$\mathcal{N}=4$ supersymmetric Schwarzian with $D(1,2;\alpha )$ symmetry

Abstract

It was recently demonstrated that super-Schwarzian derivatives can be constructed from the Cartan forms of the super-conformal 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 for superalgebra $D(1,2;\alpha )$. 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 $d{\theta }^{ia}$ component of the form for $su(2)$ automorphism.

13 pages, 0 figures; v2: section about the action added; minor corrections; v3: minor corrections, version accepted by Phys.Rev.D

References in corpus (6)

• Schwarzian mechanics via nonlinear realizations
• N=4 super-Schwarzian via nonlinear realizations
• (super)Schwarzian mechanics
• Super-Schwarzians via nonlinear realizations
• N=3 super-Schwarzian from OSp(3|2) invariants
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Cited by in corpus (1)

• Generalized Schwarzians