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 $S^3$, this near horizon geometry is $Ad{S}_2\times S^3$. We show that this is not the case: generic static, nonspherical perturbations of $Ad{S}_2\times S^3$ 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). We also show that an open set of nonextremal, $SO(3)$-invariant charged black holes develop this new near horizon geometry in the limit $T\to 0$. Our new IR geometry still has $Ad{S}_2$ 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.

44 pages, 13 figures

References in corpus (4)

• Near-horizon symmetries of extremal black holes
• Almost all extremal black holes in AdS are singular
• Scalar, Vector and Tensor Harmonics on the Three-Sphere
• Extremal black holes that are not extremal: maximal warm holes

Cited by in corpus (4)

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• Algebras and Hilbert spaces from gravitational path integrals: Understanding Ryu-Takayanagi/HRT as entropy without AdS/CFT
• EFT Corrections to Majumdar-Papapetrou Black Holes
• Charged Static AdS Black Hole Binaries