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

Understand

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\times S^3 $.
• We show that this is not the case: generic static, nonspherical perturbations of $AdS_2\times 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).