Averaged null energy condition from causality
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Unitary, Lorentz-invariant quantum field theories in flat 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, ∫ 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 ∫ duX 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.
KeywordsConformal Field Theory Field Theories in Higher Dimensions
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- V.P. Frolov and I.D. Novikov, Black hole physics: basic concepts and new developments, Kluwer Academic, Norwell MA U.S.A., (1998) [INSPIRE].
- R.F. Streater and A.S. Wightman, PCT, spin and statistics, and all that, W.A. Benjamin, New York NY U.S.A., (1964) [INSPIRE].
- N. Afkhami-Jeddi and T. Hartman, unpublished.Google Scholar