Target duality in ${\cal N}{=}\,8$N=8 superconformal mechanics and the coupling of dual pairs

Abstract

We couple dual pairs of \documentclass[12pt]{minimal}\begin{document}${\cal N}{=}\,8$\end{document}N=8 superconformal mechanics with conical targets of dimension d and 8−d. The superconformal coupling generates an oscillator-type potential on each of the two target factors, with a frequency depending on the respective dual coordinates. In the case of the inhomogeneous (3,8,5) model, which entails a monopole background, it is necessary to add an extra supermultiplet of constants for half of the supersymmetry. The \documentclass[12pt]{minimal}\begin{document}${\cal N}{=}\,4$\end{document}N=4 analog, joining an inhomogeneous (1,4,3) with a (3,4,1) multiplet, is also analyzed in detail.