Equivalence between Born-Infeld tachyon and effective real scalar field theories for brane structures in warped geometry

TL;DR

This paper establishes an analytical equivalence between Born-Infeld tachyon fields and real scalar field theories in warped geometries, enabling the mapping of brane solutions and tachyon condensation mechanisms.

Contribution

It demonstrates a simple analytical connection between Born-Infeld tachyon and scalar field theories, allowing for the transfer of brane solutions between the two frameworks.

Findings

Both systems support identical thick brane solutions.

The equivalence enables mapping of tachyon condensation to scalar field brane scenarios.

Localized energy densities characterize the brane structures.

Abstract

An equivalence between Born-Infeld and effective real scalar field theories for brane structures is built in some specific warped space-time scenarios. Once the equations of motion for tachyon fields related to the Born-Infeld action are written as first-order equations, a simple analytical connection with a particular class of real scalar field superpotentials can be found. This equivalence leads to the conclusion that, for a certain class of superpotentials, both systems can support identical thick brane solutions as well as brane structures described through localized energy densities, $T_{00}(y)$, in the $5^{th}$ dimension, $y$. Our results indicate that thick brane solutions realized by the Born-Infeld cosmology can be connected to real scalar field brane scenarios which can be used to effectively map the tachyon condensation mechanism.