Scanning spacetime with patterns of entanglement

2019. 11. 29. 10:15
Building F, stairway III., seminar room of the Dept. of Theoretical Physics
Lévay Péter (BME)

In theories of emergent gravity and holography the classical geometry of spacetime is arising from entanglement patterns of states of a conformal quantum field theory (CFT) living on its boundary. Using the AdS/CFT correspondence in this talk we elucidate how boundary entanglement patterns of the CFT vacuum are encoded into the bulk via the dynamics of a cluster algebra.

For a subdivision of the boundary into n parts the conditional mutual informations of overlapping boundary regions are mapped to triangulations of geodesic n-gons of the bulk. Such triangulations are mapped to tilings of kinematic space with causal diamonds. In this picture cluster dynamics is just a scanning of kinematic space by a seed pattern of such diamonds. We show that the space of all such tilings forms an associahedron, an object also known form recent studies of the theory of the S-matrix. Finally we observe that the flips relating the tilings are reminiscent of errors in an error correcting code.