Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 1, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP01(2013)152
Keywords
Space-Time Symmetries; Anomalies in Field and String Theories; Renormalization Group
Categories
Funding
- NSF [PHY07-57035, PHY11-25915]
- DOE [DE-FG02-91-ER40674]
- Swiss National Science Foundation [200021-125237]
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We study the possible IR and UV asymptotics of 4D Lorentz invariant unitary quantum field theory. Our main tool is a generalization of the Komargodski-Schwimmer proof for the alpha-theorem. We use this to rule out a large class of renormalization group flows that do not asymptote to conformal field theories in the UV and IR. We show that the only possible UV and IR asymptotics described by perturbation theory have a vanishing trace of the stress-energy tensor, and are therefore conformal. Our arguments hold even for theories with gravitational anomalies. We also give a non-perturbative argument that excludes theories with scale but not conformal invariance. This argument holds for theories in which the stress-energy tensor is sufficiently nontrivial in a technical sense that we make precise.
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