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.
Cite
@article{arxiv.1208.0013,
title = {Freudenthal Gauge Theory},
author = {Alessio Marrani and Cong-Xin Qiu and Sheng-Yu Darren Shih and Anthony Tagliaferro and Bruno Zumino},
journal= {arXiv preprint arXiv:1208.0013},
year = {2015}
}
Comments
1+32 pages, 1 Table; v2 : some comments and clarifications, Refs., and footnotes added