Scale without Conformal Invariance: Theoretical Foundations
Abstract
We present the theoretical underpinnings of scale without conformal invariance in quantum field theory. In light of our results the gradient-flow interpretation of renormalization-group (RG) flow is challenged, due to deep connections between scale-invariant theories and recurrent behaviors in the RG. We show that, on scale-invariant trajectories, there is a redefinition of the dilatation current that leads to generators of dilatations that generate dilatations. Finally, we develop a systematic algorithm for the search of scale-invariant trajectories in perturbation theory.
Cite
@article{arxiv.1107.3840,
title = {Scale without Conformal Invariance: Theoretical Foundations},
author = {Jean-François Fortin and Benjamín Grinstein and Andreas Stergiou},
journal= {arXiv preprint arXiv:1107.3840},
year = {2015}
}
Comments
18 pages. Added note to make clear that the results of arXiv:1106.2540 do not imply the existence of unitary theories with scale but without conformal invariance in perturbation theory in $d=4-\epsilon$ spacetime dimensions