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