Averaged null energy condition from causality

Hartman, Thomas; Kundu, Sandipan; Tajdini, Amirhossein

doi:10.1007/JHEP07(2017)066

Title: Averaged null energy condition from causality

Journal Article · Fri Jul 14 00:00:00 EDT 2017 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP07(2017)066· OSTI ID:1393403

Hartman, Thomas ^[1]; Kundu, Sandipan ^[1]; Tajdini, Amirhossein ^[1]

Cornell Univ., Ithaca, NY (United States). Dept. of Physics

Unitary, Lorentz-invariant quantum field theories in at spacetime obey mi-crocausality: commutators vanish at spacelike separation. For interacting theories in more than two dimensions, we show that this implies that the averaged null energy, $$\int$$duT_uu, must be non-negative. This non-local operator appears in the operator product expansion of local operators in the lightcone limit, and therefore contributes to n-point functions. We derive a sum rule that isolates this contribution and is manifestly positive. The argument also applies to certain higher spin operators other than the stress tensor, generating an infinite family of new constraints of the form RduX uuu∙∙∙u ≥ 0. These lead to new inequalities for the coupling constants of spinning operators in conformal field theory, which include as special cases (but are generally stronger than) the existing constraints from the lightcone bootstrap, deep inelastic scattering, conformal collider methods, and relative entropy. We also comment on the relation to the recent derivation of the averaged null energy condition from relative entropy, and suggest a more general connection between causality and information-theoretic inequalities in QFT.

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Research Organization:: Cornell Univ., Ithaca, NY (United States)

Sponsoring Organization:: USDOE; National Science Foundation (NSF)

Grant/Contract Number:: SC0014123; PHY-1316222

OSTI ID:: 1393403

Journal Information:: Journal of High Energy Physics (Online), Vol. 2017, Issue 7; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 132 works

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