A deformed IR: a new IR fixed point for four-dimensional holographic theories

Abstract

In holography, the IR behavior of a quantum system at nonzero density is described by the near horizon geometry of an extremal charged black hole. It is commonly believed that for systems on S3, this near horizon geometry is AdS2 × S3. We show that this is not the case: generic static, nonspherical perturbations of AdS2 × S3 blow up at the horizon, showing that it is not a stable IR fixed point. We then construct a new near horizon geometry which is invariant under only SO(3) (and not SO(4)) symmetry and show that it is stable to SO(3)-preserving perturbations (but not in general). We also show that an open set of nonextremal, SO(3)-invariant charged black holes develop this new near horizon geometry in the limit T → 0. Our new IR geometry still has AdS2 symmetry, but it is warped over a deformed sphere. We also construct many other near horizon geometries, including some with no rotational symmetries, but expect them all to be unstable IR fixed points.