# Geometric standing wave braneworld and field localization in Lyra manifold

## TL;DR

This paper introduces a novel 5D standing wave braneworld model based on Lyra geometry, demonstrating how geometric structures alone can trap various matter fields without additional matter sources.

## Contribution

It presents a new standing wave braneworld solution in Lyra geometry that does not require matter fields, highlighting the role of geometric structures in field localization.

## Key findings

- Scalar, gauge vector, and fermionic fields can be localized by the geometric structure.
- The model does not need matter fields to generate standing wave solutions.
- Lyra geometry modifies Einstein equations, enabling new braneworld configurations.

## Abstract

In this work, we propose a standing wave braneworld based on Lyra geometry scenario. The Lyra displacement vector provides a modification in Einstein equations which can be interpreted as a noninteracting phantom scalar. From the Einstein's equation in Lyra manifold, a 5D standing wave braneworld is constructed in the presence of a cosmological constant. Unlike other standing wave solutions presented in the literature, no matter field is necessary to obtain these new solutions. We analyze the properties of the scalar, gauge vector and fermionic fields in this model, highlighting the relevance of geometric structure in the process of trapping matter.