Three Dimensional Strings as Collective Coordinates of Four Dimensional Non-Perturbative Quantum Gravity

Abstract

A string theory in $3$ euclidean spacetime dimensions is found to describe the semiclassical behavior of a certain exact physical state of quantum general relativity in $4$ dimensions. Both the worldsheet and the three dimensional metric emerge as collective coordinates that describe a sector of the solution space of quantum general relativity. Additional collective coordinates exist which are interpreted as worldsheet degrees of freedom. The construction may be extended to the case in which the Kalb-Ramond field is included in the non-perturbative dynamics. It is possible that this mechanism is the inverse of the strong coupling limit by which some $D$ dimensional string theories are conjectured to give rise to $D+1$ dimensional field theories.