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The octonionically-induced ${\cal N}=7$ exceptional $G(3)$ superconformal quantum mechanics
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abstract
Both the ${\cal N}=7$ superconformal quantum mechanics possessing the exceptional $G(3)$ Lie superalgebra as dynamical symmetry and its associated deformed oscillator with $G(3)$ as spectrum-generating superalgebra are presented. This superconformal quantum mechanics, uniquely defined up to similarity transformations, is obtained via the octonionically-induced "quasi-nonassociative" method employed to derive the exceptional ${\cal N}=8$ $F(4)$ model. To construct the $G(3)$ theories, the covariant embedding of the $7$-dimensional representation of the Lie algebra $g_2$ within the $8\times 8$ matrices spanning the $Cl(0,7)$ Clifford algebra is derived. The Hilbert space of the $G(3)$ deformed oscillator is given by a $16$-ple of square-integrable functions of a real space coordinate. The spectrum of the theory is computed.
Forward citations
Cited by 2 Pith papers
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$\mathbb{Z}_2^3$-grading of the Lie algebra $G_2$ and related color algebras
The paper constructs a simple Z2^3-graded basis for G2 and three new Z2^3-graded color algebras of type G2, plus a Z2^2-graded color algebra in a Cartan-Weyl basis.
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Two faces of $N=7,8$ superconformal mechanics
Explicit supercharges and Hamiltonians for OSp(8|2), F(4), and G(3) superconformal mechanics are presented with two distinct R-symmetry realizations and octonionic embeddings of g2 into so(7).
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