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arXiv · 2112.14481

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

Nikolay Kozyrev·Sergey Krivonos
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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.

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Nikolay Kozyrev, Sergey Krivonos. 2021-12-29. ${\cal N}{=}4$ supersymmetric Schwarzian with $D(1,2;\alpha)$ symmetry. https://doi.org/10.1103/physrevd.105.085010

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