Gravity effects on thick brane formation from scalar field dynamics

TL;DR

This paper investigates how gravity influences the formation of thick branes from scalar fields in a five-dimensional AdS space, revealing nonperturbative effects and discrete localized states near a thin-brane defect.

Contribution

It provides a detailed analysis of gravity's impact on scalar field-driven thick brane formation, including nonperturbative effects and the role of thin-brane defects in localized state spectra.

Findings

Gravity causes nonperturbative discontinuities in scalar mass spectra.

Negative tension thin branes create potential wells with isolated localized states.

Localized scalar states form discrete spectra near thin-brane defects.

Abstract

The formation of a thick brane in five-dimen\-sional space-time is investigated when warp geometries of $AdS_5$ type are induced by scalar matter dynamics and triggered by a thin-brane defect. The scalar matter is taken to consist of two fields with $O(2)$ symmetric self interaction and with manifest $O(2)$ symmetry breaking by terms quadratic in fields. One of them serves as a thick brane formation mode around a kink background and another one is of a Higgs-field type which may develop a classical background as well. Scalar matter interacts with gravity in the minimal form and gravity effects on (quasi)localized scalar fluctuations are calculated with usage of gauge invariant variables suitable for perturbation expansion. The calculations are performed in the vicinity of the critical point of spontaneous breaking of the combined parity symmetry where a non-trivial v.e.v. of the Higgs-type scalar field is generated. The nonperturbative discontinuous gravitational effects in the mass spectrum of light localized scalar states are studied in the presence of a thin-brane defect. The thin brane with negative tension happens to be the most curious case when the singular barriers form a potential well with two infinitely tall walls and the discrete spectrum of localized states arises completely isolated from the bulk.