Topological origin of holographic principle: Application to wormholes

Abstract

In this paper, we suggest a mathematical representation to the holographic principle through the theory of topological retracts. We found that the topological retraction is the mathematical analog of the hologram idea in modern quantum gravity and it can be used to explore the geometry of the hologram boundary. An example has been given on the five-dimensional (5D) wormhole spacetime [Formula: see text] which we found can retract to lower-dimensional circles [Formula: see text]. In terms of the holographic principle, the description of this volume of spacetime [Formula: see text] is encoded on the lower-dimensional circle which is the region boundary.