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On renormalization group flows in four dimensions

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Abstract

We discuss some general aspects of renormalization group flows in four dimensions. Every such flow can be reinterpreted in terms of a spontaneously broken conformal symmetry. We analyze in detail the consequences of trace anomalies for the effective action of the Nambu-Goldstone boson of broken conformal symmetry. While the c-anomaly is algebraically trivial, the a-anomaly is “non-Abelian”, and leads to a positive-definite universal contribution to the S-matrix element of 2 → 2 dilaton scattering. Unitarity of the S-matrix results in a monotonically decreasing function that interpolates between the Euler anomalies in the ultraviolet and the infrared, thereby establishing the a-theorem.

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Authors and Affiliations

  1. Weizmann Institute of Science, Rehovot, 76100, Israel

    Zohar Komargodski & Adam Schwimmer

  2. Institute for Advanced Study, Princeton, NJ, 08540, USA

    Zohar Komargodski

Authors
  1. Zohar Komargodski
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  2. Adam Schwimmer
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Correspondence to Zohar Komargodski.

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ArXiv ePrint: 1107.3987

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Komargodski, Z., Schwimmer, A. On renormalization group flows in four dimensions. J. High Energ. Phys. 2011, 99 (2011). https://doi.org/10.1007/JHEP12(2011)099

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  • DOI: https://doi.org/10.1007/JHEP12(2011)099

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