Bulk matter fields on two-field thick branes

Abstract

In this paper, we obtain a new solution of a brane made up of a scalar field coupled to a dilaton. There is a unique parameter $b$ in the solution, which decides the distribution of the energy density and will affect the localization of bulk matter fields. For free vector fields, we find that the zero mode can be localized on the brane. And for vector fields coupled with the dilaton via ${\mathrm{e}}^{\ensuremath{\tau}\ensuremath{\pi}}{F}_{MN}{F}^{MN}$, the condition for localizing the zero mode is $\ensuremath{\tau}\ensuremath{\ge}\ensuremath{-}\sqrt{b/3}$ with $0<b\ensuremath{\le}1$, or $\ensuremath{\tau}>\ensuremath{-}1/\sqrt{3b}$ with $b>1$, which includes the case $\ensuremath{\tau}=0$. While the zero mode for free Kalb-Ramond fields cannot be localized on the brane, if only we introduce a coupling between the Kalb-Ramond fields and the dilaton via ${\mathrm{e}}^{\ensuremath{\zeta}\ensuremath{\pi}}{H}_{MNL}{H}^{MNL}$. When the coupling constant satisfies $\ensuremath{\zeta}>1/\sqrt{3b}$ with $b\ensuremath{\ge}1$ or $\ensuremath{\zeta}>\frac{2\ensuremath{-}b}{\sqrt{3b}}$ with $0<b<1$, the zero mode for the KR fields can be localized on the brane. For spin half fermion fields, we consider the coupling $\ensuremath{\eta}\overline{\ensuremath{\Psi}}{\mathrm{e}}^{\ensuremath{\lambda}\ensuremath{\pi}}\ensuremath{\phi}\ensuremath{\Psi}$ between the fermions and the background scalars with positive Yukawa coupling $\ensuremath{\eta}$. The effective potentials for both chiral fermions have three types of shapes decided by the relation between the dilaton-fermion coupling constant $\ensuremath{\lambda}$ and the parameter $b$. For $\ensuremath{\lambda}\ensuremath{\le}\ensuremath{-}1/\sqrt{3b}$, the zero mode of left-chiral fermion can be localized on the brane. While for $\ensuremath{\lambda}>\ensuremath{-}1/\sqrt{3b}$ with $b>1$ or $\ensuremath{-}1/\sqrt{3b}<\ensuremath{\lambda}<\ensuremath{-}\sqrt{b/3}$ with $0<b\ensuremath{\le}1$, the zero mode for left-chiral fermion also can be localized.