# Horndeski model in nonlinearly realized supergravity

## TL;DR

This paper constructs the Horndeski Lagrangian within non-linearly realized supergravity, demonstrating its bosonic realization and ghost-free gravitino couplings in a super-covariant framework.

## Contribution

It introduces a supergravity formulation of the Horndeski Lagrangian with consistent gravitino couplings, extending previous scalar-tensor theories.

## Key findings

- Bosonic part of Horndeski Lagrangian realized in supergravity.
- Gravitino couples to Horndeski sector in a super-covariant and ghost-free manner.
- Framework ensures consistent supersymmetric extension of scalar-tensor theories.

## Abstract

We construct the Horndeski Lagrangian within non-linearly realized supergravity. We will show that the bosonic part of the Horndeski Lagrangian can be realized. Gravitino naturally couples to Horndeski sector in a super-covariant way. Such gravitino couplings are also free from ghosts.