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Reflections on conformal spectra

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Regular Article - Theoretical Physics
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Abstract

We use modular invariance and crossing symmetry of conformal field theory to reveal approximate reflection symmetries in the spectral decompositions of the partition function in two dimensions in the limit of large central charge and of the four-point function in any dimension in the limit of large scaling dimensions Δ0 of external operators. We use these symmetries to motivate universal upper bounds on the spectrum and the operator product expansion coefficients, which we then derive by independent techniques. Some of the bounds for four-point functions are valid for finite Δ0 as well as for large Δ0. We discuss a similar symmetry in a large spacetime dimension limit. Finally, we comment on the analogue of the Cardy formula and sparse light spectrum condition for the four-point function.

Keywords

Conformal and W Symmetry Field Theories in Higher Dimensions 
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Copyright information

© The Author(s) 2016

Authors and Affiliations

  • Hyungrok Kim
    • 1
    • 2
  • Petr Kravchuk
    • 1
    • 2
  • Hirosi Ooguri
    • 1
    • 2
    • 3
  1. 1.Walter Burke Institute for Theoretical Physics, CaltechPasadenaU.S.A.
  2. 2.School of Natural SciencesInstitute for Advanced StudyPrincetonU.S.A.
  3. 3.Kavli Institute for the Physics and Mathematics of the Universe (WPI)University of TokyoKashiwaJapan

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