Gravity-induced instability and gauge field localization

Abstract The spectrum of a massless bulk scalar field Φ , with a possible interaction term of the form L int = − ξ R Φ 2 , 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).