# Localization of Gravitino Field on $f(R)$ Thick Branes

## TL;DR

This paper studies how gravitino fields can be localized on $f(R)$-thick branes in five dimensions, revealing conditions for localization and differences from Dirac fermions, with implications for higher-dimensional supergravity models.

## Contribution

It demonstrates the localization conditions for gravitino KK modes on $f(R)$-thick branes, highlighting the role of scalar fields and coupling terms, and distinguishes gravitinos from Dirac fermions by their chiral properties.

## Key findings

- Left- or right-handed zero modes can be localized depending on scalar background.
- Massive KK modes are not localized in pure geometric $f(R)$-thick branes.
- Chiral KK modes of gravitinos are similar to Dirac fermions but with opposite chiralities.

## Abstract

In this paper, we consider the localization of a five-dimensional gravitino field on $f(R)$-thick branes. We obtain the coupled chiral equations of the Kaluza-Klein (KK) modes of gravitinos with the gauge condition $\Psi_z=0$. The chiral equations of a gravitino's KK modes are found to be almost identical to those of the Dirac fermion. However, their chiralities are exactly opposite. The chiral KK modes of gravitinos could be localized in some types of $f(R)$-thick branes on introducing a coupling term. We investigate the localization of a gravitino on three types of $f(R)$-thick branes through a Yukawa-like coupling term with background scalar fields. It has been shown that all the KK modes of gravitinos cannot be localized in the pure geometric $f(R)$-thick branes by adding a five-dimensional gravitino mass term. However, for the $f(R)$-thick branes generated by one or two background scalar fields, only the left- or right-handed zero mode could be localized in the branes, and the massive KK resonant modes are the same for both left- and right-handed gravitinos despite their opposing chiralities. All these results are consistent with those of the five-dimensional Dirac fermion except their chiralities, which may be an important sign to distinguish the gravitino field and the Dirac fermion field.