Dimensional Reduction, Duality & Condensation Gravity

Abstract

Holography in Physics was introduced in a paper on dimensional reduction by Gerard ’t Hooft.  It was generalized by Susskind and Maldacena, because in addition to being describable on a surface or space with the next lower dimension; the Physics in our universe can also be seen as a projection upon a boundary with the next higher dimension.  We see dual descriptions across dimensional boundaries in both black hole horizons and cosmological scenarios or gravity theories where a precursor or extreme-distance cosmos is higher-dimensional.  A 5-d hypervolume collapsing through a black hole into a 4-d spacetime can produce a bubble similar to our observable universe.  DGP gravity and its extensions offer a scenario with these features, which provides useful insights into the nature of gravity and the early universe.  And the idea gravity is like Bose-Einstein condensation, hinted at by Sakharov in 1967, is seen in recent work by Dvali and Gomez where the event horizon of a Schwarzschild black hole is the quantum critical point for formation of a graviton condensate.  This implies boundaries may exist with dimensions both above and below our dimensionality.  The dimension reducing scenarios noted, their connection to astroparticle physics, and the associated dualities, are discussed and extended.