A proof of the conformal collider bounds

By D. Hofman, Daliang Li, David Meltzer, David Poland, F. Rejón-Barrera. Journal of High Energy Physics, 2016

157 citations recorded by the source corpus.

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 3118≥ac≥13\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \frac{31}{18}\ge \frac{a}{c}\ge \frac{1}{3} $$\end{document}. For superconformal theories this is further reduced to 32≥ac≥12\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \frac{3}{2}\ge \frac{a}{c}\ge \frac{1}{2} $$\end{document}. 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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/851efb2f5ff5466a3543347ca2f2ffce6f14c988

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Citations in the corpus

The conformal bootstrap: Theory, numerical techniques, and applications (2018, methodology): “A proof of these bounds independent from the ANEC was given in Hofman et al. (2016); see also Hartman et al. (2016a,b).”
Modular Hamiltonians for deformed half-spaces and the averaged null energy condition (2016, methodology): “In particular, using analytic bootstrap methods the HM bounds were proven for a class of three-point functions in [42], building on the work of [43, 44].”
Averaged null energy condition from causality (2016, methodology): “In particular, we will show exactly how to smear the probe operators in the previous analyses [16, 18, 19] to produce the Hofman-Maldacena inequalities.”
Light-ray operators in conformal field theory (2018, methodology): “An important application of Lorentzian inversion formulae is to the lightcone bootstrap and large-spin perturbation theory [17–26, 79].”
Analyticity in spin in conformal theories (2017, background): “The first of these inequality, which essentially states that |S| ≤ 1 holds throughout the complex lower half-plane and not only the real axis, played an important role in a recent proof of the averaged null energy condition (ANEC) [21] (see also [29]).”
Loops in AdS from conformal field theory (2016, background): “Knowing loop amplitudes in a given bulk theory would open the door to nonplanar extensions of dynamical aspects of holography and the conformal bootstrap [34–50].”