N=3 super-Schwarzian from OSp(3|2) invariants

TL;DR

This paper constructs the N=3 super-Schwarzian derivative using nonlinear realizations of the OSp(3|2) superconformal group, revealing a richer invariant structure that could aid in developing N=3 supersymmetric models like the SYK extension.

Contribution

It extends the method of nonlinear realizations to the OSp(3|2) superconformal group, uncovering new invariants in the N=3 super-Schwarzian derivative.

Findings

N=3 super-Schwarzian has a richer invariant structure.

Extra invariants may facilitate N=3 supersymmetric extensions of the SYK model.

Method parallels previous constructions for N=0,1,2,4 cases.

Abstract

It was recently demonstrated that the N=0,1,2,4 super-Schwarzian derivatives can be constructed by applying the method of nonlinear realizations to the finite-dimensional (super)conformal groups SL(2,R), OSp(1|2), SU(1,1|1), and SU(1,1|2), respectively. In this work, a similar scheme is realised for OSp(3|2). It is shown that the N=3 case exhibits a surprisingly richer structure of invariants, the N=3 super-Schwarzian being a particular member. We suggest that the extra invariants may prove useful in building an N=3 supersymmetric extension of the Sachdev-Ye-Kitaev model.