A Higgs phase of gravity in string theory

We propose a scenario realizing a Higgs phase of gravity in string theory. The setup is type IIB warped flux compactification with N3bar D3bar-branes in a warped throat and M units of RR 3-form flux through the A-cycle of the deformed conifold. If (M/N3bar)^2 > g_s N3bar >> 1 then the D3bar-branes are described by a regular non-extremal black brane located at the bottom of the throat since the horizon radius is larger than both the string scale and the radius of the nonsupersymmetric NS 5-brane ``giant graviton'' configuration. The existence of the non-extremal black brane horizon spontaneously breaks the (3+1)-dimensional Lorentz symmetry along its world-volume and a symmetry in the radial direction but preserves the 3-dimensional spatial rotational invariance and the (3+1)-dimensional translational invariance. We construct a low-energy effective field theory describing the Nambu-Goldstone boson associated with the spontaneous symmetry breaking. The structure of the effective theory is exactly the same as that of gauged ghost condensation and, thus, this setup may be considered as a UV completion of the gauged ghost condensation. If the gauge coupling in the effective theory is small enough then the setup reduces to the ghost condensation and the Nambu-Goldstone boson coupled to gravity exhibits Jeans-like instability. It is conjectured that the geometrical counter-part of the Jeans-like instability is the Gregory-Laflamme instability of the non-extremal black brane