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

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Horowitz, GT 
Santos, JE 

jats:titleAjats:scbstract</jats:sc> </jats:title>jats:pIn 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 jats:italicS</jats:italic>jats:sup3</jats:sup>, this near horizon geometry is AdSjats:sub2</jats:sub> × jats:italicS</jats:italic>jats:sup3</jats:sup>. We show that this is not the case: generic static, nonspherical perturbations of AdSjats:sub2</jats:sub> × jats:italicS</jats:italic>jats:sup3</jats:sup> 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 jats:italicT</jats:italic> → 0. Our new IR geometry still has AdSjats:sub2</jats:sub> 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.</jats:p>

AdS-CFT Correspondence, Black Holes
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Journal of High Energy Physics
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Springer Science and Business Media LLC