Scale without Conformal Invariance: Theoretical Foundations

Details Scale without Conformal Invariance: Theoretical Foundations Scale without Conformal Invariance: Theoretical Foundations

2011-07-19

arxiv.org/abs/1107.3840v2

Physics

High Energy Physics

High Energy Physics - Theory

24 pages, 1 figure, corrected statements, conclusion unchanged

Scientific paper

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 flow has to be abandoned - this observation leads to deep connections between scale-invariant theories and recurrent behaviors. We show that, on scale-invariant trajectories, there is a redefinition of the dilatation current that leads to generators of dilatations that generate dilatations. We develop a systematic algorithm for the search of scale-invariant trajectories in perturbation theory, and present several examples that are unitary, have finite correlation functions and energy bounded from below. These examples provide a laboratory for the study of scale without conformal invariance in relativistic quantum field theory.

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