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A proof of the conformal collider bounds

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  • Published: 20 June 2016
  • Volume 2016, article number 111, (2016)
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A proof of the conformal collider bounds
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  • Diego M. Hofman1,
  • Daliang Li2,
  • David Meltzer3,
  • David Poland3,4 &
  • …
  • Fernando Rejon-Barrera1 

  • 532 Accesses

  • 110 Citations

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A preprint version of the article is available at arXiv.

Abstract

In this paper, we prove that the “conformal collider bounds” originally proposed in [1] hold for any unitary parity-preserving conformal field theory (CFT) with a unique stress tensor in dimensions d ≥ 3. In particular this implies that the ratio of central charges for a unitary 4d CFT lies in the interval \( \frac{31}{18}\ge \frac{a}{c}\ge \frac{1}{3} \). For superconformal theories this is further reduced to \( \frac{3}{2}\ge \frac{a}{c}\ge \frac{1}{2} \). The proof relies only on CFT first principles — in particular, bootstrap methods — and thus constitutes the first complete field theory proof of these bounds. We further elaborate on similar bounds for non-conserved currents and relate them to results obtained recently from deep inelastic scattering.

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Authors and Affiliations

  1. Institute for Theoretical Physics, University of Amsterdam, Science Park 904, Postbus 94485, 1090 GL, Amsterdam, The Netherlands

    Diego M. Hofman & Fernando Rejon-Barrera

  2. Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD, 21218, U.S.A.

    Daliang Li

  3. Department of Physics, Yale University, New Haven, CT, 06511, U.S.A.

    David Meltzer & David Poland

  4. School of Natural Sciences, Institute for Advanced Study, Princeton, NJ, 08540, U.S.A.

    David Poland

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  1. Diego M. Hofman
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  2. Daliang Li
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Correspondence to Daliang Li.

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ArXiv ePrint: 1603.03771

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Hofman, D.M., Li, D., Meltzer, D. et al. A proof of the conformal collider bounds. J. High Energ. Phys. 2016, 111 (2016). https://doi.org/10.1007/JHEP06(2016)111

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  • Received: 18 April 2016

  • Accepted: 27 May 2016

  • Published: 20 June 2016

  • DOI: https://doi.org/10.1007/JHEP06(2016)111

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Keywords

  • AdS-CFT Correspondence
  • Conformal and W Symmetry
  • Field Theories in Higher Dimensions
  • Nonperturbative Effects
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