Spectral dimension as a tool for analyzing non-perturbative propagators

Understand

We derive general properties of the scale-dependent effective spectral dimensions of non-perturbative gauge boson propagators as they appear as solutions from different methods in Yang-Mills theories.

• In the ultraviolet and for short time scales the anomalous dimensions of the propagators lead to a slight decrease of the spectral dimension as compared to the one of a free propagator.
• Lowering the momentum scale, the spectral dimension decreases further.
• The class of propagators which display a maximum at Euclidean momenta, and thus violate positivity, always approaches a spectral dimension of one for large times.