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 near horizon geometry an extremal charged black hole. It commonly believed that for systems on $S^3$, this $AdS_2\times S^3 $. We show not case: generic static, nonspherical perturbations $ blow up horizon, showing it stable fixed point. then construct new which invariant under only $SO(3)$ (and $SO(4)$) symmetry and to $SO(3)$-preserving (but in general). also open set nonextremal, $SO(3)$-invariant holes develop limit $T \to 0$. Our still has $AdS_2$ symmetry, but warped over deformed sphere. many other geometries, including some with no rotational symmetries, expect them all be unstable points.