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2011

Scale without Conformal Invariance: Theoretical Foundations

Fortin, Jean-François, Grinstein, Benjamín, Stergiou, Andreas

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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.

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