content_image/375308.jpg content_image/375309.jpg content_image/375310.jpg content_image/375311.jpg content_image/375312.jpg content_image/375307.jpg content_image/375306.jpg content_image/375305.jpg content_image/375302.jpg content_image/375303.jpg content_image/375304.jpg content_image/375301.jpg
can be written on the brane at y = 0 as, 

<img src='content_image/375308.jpg'>

<img src='content_image/375309.jpg'>

<img src='content_image/375310.jpg'>

<img src='content_image/375311.jpg'>

<img src='content_image/375312.jpg'>

and on the brane y = L , 

<img src='content_image/375307.jpg'>

<img src='content_image/375306.jpg'>

<img src='content_image/375305.jpg'>

The minimal conditions of potential V$_{y}$$_{=0}$ are 

<img src='content_image/375302.jpg'>

<img src='content_image/375303.jpg'>

<img src='content_image/375304.jpg'>

and ∂V$_{y}$ =0 ∂χ 2 , 3 = ∂V$_{y}$ =0 ∂ψ 1 , 3 = 0 are automatically satisfied. While the minimal conditions on the brane y = L are 

<img src='content_image/375301.jpg'>

We left four independent equations for the four unknown v , v$_{χ}$ , v$_{ψ}$ , and v$_{ϑ}$ in the limit of the trilinear couplings going to be zero. Thus the configurations needed in our scenario can be realized with ad hoc constraints. 

[1] G. L. Fogli, E. Lisi, A. Marrone, A. Palazzo and A. M. Rotunno, Phys. Rev. Lett. 101 , 141801 (2008) [arXiv:0806.2649 [hep-ph]]; arXiv:0809.2936 [hep-ph]. 

[2] M. C. Gonzalez-Garcia and M. Maltoni, Phys. Rept. 460 , 1 (2008) [arXiv:0704.1800 [hep-ph]]; T. Schwetz, AIP Conf. Proc. 981 , 8 (2008) [arXiv:0710.5027 [hep-ph]]. 

