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

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 S^3, this near horizon geometry is AdS_2 x S^3. We show that this is not the case: generic static, nonspherical perturbations of AdS_2 xS^3 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.