Hidden Conformal Symmetry of Smooth Braneworld Scenarios

TL;DR

This paper explores hidden conformal symmetries in smooth braneworld models with two scalar fields, revealing new solutions and models, including standing wave, Sine-Gordon, and Randall-Sundrum scenarios, through symmetry breaking and conformal techniques.

Contribution

It generalizes previous work to include two non-minimally coupled scalar fields, identifying symmetry cases and generating new braneworld models with scalar fields and potentials.

Findings

Identified $SO(2)$ and $SO(1,1)$ symmetry cases affecting scalar field actions.

Derived new smooth braneworld models, including standing wave, Sine-Gordon, and Randall-Sundrum types.

Showed that symmetry breaking yields models with hyperbolic potentials and non-minimal couplings.

Abstract

In this paper we generalize our previous model (arXiv: 1705.09331), on a hidden conformal symmetry of smooth braneworld scenarios, to the case with two real scalar fields non-minimally coupled to gravity. The gauge condition reduces the action of the system to the action were gravity minimally couples to one of the scalar fields, plus a cosmological constant. We show that, depending on the internal symmetry of the scalar fields, the two possibilities, $SO(2)$ or $SO(1,1)$, emerge. In the $SO(2)$ case we get a ghost-like scalar field action, which can describe two models -- Standing Wave and Sine-Gordon smooth braneworlds. For the $SO(1,1)$ case we get the standard sign for the kinetic part of the scalar field. By breaking the $SO(1,1)$ symmetry (but keeping the conformal one) we are able to get two Randall-Sundrum models, with a non-minimal coupling and with a scalar field having hyperbolic potential. We conclude that this method can be seen as a solution-generating technique and a natural way to introduce non-trivial scalar fields that can provide smooth braneworld models.