Spontaneous breaking of a discrete symmetry and holography

We present an exactly solvable model of a scalar field in an AdSd+1 like background interpolating between a Z2 preserving and a Z2 breaking minima of the potential. We define its holographic dual through the AdS/CFT dictionary and argue that at zero temperature the d − dimensional strongly coupled system on the boundary of AdSd+1 exhibits a phase with a spontaneously broken discrete symmetry. In the presence of a black hole in the bulk (T≠0) we find that, although the metastable phase is present, the discrete symmetry gets restored. We compute exactly the lowest order boundary correlation functions in the spontaneously broken phase at T = 0, finding out a pole of the propagator for zero momenta that signals the presence of a massless mode and argue that it should not be present at (T≠0).