Non-Linear Realisation of the Pure N=4, D=5 Supergravity

TL;DR

This paper develops a non-linear coset formulation of pure N=4, D=5 supergravity, deriving its algebraic structure and first-order equations through a geometric approach.

Contribution

It introduces a novel Lie superalgebra and coset model that encapsulate the bosonic and fermionic dynamics of the supergravity theory.

Findings

Derived the Lie superalgebra for the coset formulation.

Obtained the bosonic field equations from the Cartan-Maurer form.

Formulated the first-order equations as a twisted self-duality condition.

Abstract

We perform the non-linear realisation or the coset formulation of the pure N=4, D=5 supergravity. We derive the Lie superalgebra which parameterizes a coset map whose induced Cartan-Maurer form produces the bosonic field equations of the pure N=4, D=5 supergravity by canonically satisfying the Cartan-Maurer equation. We also obtain the first-order field equations of the theory as a twisted self-duality condition for the Cartan-Maurer form within the geometrical framework of the coset construction.