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The a-theorem and the asymptotics of 4D quantum field theory

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Abstract

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 a-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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Author notes

  1. Markus A. Luty

    Present address: Physics Department, University of California Davis, One Shields Avenue, Davis, California, 95616, U.S.A

Authors and Affiliations

  1. Institut für Theoretische Physik der Universität Heidelberg, Heidelberg, Germany

    Markus A. Luty

  2. Kavli Institute for Theoretical Physics, University of California Santa Barbara, Santa Barbara, California, 93106, U.S.A.

    Joseph Polchinski

  3. Institut de Théorie des Phénomènes Physiques, EPFL, Lausanne, Switzerland

    Riccardo Rattazzi

Authors
  1. Markus A. Luty
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  2. Joseph Polchinski
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  3. Riccardo Rattazzi
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Correspondence to Riccardo Rattazzi.

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ArXiv ePrint: 1204.5221

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Luty, M.A., Polchinski, J. & Rattazzi, R. The a-theorem and the asymptotics of 4D quantum field theory. J. High Energ. Phys. 2013, 152 (2013). https://doi.org/10.1007/JHEP01(2013)152

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  • DOI: https://doi.org/10.1007/JHEP01(2013)152

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