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Freudenthal Gauge Theory

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arxiv 1208.0013 v2 pith:3RKYWCB6 submitted 2012-07-31 hep-th

Alessio Marrani , Cong-Xin Qiu , Sheng-Yu Darren Shih , Anthony Tagliaferro , Bruno Zumino This is my paper · ORCID
classification hep-th
keywords gaugefreudenthalalgebrastheorytheoriestriplealgebraduality
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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.

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  1. Exceptional Periodicity and Magic Star Algebras. I : Foundations

    math.RT 2019-09 conditional novelty 5.0 of 10

    The paper rigorously defines 'Magic Star algebras', periodic finite dimensional generalizations of e6, e7, and e8, which are Lie algebras only at the base level n=1.

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