Two faces of $N=7,8$ superconformal mechanics

Abstract

Two variants of $N=7$ superconformal mechanics with manifest $so(7)$ and $su(2)\times su(2)$ $R$-symmetries possessing exceptional $G(3)$ dynamical symmetry are presented. To construct these $G(3)$ theories, we developed two new versions of covariant embedding of the exceptional $g_2$ algebra into the $so(7)$ algebra and then the embedding of $so(7)$ into $so(8)$. As a result, two $N=8$ superconformal mechanics with the $OSp(8|2)$ and $F(4)$ superconformal algebras and $N=7,G(3)$ superconformal mechanics were constructed in a uniform way. The constants of the octonion multiplication play a key role in the construction of superconformal mechanics with manifest $so(7)$ symmetry.

arXiv comment13 pages, minor changes, one reference was added

References in corpus (12)

• Hidden symmetries of integrable conformal mechanical systems
• Classification of irreps and invariants of the N-extended Supersymmetric Quantum Mechanics
• A Non-Renormalization Theorem for the d=1, N=8 Vector Multiplet
• N=8 superconformal mechanics
• New Model of N=8 Superconformal Mechanics
• Critical scaling dimension of D-module representations of N=4,7,8 Superconformal Algebras and constraints on Superconformal Mechanics
• The quasi-nonassociative exceptional $F(4)$ deformed quantum oscillator
• Couplings in D(2,1;a) superconformal mechanics from the SU(2) perspective
• A new N = 8 nonlinear supermultiplet
• Multiparticle $\mathcal{N}=8$ mechanics with $F(4)$ superconformal symmetry
• Note on $\mathcal{N}=8$ supersymmetric mechanics with dynamical and semi-dynamical multiplets
• N=8 superconformal mechanics: direct construction