N=4 supersymmetric Schwarzian with D(1,2;α) symmetry

Abstract

It was recently demonstrated that super-Schwarzian derivatives can be constructed from the Cartan forms of the superconformal supergroups $OSp(1|2)$, $SU(1,1|1)$, $OSp(3|2)$, $SU(1,1|2)$. Roughly speaking, the super-Schwarzian is just the component of the corresponding Cartan forms with the lowest dimension. In this paper, we apply the same approach to superalgebra $D(1,2;\ensuremath{\alpha})$. The minimal set of constraints we used includes: (a) introducing new superspace coordinates the Cartan forms depend on, which are completely invariant with respect to the corresponding group; (b) nullifying the form for dilatation. In contrast to the $SU(1,1|2)$ case, the new super-Schwarzian appears to be a $d{\ensuremath{\theta}}^{ia}$ component of the form for $su(2)$ automorphism.