Freudenthal Gauge Theory

TL;DR

The paper introduces Freudenthal Gauge Theory, a novel gauge field theory based on ternary algebraic structures, featuring unique symmetries and connections to supergravity, but with limitations on supersymmetric extensions.

Contribution

It presents a new gauge theory based on Freudenthal Triple Systems, explores its symmetries, and establishes a No-Go Theorem on supersymmetric extensions.

Findings

FGT is invariant under gauge and Freudenthal duality symmetries.

A broad class of FGT gauge algebras are related to 'e7' type Lie algebras.

No-Go Theorem prohibits non-trivial supersymmetric extensions of FGT.

Abstract

We present a novel gauge field theory, based on the Freudenthal Triple System (FTS), a ternary algebra with mixed symmetry (not completely symmetric) structure constants. The theory, named Freudenthal Gauge Theory (FGT), is invariant under two (off-shell) symmetries: the gauge Lie algebra constructed from the FTS triple product and a novel global non-polynomial symmetry, the so-called Freudenthal duality. Interestingly, a broad class of FGT gauge algebras is provided by the Lie algebras "of type e7" which occur as conformal symmetries of Euclidean Jordan algebras of rank 3, and as U-duality algebras of the corresponding (super)gravity theories in D = 4. We prove a No-Go Theorem, stating the incompatibility of the invariance under Freudenthal duality and the coupling to space-time vector and/or spinor fields, thus forbidding non-trivial supersymmetric extensions of FGT. We also briefly discuss the relation between FTS and the triple systems occurring in BLG-type theories, in particular focusing on superconformal Chern-Simons-matter gauge theories in D = 3.