# The supersymmetric anti-D3-brane action in KKLT

## TL;DR

This paper derives the full four-dimensional supergravity action for an anti-D3-brane in string theory, including all relevant fields, to better understand its role in cosmological model building and supersymmetry breaking.

## Contribution

It provides the complete 4d $
abla$1 supergravity formulation of an anti-D3-brane coupled to all background fields, extending previous partial descriptions.

## Key findings

- Derived the full anti-D3-brane supergravity action including vectors, scalars, and fermions.
- Clarified the supersymmetry breaking mechanism in KKLT scenarios.
- Facilitated more precise modeling of uplift terms in string cosmology.

## Abstract

An anti-D3-brane plays a crucial role in the construction of semi-realistic cosmological models in string theory. Part of its action provides an uplift term that has been used to lift AdS solutions to phenomenologically viable dS vacua in the KKLT and LVS setups. In the last few years it has been shown that this uplift breaks supersymmetry spontaneously and can be described in the 4d $\mathcal{N}=1$ supergravity language by using constrained supermultiplets. Here we derive the complete 4d $\mathcal{N}=1$ supergravity action for an anti-D3-brane coupled to all closed string background fields. In particular we include the vector field, the scalar fields and all fermions that live on the anti-D3-brane.