[Paper Review] Localization of bulk matter fields on a pure de Sitter thick braneworld

Heng Guo, Yu-Xiao Liu+3 more|arXiv (Cornell University)|Mar 12, 2011

Black Holes and Theoretical Physics64 references5 citations

TL;DR

This paper studies the localization of spin-0, spin-1, and spin-1/2 matter fields on a thick brane generated solely by positive cosmological constants in 4D and 5D spacetimes, without bulk scalar fields. It shows that modified Pöschl-Teller potentials in the Kaluza-Klein Schrödinger equations lead to zero-mode localization and mass gaps for scalar and vector fields, while fermion zero modes localize only for two specific bulk mass profiles, yielding finite or infinite bound state spectra with distinct mass gaps and chiral mode shifts.

ABSTRACT

In this paper we investigate the localization and mass spectra of various matter �elds with spin 0, 1 and 1=2 on a thick brane generated by pure 4D and 5D positive cosmological constants without bulk scalarelds. For spin 0 scalar and spin 1 vector �elds, the potentials of the Kaluza{Klein (KK) modes in the corresponding Schrodinger equations are modied Poschl{Teller potentials, which lead to the localization of the scalar and vector zero modes on the brane as well as to mass gaps in the mass spectra. For spin 1=2 fermions, we introduce the bulk mass term MF(z)� �� in the action and four di୥rent cases are investigated. Localization of the massless left{chiral fermion zero mode is feasible for just two cases of F(z). In therst one we obtain Schrodinger equations with modied Poschl{Teller potentials with the corresponding mass gaps for both left{ and right{chiral fermions, the number of massive KK bound states is finite (determined by the ratio M=b) and is the same for left{ and right{chiral modes. In the second case we get a family of solutions with an infinite number of bound states where the mass spectra for left{ and right{chiral KK fermion modes are discrete. A special case resembles the one{dimensional quantum harmonic oscillator problem. For both of these cases, the mass spectrum of right{chiral fermions is shifted with respect to the mass spectrum of the left{chiral ones.

Motivation & Objective

• To investigate the localization of bulk matter fields on a thick brane generated purely by positive cosmological constants, without additional bulk scalar fields.
• To determine the conditions under which massless fermion zero modes localize on the brane.
• To analyze the Kaluza-Klein (KK) mass spectra for scalar, vector, and fermionic fields on the brane.
• To explore how different bulk fermion mass profiles affect the number and structure of massive KK bound states.

Proposed method

• Construct a thick brane solution using only 4D and 5D positive cosmological constants, avoiding bulk scalar fields.
• Derive effective Schrödinger equations for Kaluza-Klein modes of spin-0, spin-1, and spin-1/2 fields in the warped geometry.
• Introduce a bulk fermion mass term MF(z) with z-dependent profiles F(z) to study chiral fermion localization.
• Analyze the resulting potentials in the Schrödinger equations, identifying modified Pöschl-Teller forms for scalar and vector fields.
• Investigate four distinct cases of F(z) for fermions, focusing on zero-mode localization and the structure of massive KK bound states.
• Determine the number and distribution of bound states, including mass gaps and spectral shifts between left- and right-chiral modes.

Experimental results

Research questions

• RQ1 Under what conditions do spin-0 and spin-1 Kaluza-Klein modes localize on the brane, and what determines their mass gaps?
• RQ2 Can massless left-chiral fermion zero modes localize on the brane, and for which bulk mass profiles F(z) is this possible?
• RQ3 How does the number of massive KK bound states for fermions depend on the ratio M/b in different F(z) profiles?
• RQ4 What is the spectral relationship between left- and right-chiral fermion KK modes in cases with infinite bound states?
• RQ5 How do the effective potentials for KK modes transform into modified Pöschl-Teller forms, and what are the implications for localization?

Key findings

• Spin-0 and spin-1 Kaluza-Klein modes localize on the brane due to modified Pöschl-Teller potentials, which also generate mass gaps in their spectra.
• Massless left-chiral fermion zero modes localize only for two of the four considered bulk mass profiles F(z).
• In one case, both left- and right-chiral fermion modes have the same finite number of massive KK bound states, determined by the ratio M/b.
• In a second case, both chiral modes exhibit an infinite number of discrete bound states, with the right-chiral spectrum shifted relative to the left-chiral one.
• The special case resembling a one-dimensional quantum harmonic oscillator allows for an infinite number of bound states with a symmetric, shifted spectrum between chiralities.
• The modified Pöschl-Teller potentials for scalar and vector fields ensure stable localization of zero modes and discrete mass spectra with energy gaps.