AbstractWe present a novel gauge field theory, based on theFreudenthal Triple System(FTS), a ternary algebra with mixed symmetry (not completely symmetric) structure constants. The theory, namedFreudenthal Gauge Theory(FGT), is invariant under two (off-shell) symmetries: the gauge Lie algebra constructed from theFTStriple product and a novelglobalnon-polynomial symmetry, the so-calledFreudenthal duality.Interestingly, a broad class ofFGTgauge algebras is provided by the Lie algebras “of type$ {{\mathfrak{e}}_7} $” which occur as conformal symmetries of Euclidean Jordan algebras of rank 3, and asU-duality algebras of the corresponding (super)gravity theories inD= 4.We prove aNo-Go Theorem, stating the incompatibility of the invariance underFreudenthal dualityand the coupling to space-time vectorand/orspinor fields, thus forbidding non-trivial supersymmetric extensions ofFGT.We also briefly discuss the relation betweenFTSand the triple systems occurring in BLG-type theories, in particular focusing on superconformal Chern-Simons-matter gauge theories inD= 3.