# Supergravitational Conformal Galileons

## TL;DR

This paper develops the supersymmetric and supergravity extensions of conformal Galileon theories on branes in AdS space, aiming to inform cosmological models involving branes and violations of energy conditions.

## Contribution

It constructs the first $N=1$ supersymmetric and supergravity formulations of conformal Galileons on branes in AdS space, extending previous non-supersymmetric models.

## Key findings

- Supersymmetric extensions of conformal Galileons are formulated.
- Results are generalized to $N=1$ supergravity.
- Potential applications to cosmological scenarios are discussed.

## Abstract

The worldvolume actions of 3+1 dimensional bosonic branes embedded in a five-dimensional bulk space can lead to important effective field theories, such as the DBI conformal Galileons, and may, when the Null Energy Condition is violated, play an essential role in cosmological theories of the early universe. These include Galileon Genesis and "bouncing" cosmology, where a pre-Big Bang contracting phase bounces smoothly to the presently observed expanding universe. Perhaps the most natural arena for such branes to arise is within the context of superstring and $M$-theory vacua. Here, not only are branes required for the consistency of the theory, but, in many cases, the exact spectrum of particle physics occurs at low energy. However, such theories have the additional constraint that they must be $N=1$ supersymmetric. This motivates us to compute the worldvolume actions of $N=1$ supersymmetric three-branes, first in flat superspace and then to generalize them to $N=1$ supergravitation. In this paper, for simplicity, we begin the process, not within the context of a superstring vacuum but, rather, for the conformal Galileons arising on a co-dimension one brane embedded in a maximally symmetric $AdS_{5}$ bulk space. We proceed to $N=1$ supersymmetrize the associated worldvolume theory and then generalize the results to $N=1$ supergravity, opening the door to possible new cosmological scenarios.