Phase space holography with no strings attached

Abstract

We discuss the Wigner function representation from the novel standpoint of establishing a natural holographylike correspondence between the descriptions of a generic quantum system in the phase space (‘bulk’) picture versus its spacetime (‘boundary’) counterpart. In certain cases, the former may reduce to the gravity-like dynamics of a local metric-type variable while the latter takes on the form of some bosonized collective field hydrodynamics. This generic pseudo-holographic duality neither relies on any particular symmetry of the system in question, nor does it require any relation to some underlying ‘string theory’, thus providing a systematic way of constructing practical – as opposed to the previous ‘ad hoc’ – examples of genuine holographic duality.