The theory of dark energy stars illustrates how the behavior of matter near
to certain kinds of quantum critical phase transitions can be given a
geometrical interpretation by regarding the criticality tuning parameter as an
extra dimension. In the case of a superfluid with vanishing speed of sound, the
implied geometry resembles 5-dimensional anti-de-Sitter. In a dark energy star
this geometry applies both inside and outside the horizon radius, so the
AdS-CFT correspondence is consistent with the idea that the surface of a
compact astrophysical object represents a quantum critical phase transition of
space-time. The superfluid transition in a chiron gas, which was originally
proposed as a theory of high temperature superconductivity, may provide an
exact theory of this transition.Comment: Talk at the 12th Marcel Grossman Meetin