Freudenthal Gauge Theory

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.

1+32 pages, 1 Table; v2 : some comments and clarifications, Refs., and footnotes added

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Cited by in corpus (10)

• The Freudenthal gauge symmetry of the black holes of N=2,d=4 supergravity
• Exceptional Lie Algebras, SU(3) and Jordan Pairs Part 2: Zorn-type Representations
• Freudenthal Gauge Theory
• Nonlinear symmetries of black hole entropy in gauged supergravity
• Black holes and general Freudenthal transformations
• A Kind of Magic
• Weyl images of Kantor pairs
• Freudenthal duality of near-extremal black holes and Jackiw-Teitelboim gravity
• Jordan Algebraic Interpretation of Maximal Parabolic Subalgebras : Exceptional Lie Algebras
• Freudenthal Duality in Conformal Field Theory