On the Supersymmetric Extension of Gauss-Bonnet like Gravity

TL;DR

This paper constructs a supergravity theory with a Gauss-Bonnet like term, demonstrating that supersymmetry invariance in the presence of boundaries necessitates such an extension based on the $AdS$-Lorentz superalgebra.

Contribution

It explicitly constructs a supersymmetric extension of Gauss-Bonnet gravity using the $AdS$-Lorentz superalgebra, ensuring supersymmetry invariance with boundaries.

Findings

Supersymmetry invariance requires a Gauss-Bonnet like term.

Constructed a bulk Lagrangian based on $AdS$-Lorentz superalgebra.

Restored supersymmetry invariance in boundary conditions.

Abstract

We explore the supersymmetry invariance of a supergravity theory in the presence of a non-trivial boundary. The explicit construction of a bulk Lagrangian based on an enlarged superalgebra, known as $AdS$-Lorentz, is presented. Using a geometric approach we show that the supersymmetric extension of a Gauss-Bonnet like gravity is required in order to restore the supersymmetry invariance of the theory.