UC Berkeley

In this thesis, I write down a Lagrangian for an exotic gauge theory defined using Freudenthal Triple Systems (FTS). FTSs are algebraic systems that arise in the context of Lie algebras and have have been found useful in D=4 Supergravity. These systems come with a symmetry known as Freudenthal Duality (or F-duality) which preserves a certain degree four polynomials Delta(x). The Lagrangian I write down is invariant under both the exotic gauge theory defined by the FTS and Freudenthal Duality. In prepration for discussing these topics, I review FTS and touch on their relationship to Lie algebras. I then discuss F-duality and present a novel proof that only depends on the axioms of the FTS on not on a direct calculation of any particular realization. I then review N=2 Maxwell-Einstein Supergravity in 4D (and 5D) and go over how F-duality arose in the first place. The final main chapter goes over my main results, which is taken from a paper which will be published soon, with several coathurs.