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 \( {{\mathfrak{e}}_7} \)” 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.
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Marrani, A., Qiu, CX., Shih, SY.D. et al. Freudenthal Gauge Theory. J. High Energ. Phys. 2013, 132 (2013). https://doi.org/10.1007/JHEP03(2013)132
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DOI: https://doi.org/10.1007/JHEP03(2013)132