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) x S-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 AdS(2) 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.

Automated summary

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. However, we show that this is not the case and propose a new near horizon geometry that is stable under certain perturbations and develops in nonextremal, SO(3)-invariant charged black holes. Our findings suggest that the previously believed stable IR fixed point is not accurate.