Averaged null energy condition from causality

作者：Hartman Thomas^*; Kundu Sandipan; Tajdini Amirhossein

来源：The Journal of High Energy Physics, 2017, 2017(7): 066.

DOI：10.1007/JHEP07(2017)066

• Conformal Field Theory
• Field Theories in Higher Dimensions

Unitary, Lorentz-invariant quantum field theories in flat spacetime obey microcausality: commutators vanish at spacelike separation. For interacting theories in more than two dimensions, we show that this implies that the averaged null energy, integral 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 integral 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.

• 出版日期2017-7-14