Gravity-induced instability and gauge field localization

The spectrum of a massless bulk scalar field Φ, with a possible interaction term of the form Lint=−ξRΦ2, is investigated in the case of RS-geometry [L. Randall, R. Sundrum, Phys. Rev. Lett. 83 (1999) 3370; L. Randall, R. Sundrum, Phys. Rev. Lett. 83 (1999) 4690]. We show that the zero mode for ξ=0, turns into a tachyon mode, in the case of a non-zero negative value of ξ (ξ<0). As we see, the existence of the tachyon mode destabilizes the Φ=0 vacuum, against a new stable vacuum with nonzero Φ near the brane, and zero in the bulk. By using this result, we can construct a simple model for the gauge field localization, according to the philosophy of Dvali and Shifman (Higgs phase on the brane, confinement in the bulk).