical forms of these holonomy groups are identified and analyzed.

Abstract

We study holonomy groups coming from F-theory compactifications. We focus mainly on SO(8) as 12-4=8 and subgroups SU(4), Spin(7), G2 and SU(3) suitable for descent from F-theory, M-theory and Superstring theories. We consider the relation of these groups with the octonions, which is striking and reinforces their role in higher dimensions and dualities. These holonomy groups are related in various mathematical forms, which we exhibit.