A Proof of the Conformal Collider Bounds

Diego M. Hofman; Daliang Li; David Meltzer; David Poland; Fernando Rejon-Barrera

doi:10.1007/jhep06(2016)111

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arXiv · 1603.03771

A Proof of the Conformal Collider Bounds

Diego M. Hofman·Daliang Li·David Meltzer·David Poland·Fernando Rejon-Barrera

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Abstract

In this paper, we prove that the "conformal collider bounds" originally proposed by Hofman and Maldacena hold for any unitary parity-preserving conformal field theory (CFT) with a unique stress tensor in spacetime dimensions larger than 2. In particular this implies that the ratio of central charges for a unitary 4d CFT lies in the interval $\frac{31}{18} \geq \frac{a}{c} \geq \frac{1}{3}$. For superconformal theories this is further reduced to $\frac{3}{2} \geq \frac{a}{c} \geq \frac{1}{2}$. 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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Diego M. Hofman, Daliang Li, David Meltzer, David Poland, Fernando Rejon-Barrera. 2016-03-11. A Proof of the Conformal Collider Bounds. https://doi.org/10.1007/jhep06(2016)111

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