Abstract
Current studies of supersymmetric extensions of the Sachdev-Ye-Kitaev model stimulate a renewed interest in super-Schwarzian derivatives. In this work, we apply the method of nonlinear realizations to the finite-dimensional superconformal group SU(1,1|2) and link its invariants to the N=4 super-Schwarzian.
Highlights
Current studies of supersymmetric extensions of the Sachdev–Ye–Kitaev model stimulate a renewed interest in super-Schwarzian derivatives [4,5,6,7]
We apply the method of nonlinear realizations to the finite-dimensional superconformal group SUð1; 1j2Þ and link its invariants to the N 1⁄4 4 super-Schwarzian
In a recent work [11], a third alternative was studied, which consists in applying the method of nonlinear realizations [12] to finite-dimensional superconformal groups
Summary
Current studies of supersymmetric extensions of the Sachdev–Ye–Kitaev model (see [1,2,3] and references therein) stimulate a renewed interest in super-Schwarzian derivatives [4,5,6,7]. An N -extended super-Schwarzian acts upon a fermionic superfield which specifies superconformal diffeomorphisms of the odd sector of S1jN superspace [8]. It enjoys a remarkable composition law which implies invariance of the N 1⁄4 1, 2, 3, 4 super-Schwarzian under finite transformations forming OSpð1j2Þ, SUð1; 1j1Þ, OSpð3j2Þ, and SUð1; 1j2Þ superconformal group, respectively. In a recent work [11], a third alternative was studied, which consists in applying the method of nonlinear realizations [12] to finite-dimensional superconformal groups. In this setting, a super-Schwarzian derivative is linked to the supergroup invariants.
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