N=4 Super-Schwarzian Theory on the Coadoint Orbit and PSU(1,1|2)

TL;DR

This work constructs an $N=4$ super-Schwarzian theory through the coadjoint orbit framework, identifying a central extension and the $N=4$ superconformal diffeomorphism as the foundation for the action. The $N=4$ super-Schwarzian derivative ${ m S}(f,oldsymbol heta;x, heta)$ is defined via a super-determinant and transforms anomalously under superdiffeomorphisms, enabling a Hamiltonian $H$ that generates the coadjoint action. A Kirillov–Kostant 2-form is employed to derive the Schwarzian action, with a 1-form $y$ solving a key compatibility equation and a resulting density that yields PSU$(1,1|2)$ symmetry under specific conditions. The symmetry analysis covers the $b=0$ case, realized on a PSU$(1,1|2)/igl(SU(2) imes U(1)igr)$ coset, and a nonzero $b$ case via targeted diffeomorphism modes and a special $b(x, heta)$ configuration, suggesting rich structure for quantum study and extensions to supersymmetric 2D gravity.

Abstract

An N=4 super-Schwarzian theory is formulated by the coadjoint orbit method. It is discovered that the action has symmetry under PSU(1,1|2).