Remarks on D(2,1;a) super-Schwarzian derivative

TL;DR

This paper explores constructing a super-Schwarzian derivative associated with the exceptional supergroup D(2,1;a), extending previous methods used for other superconformal groups to the most general N=4 supersymmetric extension of SL(2,R).

Contribution

It applies the nonlinear realisation method to D(2,1;a), aiming to identify potential super-Schwarzian derivatives for this exceptional supergroup.

Findings

Constructed candidates for D(2,1;a) super-Schwarzian derivatives.

Extended the nonlinear realisation approach to an exceptional supergroup.

Provided insights into N=4 supersymmetric extensions of SL(2,R).

Abstract

It was recently demonstrated that N=1,2,3,4 super-Schwarzian derivatives can be constructed by applying the method of nonlinear realisations to finite-dimensional superconformal groups OSp(1|2), SU(1,1|1), OSp(3|2), SU(1,1|2), respectively, thus avoiding the use of superconformal field theory techniques. In this work, a similar construction is applied to the exceptional supergroup D(2,1;a), which describes the most general N=4 supersymmetric extension of SL(2,R), with the aim to study possible candidates for a D(2,1;a) super-Schwarzian derivative.