# Constrained superfields on metastable anti-D3-branes

## TL;DR

This paper investigates how brane polarization affects supersymmetry in anti-D3-branes within a specific string theory setup, revealing non-linear supersymmetry realization and challenges in decoupling higher-order effects.

## Contribution

It provides a detailed analysis of the supersymmetry transformations and effective potential of polarized anti-D3-branes, highlighting the non-linear realization of supersymmetry and limitations of standard superfield descriptions.

## Key findings

- Supersymmetry is non-linearly realized at the metastable minimum.
- A strict decoupling limit with a nilpotent superfield does not seem to exist.
- Implications for low-energy models of inflation and de Sitter vacua.

## Abstract

We study the effect of brane polarization on the supersymmetry transformations of probe anti-D3-branes at the tip of a Klebanov-Strassler throat geometry. As is well known, the probe branes can polarize into NS5-branes and decay to a supersymmetric state by brane-flux annihilation. The effective potential has a metastable minimum as long as the number of anti-D3-branes is small compared to the number of flux quanta. We study the reduced four-dimensional effective NS5-brane theory and show that in the metastable minimum supersymmetry is non-linearly realized to leading order, as expected for spontaneously broken supersymmetry. However, a strict decoupling limit of the higher order corrections in terms of a standard nilpotent superfield does not seem to exist. We comment on the possible implications of these results for more general low-energy effective descriptions of inflation or de Sitter vacua.