Stability of the large-scale metric in fractal structures

Abstract

Scalar-field propagation on fractal structures is used to select an effective metric from the symmetry properties of infrared fixed points. There are two fixed-point metrics, a minkowskian and a euclidean metric. It is ahown that both are locally stable, though only the euclidean metric is globally stable. This analysis suggests that minkowskian symmetry at large scales cannot be simply the outcome of random metrics at small scales, as was sometimes proposed.